Category Archives: Organic chemistry

Discovery of Astatine and Francium element

Astatine and Francium

In July 1925 the British scientist W. Friend went to Palestine but not as a pilgrim. Moreover, he was neither an archeologist nor a tourist visiting exotic lands. He was just a chemist and his luggage contained mostly ordinary empty bottles which he hoped to fill with samples of water from the Dead sea. Which has the highest concentration of dissolved salts on Earth. Fish cannot live in it and a man can swim in it without any danger of drowning–so high is the density of water in it.

The somber Biblical landscapes failed to dampen Friend’s hopes for success. His goal was to find in the water of the Dead Sea eka–iodine and eka–cesium which chemists had sought in vain. Sea water contains many dissolved salts of alkali metals and halogens and their concentration in the Dead Sea water must be exceptionally high. The higher the probability that they hide among them the unknown elements, namely the heaviest halogen and the heaviest alkali metal, even if in trace amounts.

Of course, Friend was not entirely original in choosing the direction of his search. As early as the end of the 19th century a chemist would not hesitate to answer the question where to look for eka–iodine and eka–cesium on Earth. The obvious answer was where natural compounds of alkali metals, in sea and ocean water, in various minerals, in deep well water, in some sea algae, and soon. In other words, the field of search was quite wide.

But all the attempts to find eka–iodine and eka–cesium failed and efforts of Friend were no exception. Now let us turn back to the last decades of the 19th century. When Mendeleev developed the periodic system of elements it contained many empty slots corresponding to unknown elements between bismuth and uranium. These empty slots were rapidly filled after the discovery of radioactivity. Polonium, radium, radon, actinium and finally protactinium took their places between uranium and thorium. Only eka–iodine and eka–cesium were late. This fact, however, did not particularly trouble scientists. These unknown elements had to be radioactive since there was not even a hint of doubt that radioactivity was the common feature of elements heavier than bismuth. Therefore, sooner or later radiometric methods would demonstrate the existence of elements 85 and 87.

The natural isotopes of uranium and thorium in long series of successive radioactive transformations give rise to secondary chemical elements. In the first decade of the 20th century scientists had in their disposal about forty radioactive isotopes of the elements at the end of the periodic system, that is, from bismuth to uranium. These radioelements comprised three radioactive families headed by thorium–232, uranium–235, and uranium–238. Each radioactive element sent its representatives to these families with the only exception of eka–iodine and eka–cesium. None of the three series had links that would correspond to the isotopes of element 85 or 87. This suggested an unexpected idea that eka–iodine and eka–cesium were not radioactive.But why? Nobody dared to answer this question. Under this assumption it was meaningless to look for these element in the ores of urnium and thorium which contained all the radioactive elements without exception.     

The assumption about stability of eka–iodine and eka–cesium was not confirmed. But all efforts to find isotopes of these elements in the radioactive families met with failure. But there remained one path of investigation which seemed promising. Does a given radioactive isotope have only one or two decay mechanisms? For instance, it emits both alpha and beta particles. If so the products of decay of this isotope are isotopes of two different elements and the series of radioactive transformations at the place of this isotope experiences branching. This problem was discussed for a long time and for some isotopes this effect seemed to take place.

In 1913 the British scientist A. Cranston worked with the radioelement MsTh–II (an isotope of actinium–228). This isotope emits beta particles and converts into thorium–228. But Cranston thought that he detected a very weak alpha decay, too. If that was true the product of the decay had to be the long–expected eka–cesium. Indeed, the process is described by

\[_{89}^{228}Ac{{\xrightarrow{\alpha }}^{224}}87\

But Cranston just reported his observation and did not follow the lead.

Just a year later three radiochemists from Vienna–S. Meyer, G. Hess, and F. Paneth–studied actinium–227, an isotope belonging to the family of uranium–235. They repeated their experiments and at last their sensitive instruments detected alpha particles of unknown origin. Alpha particles emitted by various isotopes have specific mean paths in air (of the order of a few centimetres). The mean path of the alpha particles in the experiments of the Austrian scientists was 3.5 cm. No known alpha–active isotope had such mean path of alpha particles. The scientists from the Vienna Radium Institute concluded that these particles were the product of alpha decay of the typically beta–active actinium–227. A product of this decay had to be an isotope of element 87.

The discovery had to be confirmed in new experiments. The Austrians were ready for this but soon the World War I started. They indeed observed alpha radiation of actinium–227 and this meant that atoms of element 87 were produced in their presence. But this fact had to be proved. It was easier to refute their conclusions. Sceptics said that the observed alpha activity was too weak and the results were probably erroneous. Others said that an isotope of the neighbouring element, protactinium, also emitted alpha particles with mean path close to 3.5 cm. Perhaps, an error was caused by an admixture of protactinium.

Elements 85 and 87 were discovered several times and given such names as dacinum and moldavium, alcalinium and helvetium, or leptinum and anglohelvetium. But all of them were mistakes. The fine–sounding names covered emptiness.

The mass numbers of all isotopes in the family of thorium–232 are divided by four. Therefore, the thorium family is sometimes referred to as the 4n family. After division by four of the mass numbers of the isotopes in the two uranium families we get a remainder of two or three. Re–spectively, the uranium–238 family is known as the (4n + 2) family and the uranium–235 family as the (4n + 3) family.

But where is the (4n + 1) family? Perhaps it is precisely in this unknown fourth series of radioactive transformations that the isotopes of eka–iodine and eka–cesium can be found. The idea was not unreasonable but not a single known radioactive isotope could fit into this hypothetical family by its mass number.

Sceptics declared, not without reason, that indeed there had been the fourth radioactive series at the early stages of Earth’s existence. But all the isotopes that comprised it including the originator of the series had too short half–lives and hence disappeared from the face of Earth long ago. The fourth radioactive tree had withered away long before mankind appeared.

In the twenties theorists attempted to reconstruct this family, to visualize its composition if it had existed. This imaginary structure had positions for the isotopes of elements 85 and 87 (but not for the radon isotopes). But this direction of search did not bring results, too. Perhaps the elusive elements did not exist at all?

But the goal was not that far. But before we start the tale about the realization of the scientists’ dreams let us turn back to the first synthesized element, namely, technetium.

Why was technetium the first? Primarily, because the choice of the target and the bombarding particles was obvious. The target was molybdenum, which could be made sufficiently pure at the time. The bombarding particles were neutrons and deutrons and accelerators were available for accelerating deutrons. This is why the discovery of technetium manifested the dawn of the age of synthesized elements. The work on promethium proved more complicated because in belonged to the rare–earth family and the main difficulties were met in determining its chemical nature.

But the task for elements 85 and 87 looked much more formidable. In their attempts to produce eka–iodine the scientists could only have one material for the target, namely, bismuth, element 83. The bombarding particles were a case of Hobson’s choice, too–only alpha particles could be used. Polonium, which precedes eka–iodine, could not be used as the material for the target. The elements with lower numbers than bismuth could not be used as targets because the scientists lacked appropriate bombarding particles to reach number 85.

Eka–cesium looked totally inaccessible for artificial synthesis. No suitable targets and bombarding particles existed in the thirties. But such is the irony of history that it was precisely element 87 that became the second after technetium reliably discovered element out of the four missing elements within the old boundaries of the periodic system. At this point in history the line of eka–iodine and eka–cesium, which had travelled parallel for such a long time, started to diverge and therefore we shall consider their discoveries separately.

Element 85 was synthesized by D. Corson, C. Mackenzie, and E. Segre who worked at Berkley (USA). The Italian physicist Segre by that time had settled in the USA and was the only one in the group who had an experience in artificial synthesis of a new element (technetium). On July 16, 1940, these scientists submitted to the prestigious physical journal Physical Review a large paper entitled “Artificial radioactive element 85”. They reported how they had bombarded a bismuth target with alpha particles accelerated in a cyclotron and obtained a radioactive product of the nuclear reaction . The product, most probably, was an isotope of eka–iodine with a half–life of 7.5 hours and a mass number of 211. Segre and his coworkers performed fine chemical experiments with the new element produced in negligible amounts and found that it was similar to iodine and exhibited weakly metallic properties.

The results seemed convincing enough. But the new element remained nameless for the time being. Further work on eka–iodine had to be delayed as the war started. It was resumed only in 1947 and the same group announced synthesis of another isotope with a mass number of 210. Its half–life was somewhat longer but still only 8.3 hours. Later it was found to be the longest–lived isotope of element 85. It was produced with a similar technique as the first isotope though the energy of the bombarding alpha particles was somewhat higher. As a result the intermediate composite nucleus (209Bi + α) emitted three rather than two neutrons and hence, the mass number of the isotope was lower by 1. Only now the new element was given the name astatine from the Greek for “unstable” (the symbol At).

But in the interval between the syntheses of the isotopes 211At and 210At a remarkable event occurred. The scientists from the Vienna Radium Institute B. Karlik and T. Bernert managed to find natural astatine. This was an extremely skillful study straining to the utmost the capacity of radiometry. The work was crowned with success and element 85 was born for the second time. As in the cases of technetium and promethium, we can name two dates in the history of astatine, namely, the year of its synthesis (1940) and the year of its discovery in nature (1943).

But when the Segre and his coworkers were preparing for irradiating a bismuth target with alpha particles the scientific community had known about the discovery of eka–cesium for more than a year. Transactions of the Paris Academy of Science published a paper headed “Element 87: AcK formed from actinium” and dated January 9, 1939. Its author was M. Perey, the assistant of the eminent radiochemist Debierne who had announced his discovery of actinium forty years earlier.

Marguerite Perey did not invent any fundamentally new methods and did not indulge in any vague and complicated speculations about possible sources of natural eka–cesium. In 1938 she came upon a paper published in 1914. The paper was signed by the Austrian chemists Meyer, Hess and Peneth. Perey attempted to prove their ideas. She obtained a carefully purified specimen of actinium–227. This isotope has a high beta–activity but sometimes it emits alpha particles, too. The mean path of such particles in air is 3.5 cm. This alpha radiation is by no means due to protactinium as the actinium specimen was sufficiently purified. Since alpha particles are emitted the eka–cesium isotope with a mass number of 223 must continuously be accumulated in the specimen. A series of experiments definitely demonstrated that, indeed, some substance with a half–life of 21 min is accumulated in the actinium specimen. Now it is the turn of chemical analysis to prove that this substance is a new element. Its properties proved to be similar to those of cesium. Perey named the new element francium in honour of her country. Only for a short period it was called actinium K (AcK) in accordance with the old nomenclature of radioelements.

The first description given by Perey to the newborn element was extremely brief: the element is formed with alpha decay of actinium –227 in the reaction

\[_{89}^{227}Ac{{\xrightarrow{\alpha }}^{223}}85\

and it is alpha–active with a half–life of 21 min. Then she spent several months studying its chemical properties and demonstrated convincingly that francium is similar to cesium in all its characteristics.

None of the natural radioactive elements had such a short half–life, even the artificially synthesized element 85 had a half–life measured in hours. There were hopes to find other natural isotopes of francium with longer half–lives. But in fact francium–223 proved to be the only francium isotope found on Earth.

The only remaining path to success was synthesis but it proved very difficult. More than ten years passed after the discovery of Perey when francium isotopes were artificially synthesized. The nuclear reaction giving rise to the francium isotope with a mass number of 212 can be written in short as

\[_{92}^{232}U(p,\,\,6p21n)\,\,_{87}^{212}Fr\

This reaction is the fission of uranium nucleus by protons accelerated to very high energies. When such a fast proton hits uranium nucleus it produces something like an explosion with ejection of a multitude of particles, namely, six protons and 21 neutrons. Of course, the reaction is not due to a blind chance but is based on careful theoretical predictions. Uranium may be replaced with thorium. The reaction product, francium–212, for some time was considered to be the longest–lived isotope (a half–life of 23 min) but later the half–life was found to be only 19 min.

Artificial synthesis of francium is much more difficult and less reliable method than extraction of francium as a product of decay of natural actinium. But natural actinium is rare. What to do? A current method is to irradiate the main isotope of radium with a mass number of 226 (its half–life is 1622 years) with fast neutrons. Radium–226 absorbs a neutron and converts into radium–227 with a half–life of about 40 min. Its decay gives rise to pure actinium–227 whose alpha decay in its turn produces francium–223. The symbols At and Fr were permanently installed in boxes 85 and 87 of the periodic table and their properties proved to be exactly the same as predicted from the table. But in comparison with their unstable mates born by nuclear physics, technetium and promethium, their position is clearly unfavourable.

According to estimates, the 20-km thickness of the Earth crust contains approximately 520 g of francium and 30 g of astatine (this is an overestimation in some respects). These amounts are of the same order as the terrestrial “resources” (quotation marks are more than suitable here) of technetium and promethium. We are probably making a mistake when we talk condescendingly about astatine and francium? Not at all. Technetium and promethium are produced in large amounts, kilograms and kilograms of them. The fact is that technetium and promethium have much longer half–lives and can therefore be accumulated in larger amounts. But accumulation of astatine and francium is just unfeasible. In fact, each time their properties have to be studied they have to be produced a new.

In the radioactive families the isotopes of astatine and francium are placed not on the principle pathways of radioactive transformations but at the side branches. Here is the branch on which natural francium is born:

         

The isotope Ac in 99 cases out of 100 emits beta particles and only in one case it undergoes alpha decay.

The situation is even less easy in the case of the branches responsible for the formation of astatine:

What may be said about these branches? The producers of natural astatine (the polonium isotopes) are by themselves extremely rare. For them alpha decay is not just predominant but practically the only radioactivity mechanism. Beta decays for them seem something like a mishap as can be clearly seen from the following data.

There is only one beta decay event per 5 000 alpha decays of polonium–218. Things are even sadder for polonium–216 (1 per 7 000) and polonium–215 (1 per 200 000). The situation speaks for itself. The amount of natural francium on Earth is larger. It is produced by the longest–lived actinium isotope 227Ac (a half–life of 21 years) and its content is, of course, much higher than that of the extremely rare polonium isotopes capable of producing astatine.

Discovery of element : Promethium

Promethium

The history of one rare–earth element is so unusual that it merits individual discussion. Promethium, as it is known now, is practically non–existent in nature (we write practically but not absolutely and the reason for that will be clear later). Event which can only be described as amazing preceded the discovery of element 61 by means of nuclear synthesis.

The work of Moseley made clear the existence of an unknown element between neodymium and samarium. But the situation proved to be not so clear and dramatic events rapidly followed in the history of element 61.

The New World was unlucky in discoveries of new elements. All the elements known by the twenties of this century (not counting the elements known from ancient times) had in fact been discovered by the European scientists. This is why the American scientific community was particularly happy to learn about the discovery of element 61 by the chemists from Chicago B. Hopkins, L. Intema, and J. Harris in 1926.

Starting from 1913 scientist from various countries had been searching intensely for the elusice rare–earth element and it seemed strange that they had not found it earlier. Indeed the elements of the first half of the rare–earth family known as the cerium elements (from lanthanum to gadolinium) had been shown by geochemists to be more abundant in nature than the yttrium elements of the second half of the family (from terbium to lutecium). But all the yttrium elements had been found while an empty box had remained in the cerium group between neodymium and samarium.

The straightforward explanation was that element 61 was not just rare but rarest element. Its abundance was assumed to be much lower than that of other rare–earth elements, and the available analytical techniques were not sensitive enough to identify its traces in the terrestrial minerals. New more sensitive methods were needed for the purpose.

The American chemists employed X–ray and optical spectral techniques to study the minerals where they hoped to find element 61. These well versed in the history of range earth elements could say that the path the Americans took was a troublesome one as spectral analysis not infrequently had acted as an evil genius of rare–earth studies despite all the benefits it had brought to them. But in the twenties the feet spectroscopy stood on were not so unsteady as a few decades earlier and the Moseley law could be used for predicting the X–ray spectra of any element.

The American chemists worked hard, analysed numerous specimens of various minerals and in april 1926 reported the discovery of element 61. But they did not extract even a grain of the new element and its existence was inferred from the X–ray and optical spectral data.

The discoverers University named the element illinium in honour of the Illinois University where they worked and the symbol Il took its place in box 61 of the periodic system but just a half–year later a new claimant of box 61 came into the limelight. It had been discovered by two Italian scientists L. Rolla and L. Fernandes who had named it florencium (Fl).  Allegedly, they had discovered element 61 two years earlier than the Americans but failed to report the discovery owing to some undisclosed reasons. They had sealed the report of their discovery into an envelope and left it for safe–keeping in the Florence Academy.

If different people obtain the same result with different means that would seem to prove that the result is genuine. Americans and Italians could be only too happy. As for the question of priority it was nothing new to science. But no one of the alleged discoverers of element 61 could imagine that their argument about periodic would soon become superfluous and both symbols, Il and Fl, would be shown to be illegal squatters in box 61 of the periodic table.

To trace the events now we have to go not further but some time back to the facts that were simply unknown at the time. The report of the discoverers of element 61 started with the words: “There had been absolutely no grounds for assuming the existence of an element between neodymium and samarium until it was demonstrated through the Mosely law”. Typical dry style of a scientific report, everything would seem to be correct. But….

The following remarkable conclusion in German (please, do not look it up in a dictionary yet) appeared in the margin of a hard–written manuscript of the element table found in the papers of certain scientist (we shall supply the name a little later): “NB. 61 ist das von mir 1902 vorhergesagte fehlende Elemente”.

The real history of element 61 should prominently feature the name we have already met on these pages. It is the Czech scientist Boguslav Brauner, Mendeleev’s friend and an eminent expert in the chemistry of rare–earth elements.

Illinium had been discovered, the discoverers accept congratulations and learn about the second, third, fourth confirmation of the discovery from the scientists of other countries. The pedigree of element 61 could be started thus: “Moseley had predicted and American chemists discovered”. But a discordant not unexpectedly sounded in November 1926 from the pages of Nature. It was none other than Brauner. He congratulated him American colleagues but voiced his disagreement with the above–cited beginning of their report. He argued that it was really not important who first discovered element 61 –American or Italians; in the twenties scientists became increasingly aware that the discovery by itself was a purely technical matter. The important issue is who predicted the new element. Was it Moseley? No, declared the Czech scientist. Who then? Of course, he himself, Boguslav Brauner…..

But nothing could be further from the truth if we thought that he was immodest. His claim was based on his vast experience of work with rare earths, on his profound understanding of the spirit of the periodic system, on his superb appreciation of slight changes of properties in the series of extremely similar rare–earth elements, and, finally, on his intuition of a dedicated researcher.

But these words of praise must be substantiated with facts. Let us turn back to 1882. The old didymium of K. Mosander is close to its death. P. Lecoq de Boisbaudran had already extracted a new element, samarium, from it. B. Brauner carefully analyses the residue and employing extremely complicated chemical procedures separates it into three fractions with different atomic masses. Owing to a number of reasons he has to discontinue his work and in 1885 K. Auer von Welsbach overtakes the Czech scientist. The old didymium is dead but praseodymium and neodymium have appeared, the first and the third fractions of Brauner. But what about the intermediate second fraction? No, its tine has not come. The chemistry of rare–earth elements is in a turmoil. The muddy stream of erroneous discoveries of new elements overflows with doubts the very periodic system. But life goes on. The chaos in rare earths gradually diminishes and the known rare–earth elements form an ordered series. Now Brauner notices that the difference between the atomic masses of neodymium and samarium is rather large; it is larger than the respective difference between any two neighbouring rare–earth elements. His brilliant knowledge of rare earths suggests to Brauner that there is a discontinuity in the variations of their properties in the part of the series between neodymium and samarium. At last, he recalls his work of 1882. The clues fit into a pattern leading to premonition and even certainty that an unknown element can be found between neodymium and samarium. But as his friend, Mendeleev, Brauner was never too hasty in his conclusions. It was only in 1901 that he placed an empty box between neodymium and samarium when he put forward his views on the place of the rare–earth elements in the periodic system.

Now we can give a translation of the note he wrote in margin of his hand–written table of elements. It reads: “61st element is the missing element predicted by me in 1902”.

His short letter to Nature was an attempt by Brauner to put the record straight. This would seem to simplify the task of science historians in writing the history of element 61. But a history is meaningful only if it treats a subject which really exists. As for illinium the element proved to be still–born.

While the hotheads kept trying to squeeze the symbol Il into box 61 of the periodic table meticulous critics tried to verify the discovery. The careful experiments by the first of them, Prandtl, could be doubted by nobody. But his results did not even hint at the existence of element 61.

In 1926 the Noddacks who had just announced their discovery of masurium and rhenium (Nos. 43 and 75) started their tests. They used all available techniques to analyse fifteen various minerals suspected of containing illinium. The processed 100 kilograms of rare–earth materials and could not detect a new element. The Noddacks claimed that if the American’s results had been correct they, the Noddacks, would undoubtedly extracted the new element. Even if the element were 10 million times rarer than niodymium or samarium they would still find it… There are two possible explanations: either element 61 is so rare that the existing experimental techniques are not fine enough to find it or wrong mineral specimens were taken.

Geochemists were against the first explanation. The abundances of rare–earth elements are more or less similar. There are no reasons to think that illinium is an exception. They suggested looking for illinium in minerals of calcium and strontium. All rare–earth elements are typically trivalent but some of them can exhibit a valence of two or four. For instance, europium rather easily gives rise to cations with a charge of two. Their size is closer to those of calcium and strontium cations and they can replace the letter in the respective alkaline–earth minerals. Perhaps, illinium has a similar more pronounced capacity and can be found in some rare natural compound of strontium. One hypothesis replaced another, one assumption stemmed from another, unsubstantiated one. Just in case, the Noddacks analysed several alkaline–earth minerals. Alas, they failed once more.

The search for illinium seemed to come to a dead end; though it still went on the reported results were little believed. Chemists failed in looking for element 61 in the terrestrial minerals it was theoretical physics whose fate it was to open up the “envelope” where nature had “sealed” element 61. But when the envelope was open the scientist (not for the first time!) were disappointed. The envelope was empty.

At this point the fate of element 61 directly involves the fate the element 43, that is, technetium. According to the law formulated by the German theoretical physicist Mattauch, technetium in principal cannot have stable isotopes. This law also forbids existence of stable isotopes of element 61. Illinium is dead but element 61 must survive.

But what if it really does not exist? I. Noddack put forward a daring idea that illinium (we shall use this name for the time being) had existed on Earth in early geological periods. But it had been a highly radioactive element with a short half–life and it had decayed fairly soon and disappeared from the face of Earth. If we agree with this idea we have to make two extremely unlikely assumptions. First, illinium which is at the centre of the periodic table has no stable isotopes. Second, the half–lives of its isotopes a e much shorter than the age of Earth.

Indeed, illinium neighbours in the periodic system (neodymium and samarium) have many (seven each) natural isotopes with a wide range of mass numbers–from 142 to 154. Any feasible isotopes of element 61 would have its mass number in this range. Thus, any illinium isotopes proves to be unstable in this range of mass numbers. The Mattauch law seem to bury for good the hopes to find element 61 on Earth. But then a gleam of hope appeared. All right, the illinium isotopes are all radioactive. But to what extent? Perhaps the half–lives of some of them are very long. At that time the theory had not learned how to predict half–lives of isotopes. The search for element 61 had to continue in the dark. Physicists believed that only nuclear synthesis could solve the riddle of element 61 the more so as the case of technetium was fresh in their minds.

As if trying to restore the honour of American science after its setback in 1926 two physicists from the University of Ohio conducted the first experiment of artificial synthesis of element 61 in 1938. They bombarded a neodymium target with fast deuterons (the nuclei of heavy hydrogen). They believed that the resulting nuclear reaction Nd + d → → 61 + n gave rise to an isotopes of element 61. Their results were inconclusive but nevertheless they thought that they obtained an isotope of the new element with the mass number of 144 and the half–life of 12.5 hours.

Again sceptics said that these results were erroneous and not without a reason since nobody could be sure that the neodymium target was ideally pure. The method of identification could hardly be considered reliable, too. Even uncomplicated optical and X–ray spectra evidenced the presence of element 61 as in the study of 1926; the conclusion was made from the radiometric data.

In fact, chemistry was not involved in this work and the chemical nature of the mysterious radioactive product was not determined. Therefore, one may ask whether 1938 can be regarded as the actual data of discovery of element 61. It can rather be said that only the consistent efforts to synthesize it started at the time.

As time passed the range of bombarding particles was extending, targets of other rare–earth elements were used, and the techniques of activity measurements were improved. Reports on other illinium isotopes started to appear in scientific journals. Element 61 was becoming a reality albeit an artificially created one. Its name was changed to cyclonium in commemoration of the fact that it was produced in a cyclotron but the symbol Cy did not remain for long in box 61 of the periodic table.

Researchers had detected the radioactive “signal” of cyclonium but nobody had seen even a grain of the new element and its spectra had not been recorded. Only indirect evidence of the existence of cyclonium had been obtained.

The history of science of the 20th century knows of many great discoveries and one of the greatest is the discovery of uranium fission under the effect of slow neutrons. The nuclei of uranium–235 isotopes are split into two fragments, each of which is an isotope of one of the elements at the centre of the periodic table. Isotopes of thirty odd elements from zinc to gadolinium can be produced in this way. The yield of the isotopes of element 61 has been calculated to be fairly high–approximately 3 per cent of the total amount of the fission products.

But the task of extracting the 3 per cent amount proved to be very difficult. The American chemists J. Marinsky, L. Glendenin, and Ch. Coryell applied a new chemical technique of ion–exchange chromatography for separation of the uranium fission fragments.

Special high–molecular compounds known as the ion–exchange resins are employed in this technique for separating elements. The resins act as a sieve sorting up elements in an order of the increasing strength of the bonds between the respective elements and the resin. At the bottom of the sieve the scientists found a real treasure–two isotopes of element 61 with the mass numbers 147 and 149.

At last, element 61 known as illinium, florencium, and cyclonium could be given its final name. According to recollections of the discoverers, the search for a new name was no less difficult than the search for the element itself. The wife of one of them, M. Coryell, resolved the difficulty when she suggested the name promethium for the element. In an ancient Greek myth Prometheus stole fire from heaven, gave it to man and was consequently put to extreme torture by Zeus. The name is not only a symbol of the dramatic way of obtaining the new element in noticeable amounts owing to the harnessing of nuclear fission by man but also a warning against the impeding danger that mankind will be tortured by the hawk of war, wrote the scientists.

Promethium was obtained in 1945 but the first report was published in 1947. On June 28, 1948, the participants at a symposium of the American Chemical Society in Syracuse had a lucky chance to see the first specimens of promethium compounds (yellow chloride and pink nitrate) each weighing 3 mg. These specimens were no less significant than the first pure radium salt prepared by Marie Curie. Promethium was born by the great creative power of science. The amounts of promethium prepared now weigh tens of grams and most of its properties have been studied.

The Mattauch law denied the existence of terrestrial promethium but this denial was not absolute. The search for promethium in terrestrial ores and minerals would be quite in order if promethium had long–lived isotopes with half–lives of the order of the age of Earth.

But in this respect nuclear physics proved to be a foe of natural promethium. With each newly synthesized promethium isotope a possible scope for search became increasingly narrow. The promethium isotopes were found to be short–lived. Among the fifteen promethium isotopes known today the longest–lived one had a half–life of only 30 years. In other words, when Earth had just formed as a planet not a trace of promethium could exist on it. But what we mean here is the primary promethium formed in the primordial process of origination of elements. What was discussed was the search for the secondary promethium which is still being formed on Earth in various natural nuclear reactions.

Technetium was finally found on Earth among the fragments of spontaneous fission of uranium. These fission products could contain promethium isotopes. According to estimates, the amount of promethium that can be produced owing to spontaneous fission of uranium in the Earth’s crust is about 780 g, that is, practically, nothing. To look for natural promethium would be tantamount to dissolving a barrel of salt in the lake Baikal and then trying to find individual salt molecules.

But this titanic task was fulfilled in 1968. A group of American scientists including the discoverer of natural technetium P. Kuroda managed to find the natural promethium isotope with a mass number of 147 in a specimen of uranium ore (pitchblende). This was the final step in the fascinating history of the discovery of element 61.

As in the case of technetium, we can name two dates of discovery of promethium. The first date is the date of its synthesis, that is, 1945. But under the circumstances synthesis was unconventional (it could be called fission synthesis). The first two promethium isotopes were extracted from the fragments of fission of uranium irradiated with slow neutrons rather than in a direct way as was the case with technetium, which was produced in a direct nuclear reaction. This makes promethium a unique case among all over synthesized elements.

The second date is the date of the discovery of natural promethium, that is, 1968. This achievement is of independent significance as it stretched to the utmost the capabilities of the physical and chemical methods of analysis. Of course, the achievement is of a purely theoretical significance since nobody can hope to extract natural promethium for practical uses.

The Boiling Point of Water

Water always boils at 100˚C, right? Wrong! Though it’s one of the basic facts you probably learnt pretty early on back in school science lessons, your elevation relative to sea level can affect the temperature at which water boils, due to differences in air pressure. Here, we take a look at the boiling points of water at a variety of locations, as well as the detailed reasons for the variances.

From the highest land point above sea level, Mount Everest, to the lowest, the Dead Sea, water’s boiling point can vary from just below 70 ˚C to over 101 ˚C. The reason for this variation comes down to the differences in atmospheric pressure at different elevations.

Atmospheric pressure the pressure exerted by the weight of the Earth’s atmosphere, which at sea level is simply defined as 1 atmosphere, or 101,325 pascals. Even at the same level, there are natural fluctuations in air pressure; regions of high and low pressure are commonly shown as parts of weather forecast, but these variances are slight compared to the changes as we go higher up into the atmosphere. As your elevation (height above sea level) increases, the weight of the atmosphere above you decreases (since you’re now above some of it), and so pressure also decreases.

In order to understand how this affects water’s boiling point, we first need to understand what’s going on when water boils. For that, we’ll need to talk about something called ‘vapour pressure’. This can be thought of as the tendency of molecules in a liquid to escape into the gas phase above the liquid. Vapour pressure increases with increasing temperature, as molecules move faster, and more of them have the energy to escape the liquid. When the vapour pressure reaches an equivalent value to the surrounding air pressure, the liquid will boil.

At sea level, vapour pressure is equal to the atmospheric pressure at 100 ˚C, and so this is the temperature at which water boils. As we move higher into the atmosphere and the atmospheric pressure drops, so too does the amount of vapour pressure required for a liquid to boil. Due to this, the temperature required to reach the necessary vapour becomes lower and lower as we get higher above sea level, and the liquid will therefore boil at a lower temperature.

This is, of course, a fact that’s true for all liquids, not just water. And it’s also not just atmospheric pressure that can affect water’s boiling point. Most of us are probably aware that adding salt to water during cooking increases water’s boiling point, and this is also related to vapour pressure. In fact, adding any solute to water will increase the boiling temperature, as it reduces the vapour pressure, meaning a slightly higher temperature is required in order for the vapour pressure to become equal to atmospheric pressure and boil the water.

Another factor that can affect the boiling temperature of water is the material that the vessel it’s being boiled in is made of. Experiments have shown that, at the same pressure, water will boil at different temperatures in metal and glass vessels. It’s theorised that this is because water boils at a higher temperature in vessels which its molecules adhere to more strongly – there’s much more detail on this phenomenon here.

So, water’s boiling point is anything but absolute, and it can be affected by a whole range of factors. Useful information if you ever find yourself wanting to make a cup of tea on Everest – the lower boiling point would mean the cup you end up with is rather weak and unpleasant

 

Discovery of element : Technetium

Technetium

The upper part of the periodic system down to the sixth period (where the rare–earth elements are located) always seemed relatively quiet, particularly after the discovery of the group of noble gases which harmoniously closed the right–hand side of the system. It was quiet in the sense that one could hardly expect any sensational discoveries there. The debates concerned only a possible existence of elements that were lighter than hydrogen and elements lying between hydrogen and helium. On the whole, we can say in the parlance of mathematicians that this part of the periodic system was an ordered set of chemical elements.

Therefore, the more awkward and confusing seemed to be the mysterious blank slot No. 43 in the fifth period and seventh group.

Mandeleev named this element eka–manganese and tried to predict its main properties. A few times the element seemed to have been discovered but soon it proved to be an error. This was the case with ilmenium allegedly discovered by the Russian chemist R. Hermann, back in 1846. For some time even Mendeleev tended to believe that ilmenium was eka–manganese. Some scientists suggested placing devium  between molybdenum and ruthenium. The German chemist A. Rang even put the symbol Dv into this box of periodic table. In 1896 there flashed and burned like a meteor lucium supposedly discovered by P. Barriere.

Mandeleev did not live to see the happy moment when eka–manganese was really found. A year after his death, in 1908, the Japanese scientist M.  Ogawa reported that he found the long–awaited element in the rare mineral, molybdenite and named it nipponium (in honour of the ancient name of Japan). Alas, Asia once more failed to contribute a new element to the periodic system. Ogawa, most probably, dealt with hafnium (which was also discovered later).

Chemists grew accustomed to a few chemical elements being discovered every year and they were at a loss in the case of eka–manganese. They began to think that Mendeleev could make a mistake and no manganese analogues existed. 

H. Moseley decisively refuted this skepticism in 1913. He clearly demonstrated that these analogues have their own place among the elements. In a paper dated September 5, 1925, W. Noddack, I. Tacke, O. Berg announced that they had discovered, together with element No. 75 (rhenium), its lighter analogue in the seventh group of the periodic system, namely, masurium whose number was 43. Two new symbols, Ma and Re, appeared in the periodic table, in chemical textbooks, and numerous scientific publications. The discoverers saw nothing odd in the fact that masurium and rhenium had not been discovered earlier. These elements were thought to be not too rare, however. The lateness of their discovery was attributed to another cause. A large group of trace elements in known to geochemistry. The trace elements are classified as those elements which have no or almost no own minerals but are spread in various amounts over minerals of other elements as if the nature has sprayed them with a giant atomizer. This is why the traces of masurium and rhenium were so hard to identify. Only the powerful eye of X–ray spectral analysis could distinguish them against the formidable background of other elements. There is an ancient saying that if two people do the same things this does not mean that the results will be identical. Two biographies started under the same conditions typically follow different paths. The same can be said about the fates of elements 43 and 75; one of them went a long way and found its proper place while the other’s way soon led it to a forest of errors, misunderstandings, and controversies. This was the path of masurium.

W. Prandtl got interested in the empty slots in the seventh group of the periodic table. He had his own outlook and put forward original ideas on the structure of the periodic system. He did not compile a new version of the table, though. He suggested placing the rare–earth elements each to a group though by that time most chemists had put down such an arrangement. But in Prandtl’s version of the table the seventh group happens to reveal as many as four empty slots below manganese corresponding to yet undiscovered elements (this was in 1924) whose numbers were 43, 61, 75, and 93. Prandtl believed this to do no chance occurrence but a result of a common cause that had prevented four elements from having been discovered. The German scientist, however, made his table structure too elaborate and artificial to be accepted. The final discovery of rhenium was the first indication of his errors, and his ideas on the first transuranium element (No. 93) were little thought of at the time. But he was intuitively right in thinking of a close common link between elements 43 and 61.

The belief in masurium’s existence gradually diminished. Only the original discoverers were firm. As late as the beginning of the thirties I. Noddack continued to say that in time element 43 would be commercially available as it happened with rhenium. But as the time passed and chemists again and again failed to find masurium in whatever minerals they analysed they came to believe that I. Noddack was right only by half, that is, only about rhenium. Rarest mineral specimens were tested for masurium. Some people even went as far as to claim that masurium minerals had yet to be found and would possess unheard of properties. Naturally, geochemists were quite sceptical. The imagination of some people went even further and masurium was suggested to be radioactive. That was too much, others said. But it was precisely this shot that did not go wild.

Let us talk about some concepts of nuclear physics. We have discussed isotopes. Now we meet another term–isobars–elements having the same atomic weight or mass numbers but different atomic numbers (from the Greek for “heavy”). Isobars, in other words, are isotopes of different chemical elements with different nuclear charges but identical mass numbers. Take, for instance, potassium–40 and argon–40 which have different nuclear charges (respectively, 19 and 20). Their mass numbers are identical because their nuclei contain different numbers of protons and neutrons but their total numbers are the same; potassium nucleus contains 19 protons 21 neutrons while argon nucleus has 20 protons and 20 neutrons.

Thus, the concept of isobars turned out to be the magic key that opened the door to the mystery of masurium.

When the majority of stable chemical elements were found to have isotopes–up to ten isotopes per element–the scientists started to study the laws of isotopism. The German theoretical physicist J. Mattauch formulated one of such laws at the beginning of the thirties (the basic premise of this law was noted back in 1924 by the Soviet chemist S. Shchukarev). The law states that if the difference between the nuclear charges of two isobars is unity one of them must be radioactive. For instance, in the 40K–40Ar isobar pair the first is naturally weakly radioactive and transforms into the second owing to the so–called process of K–capture. Then Mattauch compared with each other the mass numbers of the isotopes of the neighbours of masurium, that is, molybdenum (Z = 42) and ruthenium (Z = 44):

            Mo isotopes      94         95         96         97         98         –          100       –          –

            Ru isotopes         –           –          96         –          98         99         100       101       102

What did he deduce from this comparison? The fact that the wide range of mass numbers from 94 to 102 was forbidden for the isotopes of element 43 or, in other words, that no stable masurium isotopes could exist.

If that was really so that meant a peculiar anomaly linked to the number 43 in the periodic system. All the atom species with Z = 43 had to be radioactive as if this number was a small island of instability amidst a sea of stable elements. This, of course, would be unfeasible to predict within the framework of purely chemical theory. When Mendeleev predicted his eka–manganese he could never imagine that this member of the seventh group of the periodic system could not exist on Earth. Of course, in those times (the early thirties) Mattauch’s law was no more than a hypothesis, though one that looked like quite capable of becoming a law. And it became just that. The physicist’s idea opened the eyes of chemists who lost all hope of finding element 43 and they saw the source of their errors. However, the symbol Ma remained in box 43 of the periodic system for a few more years. And not without a reason. All right, all masurium isotopes are radioactive. But we know radioactive isotopes existing of Earth–uranium–238, thorium–232, potassium–40. They are still found on Earth because their half–lives are very long. Masurium isotopes are, perhaps, long–lived, too? If so, one should not be too hasty in dismissing the chances of successful search for element 43 in nature.

The old problem remained open. Who knows which way the biography of masurium would take if not for the dawn of a new age–that of artificial synthesis of elements.

Nuclear synthesis became feasible after invention of the cyclotron and the discoveries of neutrons and artificial radioactivity. In early thirties a few artificial radioisotopes of known elements were synthesized. Syntheses of heavier–than–uranium elements were even reported. But physicists just did not dare to take the challenge of the empty boxes at the very heart of the periodic system. It was explained by a variety of reasons but the major one was enormous technical complexity of nuclear synthesis. A chance helped. At the end of 1936 the young Italian physicist E. Segre went for a post–graduate work at Berkley (USA) where one of the first cyclotrons in the world was successfully put into operation. A small component was instrumental in cyclotron operation. It directed a beam of charged accelerated particles to a target. Absorption of a part of the beam led to intense heating of the component so that it had to be made from a refractory material, for instance, molybdenum.

The charged particles absorbed by molybdenum gave rise to nuclear reactions in it and molybdenum nuclei could be transformed into nuclei of other elements. Molybdenum is a neighbour of element 43 in the periodic system. A beam of accelerated deutrons could, in principle, produce masurium nuclei from molybdenum nuclei.

That was just Segre’s thought. He was a competent radiochemist and understood that if masurium really were produced its amount would be literally negligible and its separation from molybdenum would present an enormously intricate task. Therefore, he took an irradiated molybdenum specimen with him back to the University of Palermo where he was assisted in his work by the chemist C. Perrier.

They had had to work for nearly half a year before they could present their tentative conclusions in a short letter to the London journal nature. Briefly, the letter reported the first in history artificial synthesis of a new chemical element. This was element 43 the futile search for which on Earth wasted so much efforts of scientists from many countries. Professor E. Lawrence from the University of California at Berkley gave the authors a molybdenum plate irradiated with deutrons in the Berkley cyclotron. The plate exhibited a high radioactivity level which could hardly be due to any single substance. The half–life was such that the substances could not be radioactive isotopes of zirconium, niobium, molybdenum, and ruthenium. Most probably they were isotopes of element 43.

Though the chemical properties of this element were practically unknown Segre and Perrier attempted to analyse them radiochemically. The element proved to be closely similar to rhenium and exhibited the same analytical reactions as rhenium. However, it could be separated from rhenium with technique used for separating molybdenum and rhenium. The letter was written in Palermo and dated June 13, 1937. It was by no means a sensation. The scientific community regarded it as just the authors going on record. The reported data were too patchy while what was needed to be convincing was precisely the details and clear results of radiochemical analysis.

Only later Segre and Perrier were recognized as heroes; indeed, they extracted from the irradiated molybdenum just 10–10g of the new element–an amount formerly undetectable Never before radiochemists worked with such negligible amounts of material. The discoverers suggested naming the new element technetium from the Greek for “artificial”. Thus, the name of the first synthesized element reflected its origin. The name, though, became generally accepted only ten years later.

Perrier and Segre received new specimens of irradiated molybdenum and continued their studies. Their discovery was confirmed by other scientists. By 1939 it was understood that bombardment of molybdenum with deutrons or neutrons produces at least five technetium isotopes. Half–lives of some of them were sufficiently long to make possible substantial chemical studies of the new element. It no longer sounded fantastic to speak about “the chemistry of element 43”. But all attempts to measure accurately the half–lives of the technetium isotopes failed. The available estimates were disheartening since none of them exceeded 90 days and this put a stop to all hopes of finding the element on Earth.

So what was technetium in the late thirties and early forties? Nothing more than an expensive toy for curious scientists. Any prospects of accumulating it in a noticeable amount were, apparently, non–existent. The fate of technetium (and not only of it) was reversed when nuclear physics discovered an amazing phenomenon–fission of uranium by slow neutrons.

When a slow neutron hits a nucleus of uranium–235 it in effect breaks the nucleus down into two fragments. Each of the fragments is a nucleus of an element from the central part of the periodic table, including technetium isotopes. It is not without a reason that a fission reactor (a large–scale nuclear energy producer) is known as a factory of isotopes. Cyclotron made possible the first ever synthesis of technetium and fission reactor allowed the chemists to produce kilograms of technetium. But even before the first fission reactor started operating Segre in 1940 found the technetium isotope with a mass number of 99 in uranium fission products in his laboratory. Having found its new birthplace in a fission reactor technetium started to turn into an everyday (paradoxical as it may be) element. indeed, fission of 1 g of uranium–235 gives rise to 26 mg of technetium–99.

As soon as technetium ceased to be a rare bird scientists found the answers to many questions that had puzzled them, and first of all about its half–lives. In the early fifties it became clear that three of technetium isotopes are exceptionally long–lived in comparison with not only its other isotopes but also many other natural isotopes of radioactive elements. The half–life of technetium–99 is 212 000 years, that of technetium–98 is one and a half million years, while that of technetium–97 is even more, namely, 2 600 000 years. The half–lives are long but not long enough for primary technetium to be conserved on Earth since its origin. The primary technetium would survive on Earth if its half–life were not shorter than one hundred fifty million years. This makes obvious the hopelessness of all search for technetium of Earth.

But technetium can still be produced in the course of natural nuclear reactions, for instance, when molybdenum is bombarded by neutrons. How can free neutrons appear on Earth? They can be produced in spontaneous fission of uranium. The process occurs as described above, only spontaneously, and gives rise to a few neutrons, apart from two large fragments, i.e. nuclei of lighter elements.

The search for technetium in molybdenum ores failed and scientists turned their attention to another possibility. If technetium isotopes are produced in fission reactors why cannot they be born in natural processes of spontaneous uranium fission?

Using as a basis the Earth uranium resources (taking the figure for the mean abundance of uranium in the 20–km thickness of the Earth crust) and assuming the same proportion of produced technetium as in the case of reactor fission we can calculate that there are just 1.5 kg of technetium on Earth. Such a small amount (though it is larger than for other synthesized elements) could hardly be taken seriously. Nevertheless, scientists attempted to extract natural technetium from uranium minerals. This was done in 1961 by the American chemist B. Kenna and P. Kuroda. Thus, technetium acquired another birthday–the day when it was discovered in nature. If the methods of artificial synthesis of technetium had failed to materialize, even then it would, sooner or later, be brought to light from the bowels of the Earth.

But ten years earlier, in 1951, sensational news about element 43 was heard. The American Astronomer S. Moore found characteristic lines of technetium in the solar spectrum. The spectrum of technetium had been recorded immediately when it had become feasible, that is, when a sufficient amount of the element had been synthesized. The spectral data had been compared with those reported by the Noddacks and Berg for masurium. The spectra had proved to be quite different making ultimately clear the mistake of the discoverers of masurium. The spectrum of the solar technetium was identical to that of the terrestrial technetium. An analogy with helium was apparent–both elements sent messages from the Sun before to be found on Earth. True, astronomers questioned the data on the solar technetium.  But in 1952 the cosmic technetium once more sent a message when the British astrophysicist P. Merril found technetium lines in the spectra of two stars with the poetic names of R Andromedae and Mira Ceti. The intensities of these lines evidenced that the content of technetium in these stars was close to that of its neighbours in the periodic system, namely, niobium, zirconium, molybdenum, ruthenium, rhodium and palladium. But these elements are stable while technetium is radioactive. Though its half–life is relatively long it is still negligible on cosmic scale. Therefore, the existence of technetium on stars can mean only that it is still born there in various nuclear reactions. Chemical elements continue to be produced in stars on a gigantic scale. A witty astrophysicist named technetium the acid test of cosmogonic theories. Any theory of the origin of elements must elucidate the sequence of nuclear reactions in stars giving rise to technetium.

Reason for the formation of large number of organic compounds : Catenation

Reason for the formation of large number of organic compounds

 What makes the carbon so special ?

What is it that sets carbon apart from all other elements in the periodic table ?

Why are there so many organic compounds ?

The answer lies in carbon’s position in the periodic table. Carbon is in the centre of second row elements

Li > Be >  B > C > N > O > F

First think why molecules are formed from atoms ? It is because of the reason that atom combines with same or with other atoms to form molecule so as to complete its octet and attain lower energy stable and hence become stable. That is the reason why noble gases are considered as inert gases, they generally do not combine with itself or with other atoms because they have complete octet. But what about other atoms ? They have incomplete octet, so they must combines with same or other atoms to form molecule for better stability.

Elements on the left hand side of carbon have less than 4 electrons in the valence shell (Li-1, Be-2, B-3) so they have more tendencies to loose electron to attain noble gas configuration for stability. That’s why they generally forms compounds with Li+, Be2+, B3+ by losing 1, 2, 3 electrons respectively. Elements present downside in the same group too have similar tendency as that of Li, Be and B, hence form compounds in the following states; Na+, K+, Rb+, Cs+, Mg2+, Ca2+, Sr2+, Al3+, Ga3+, etc.

Elements on the right hand side of carbon have more than 4 electrons in the valence shell (N-5, O-6, F-7). To complete their octet, valance electron must be subtracted from 8 that’s why the valency of N is (8-5) i.e. 3, O is (8-6) i.e. and that of F is (8-7) i.e. 1. It is much easier to gain 3, 2, 1 electrons to complete their octet as compared to loosing 5, 6, 7 electrons to complete their octet. So these elements have more tendency to gain electrons and form compounds in the following states; N3, P3, As3, Sb3, Bi3, O2, S2, Se2, Te2, Po2, F, Cl, Br, I.

As elements present on the left hand side of carbon loose electrons to form compounds and elements of right hand gain electrons to form compounds so compounds formed are ionic in nature.

But think about carbon and the elements present down side, which are present in the middle of each period and have equal tendency to loose or gain electrons as they have 4 electrons in their octet. This led carbon and other elements of this group (Si, Ge, Sn & Pb) to share electrons with itself and other elements of periodic table to complete octet. As these compounds are formed by sharing of electrons so they are considered to be covalently bonded.

Carbon by sharing its electrons with other carbon atoms leads to formation of long chain carbon compounds which may be single, double or triple bonded, cyclic or acyclic, linear or branched. This self-linking property of carbon is called catenation. All the atoms of 14th group show the property of catenation but it decreases down the group because of weak overlapping due to large size and follows order :

C >> Si >> Ge > Sn > Pb

Carbon may also form multiple bonds with N, P, O, S etc. forming large number of functional group, which we will discuss later.

This is not the end of compound formation, carbon forms many abnormal compounds with elements of s, p & d blocks. So for sake of simplicity we are constructing an organic chemist’s periodic table with the most important elements emphasized.

Elements, which are in dark box, are generally involved in making organic compounds along with deuterium (D), which is an isotope of hydrogen (H).

As there are large number of atoms in periodic table which have valence electrons, atomic orbital of carbon may overlap with them and share its electron to form large number of compounds. But for that many other factors such as size, activation energy, electronegativity, electron affinity, catenation etc. are responsible which all come under one word “Position” i.e. position for carbon in the periodic table. This word “position” include everything related with molecule formation therefore the main reason behind large number of organic compounds is the position of carbon in the periodic table.

 

Baeyer’s strain theory

Baeyer’s strain theory : To compare stability of cycloalkanes 

 When we carefully look over the cyclic saturated compounds, we find that each atom is sp3  hybridized.  The ideal bond angle 109028’ but in cycloalkanes this angle is mathematically 180-(360/n) where n is the number of atoms making ring. 

for example Cyclopropane, angle is 600; in Cyclobutane it is 900 and so on.

Angle Strain : This difference in ideal bond angle and real bond angle, is called angle strain and it causes strain in bond which affects the stability of molecule. 

Greater is the deviation from the theoretical angle, greater is the Angle strain ; lesser the stability. 

To calculate the distortion or angle strain in cycloalkane we assume the atoms of ring in a plane, such as in cyclopropane, all the 3 carbon atoms occupy one corner of an equilateral triangle with bond angle 60o. As two corners bent themselves to form bond so strain too is divided equally. So strain in cyclopropane will be ½ (109o28’ – 600) = 24044’.

Deviation of bond angle in cyclopropane from normal tetrahedral angle

Distortion or strain = ½ (109028’ bond angle of ring). So angle strains in some cycloalkanes are listed in the table below.

Compound

No. of C in the ring

Angle between the C atoms

Distortion or strain

Cyclopropane

3

600

24o44’

Cyclobutane

4

900

9o44’

Cyclopentane

5

108o

0o44’

Cyclohexane

6

120o

-5o16’

Cycloheptane

7

128o34’

-9o33’

Cyclooctane

8

135o

-12o62’

 

From the table it is clear that cyclopropane has the maximum distortion, so it is highly strained molecule and consequently more reactive than any of one monocylic alkanes, which is clear from the reaction that ring can be opened very easily to relieve strain on reaction with Br2, HBr or H2/Ni at high temperature.

In contrast, cyclopentane & cyclohexane have least strain so they are found more readily and are very stable as compared to cyclopropane.

Baeyer strain theory satisfactorily explains the typical reactivity and stability of smaller rings (from C3 to C5) i.e. Stability order follows : Cyclopropane < Cyclobutane < Cyclopentane

But not valid for cyclohexane onwards because the strain again increases with the increase in number of carbon atom but actually large rings are more stable. So molecular orbital theory is also considered according to which covalent bond is formed by coaxial overlapping of atomic orbitals. The greater is the extent of overlap the stronger is the bond formed. In case of sp3 carbon, C – C bond will have maximum strength if the C-C-C bond have the angle 109o28’. If cyclopropane is an equilateral triangle then the bond angle of each C-C-C bond would be 60o. Therefore it was proposed by Couson that in cyclopropane the sp3 hybridized orbitals are not present exactly in one straight line due to mutual repulsion of orbital of these bonds resulting thereby loss of overlap. This loss of overlap weakens the bond and is responsible for its instability and strain in molecule. Similarly, in case of cyclobutane, there is also loss of overlap but the loss is less than in cyclopropane, so cyclobutane is more stable than cyclopropane. Overlapping of orbitals in large ring compound (5 more carbon atoms) is however much better which accounts for the greater stability of such compound.

It is natural that when a molecule has strain within it, it will affect the stability of molecule. The stability of molecules can be calculated easily by measuring heat of combustion which will give the measure of total strain and thermochemical stability which can be calculated mathematically.

Total strain = (No of C atom is the ring × observed heat of combustion/CH2) observed heat of combustion/CH2 for n alkane.

 

Experimental data of total strain for different cycloalkanes*

No. of C in the ring

Heat of combustion kJ per CH2 group

Total strain in kJ

3

697

115

4

686

109

5

664

27

6

659

0

7

662

27

8

663.8

42

664.6

54

* data from Organic chemistry solomons & Fryhle

From the data above it is clear that strain decreases from C3 to C6i.e. stability increases, but stability again deteriorates from C7 to C9 ring system. 

 According to this theory, the carbon atoms in 5 membered and smaller rings can lie in one plane as explained by Baeyer but Sachse suggested that in six membered and higher rings the carbon atoms are non planar . In this way the ideal angle 109028’ is retained and the ring is free from angle strain. Thus Sachse proposed that cyclohexane exist in two puckered forms as boat and chair form. These forms are readily inter-convertible through half chair and twist boat forms simply by rotation about the single bonds.  

 

center of symmetry
Molecular Symmetry

 

Molecular Symmetry

Any object is called as symmetrical if it has mirror symmetry, or ‘left-right’ symmetry i.e. it would look the same in a mirror.

For example : a cube , a matchbox, a circle 

Further it can be said ; a sphere is more symmetrical compare to a cube. Cube looks the same after rotation through any angle about the diameter while during the rotation of a cube, it looks similar only with certain angles like 90°, 180°, or 270° about an axis passing from the centers of any of its opposite faces, or by 120° or 240° about an axis passing from any of the opposite corners.

Similarly Molecules can also be classified as Symmetric or Asymmetric.

Symmetry Operations

An action on an object which leaves the object at same position after the action carried out. Such type of action is called as Symmetry operations.

All known molecules can classify in groups possess the same set of symmetry elements.

Such type of classification is helpful to assign the molecular properties without calculation and in the determination of polarity and degeneracy of molecular states.

It provides the systematic treatment of symmetry in chemical systems in a mathematical framework which is called as group theory.

Group theory is also helpful is some other investigations

  • Prediction of polarity and chirality of molecule.
  • In examination of bonding and visualizing molecular orbitals of molecules.
  • In prediction of polarization a molecule.
  • In investigation of vibrational motions of the molecule.

 

The simplest example of symmetry operations is water molecule. If we rotate the molecule by 180° about an axis which is passing through the central Oxygen atom it will look the same as before. Similarly reflection of molecule through both axis of molecule show same molecule.

There are five types of symmetry operations and five types of symmetry elements.

1. The identity (E)
This symmetry operation is consists of doing nothing. In other words; any object undergo this symmetry operation and every molecule consists of at least this symmetry operation. For example; bio molecules like DNA and bromo fluoro chloro methane consist of only this symmetry operation. ‘E’ notation used to represent identity operation which is coming from a German word ‘Einheit’stands for unity.

 

2. An n-fold axis of symmetry (Cn)

  • This symmetry operation involves the clockwise rotation of molecule through an angle of 2 π /n radian  or  360º/n where n is an integer. The notation used for n-fold of axis is Cn
  • For principal axis, the value of n will be highest. The rotation through 360°/n angle is equivalent to identity (E). 
  • For example, one twofold axis rotation of water (H2O) towards oxygen axis leaves molecule at same position, hence has C2axis of symmetry. Similarly ammonia (NH3) has one threefold axis, C3 and benzene (C6H6) molecule has one sixfold axis C6and six twofold axis (C2) of symmetry.

Linear diatomic molecules like hydrogen, hydrogen chloride have C∞ axis as the rotation on any angle remains the molecule the same.

 

3. Improper rotation (Sn)

Improper clockwise rotation through the angle of 2π/n radians is represented by notation ‘Sn’ and called as n-fold axis of symmetry which is a combination of two successive transformations. During improper rotation, the first rotation is through 360°/n and the second transformation is a reflection through a plane perpendicular to the axis of the rotation. Improper rotation is also known as alternating axis of symmetry or rotation-reflection axis. For example; methane (CH4) molecule has three S4axis of symmetry.

4. A plane of symmetry (σ)

There are some plane in molecule through which reflection leaves the molecule same. The vertical mirror plane is labelled as σv and one perpendicular to the axis is called a horizontal mirror plane is labelled as σh , while the vertical mirror plane which bisects the angle between two C2axes is known as a dihedral mirror plane, σd. For example, H2O molecule contains two mirror planes (a YZ Reflection (σyz) and a XZ Reflection (σxz)) which are mirror planes contain the principle axis and called as vertical mirror planes (σv).


5. Center of symmetry (i)
It is a symmetry operation through which the inversion leaves the molecule unchanged. For example, a sphere or a cube has a centre of inversion. Similarly molecules like benzene, ethane and SF6have a center of symmetry while water and ammonia molecule do not have any center of symmetry.

Overall the symmetry operations can be summarized as given below.

Inversion Center

The inversion operation is a symmetry operation which is carried out through a single point, this point is known as inversion center and notated by ‘ i’. This point is located at the center of the molecule and may or may not coincide with an atom in the molecule. 

When we are moving each atom in a molecule along a straight line through the inversion center to a point an equal distance from the inversion center and get same configuration, we say there is an inversion center in the molecule. It can be in such molecules which do not have any atom at center like benzene, ethane. 

Geometries like tetrahedral, triangles, pentagons don’t contain an inversion center. Hence a cube, a sphere contains a center of inversion but tetrahedron does not contain this symmetry operation. The molecule must be achiral for the presence of inversion center.

Some of the common examples of molecules contain center of inversion are as follow.

(a) Benzene molecule: Inversion center located at the center of molecule.

 

(b) 1,2-Dichloroethane: The staggered form of 1,2-Dichloroethane contains one inversion center at the center of molecule.

 

 

(c) trans-diaminedichlorodinitroplatinum complex: trans- form of some Coordination compounds like trans diaminedichlorodinitroplatinum complex contains inversion center.

Another example of coordination compound is hexacarbonylchromium complex [Cr(CO)6], where the inversion center located at the position of metal atom in complex.

(d) Ethane molecule: The staggered form of ethane contains inversion center while eclipsed form does not.

 

(e) Meso-tartaric acid: The anti-periplanar conformer of meso-tartaric acid has an inversion center.

(f) Dimer of D and L-Alanine: The dimer of two configurations of Alanine; D-alanine and L-alanine contains one inversion center.

(g) 18-Crown-6: An organic compound with the formula [C2H4O]6 named as 18-crown-6 (IUPAC name: 1,4,7,10,13,16-hexaoxacyclooctadecane) also contains inversion center located at center of molecule.

(h) Cyclohexane: The chair conformation of cyclohexane contains an inversion center while boat form does not.

Molecular Symmetry Examples

A molecule or an object may contains one or more than one symmetry elements, therefore molecules can be grouped together having same symmetry elements and classify according to their symmetry. Such type of groups of symmetry elements are known as point groups because there is at least one point in space which remains unchanged no matter which symmetry operation from the group is applied. 

For the labelling of symmetry groups, two systems of notation are given, known as the Schoenflies and Hermann-Mauguin (or International) systems. The Schoenflies notations are used to describe the symmetry of individual molecule. The molecular point groups with their example are listed below.

Point group  Explanation  Example 
C1 Contains only identity operation(E) as the C1 rotation is a rotation by 360o Bromochlorofloromethane (CFClBrH)
Ci  Contains the identity (E) and a center of inversion center (i). Anti-conformation of 1, 2-dichloro-1, 2-dibromoethane.
Cs Contains the identity E and plane of reflection σ. Hypochlorus acid (HOCl), Thionyl chloride (SOCl2).
Cn Have the identity and an n-fold axis of rotation. Hydrogen Peroxide (C2)
Cnv Have the identity, an n-fold axis of rotation, and n vertical mirror planes (σv). Water (C2v), Ammonia (C3v)
Cnh Have the identity, an n-fold axis of rotation, and σh (a horizontal reflection plane). Boric acid H3BO3 (C3h), trans-1,2-dichloroethane (C2h)
Dn Have the identity, an n-fold axis of rotation with n2-fold rotations about the axis which is perpendicular to the principal axis. Cyclohexane twist form (D2)
Dnh Contains the same symmetry elements as Dn with the addition of a horizontal mirror plane. Ethene (D2h), boron trifluoride (D3h), Xenon tetrafluoride (D4h).
Dnd Contains the same symmetry elements as Dwith the addition of n dihedral mirror planes. Ethane (D3d), Allene(D2d)
Sn Contains the identity and one Sn axis. CClBr=CClBr
Td Contains all the symmetry elements of a regular tetrahedron, including the identity, four C3 axis, three-C2 axis, six dihedral mirror planes, and three S4 axis. Methane (CH4)
T
Th
Same as Td but no planes of reflection.
Same as for T but contains a center of inversion .
 
Oh
O
The group of the regular octahedron.
Same as Oh but with no planes of reflection.
Sulphur hexafluoride (SF6)

 

Different point groups correspond to certain VSEPR geometry of molecule. Out of them some are as follow.

VSEPR Geometry of molecule  Point group 
Linear D∞h
Bent or V-shape  C2v 
Trigonal planar  D3h 
Trigonal pyramidal  C3v 
Trigonal bipyramidal  D5h 
Tetrahedral  Td 
Sawhorse or see-saw  C2v 
T-shape  C2v
Octahedral  Oh 
Square pyramidal C4v
Square planar  D4h 
Pentagonal bipyramidal  D5h

 

A molecule may contain more than one symmetry operation and show symmetrical nature. Some of the examples of symmetry operation on molecule with their point group are as given below.

(a) Benzene: The point group of benzene molecule is D6h with given symmetry operations.

  • Inversion center: i
  • The Proper Rotations: seven C2axis and one C3 and one C6 axis
  • The Improper Rotations: Sand S3axis
  • The Reflection Planes: one σh , three σvand three σd

(b) Ammonia: The point group of ammonia molecule is C3v with following symmetry operations.

  • The Proper Rotations: one C3axis
  • The Reflection Planes: three σplane

(c) Cyclohexane: The chair conformation of Cyclohexane has D3d point group with given symmetry operations;

  • Inversion center: i
  • The Proper Rotations: Three C2axis and one C3 axis
  • The Improper Rotations: S6axis
  • The Reflection Planes: Three σdplane

(d) Methane: The point group of methane is Td (tetrahedral) with C3 as principal axis and other symmetry operations are as follows;

  • The Proper Rotations: Three Caxis and Four C3axis
  • The Improper Rotations: Three S4axis
  • The Reflection Planes: Five σdplane

(e) 12-Crown-4: This has S6 point group with C3 and S6 axis with inversion center (i).

(f) Allene: The point group of methane is D2d with given symmetry operations.

  • The Proper Rotations: Three C2axis 
  • The Improper Rotations: One S4axis
  • The Reflection Planes: Two σplane

Molecular Symmetry and Group Theory

Group theory deals with symmetry groups which consists of elements and obey certain mathematical laws. Each point group is a set of symmetry operation or symmetry elements which are present in molecule and belongs to this point group. To obtain the complete group of a molecule, we have to include all the symmetry operation including identity ‘E’. A character table represents all the symmetry elements correspond to each point group. Hence we can make separate character table for each point group like C2v, C3v, D2h… etc.

For example, in the character table of C2v point group; all the symmetry elements has to written in first row and the symmetry species or Mulliken labels are listed in first column. These symmetry species specify different symmetries within one point group. For C2v, there are four symmetry species or Mulliken labels; A1, A2, B1, B2.
Remember

  • The symmetry species for one-dimensional representations: A or B
  • The symmetry species for two-dimensional representations: E
  • The symmetry species for three-dimensional representations: T

The best example of C2v point group is water which has oxygen as center atom. The px orbital of oxygen atom is perpendicular to the plane of water molecule, hence it is not symmetric with respect to the plane σv(yz). So this orbital is anti-symmetric with respect to the mirror plane and its sign get change when symmetry operations applied. On the other hand, the s orbital is symmetric with respect to mirror plane. The symmetric and anti-symmetric nature can be represents by using mathematical sign; +1 and -1; here +1 stands for symmetric and –1 stands for anti-symmetric which are the characters in character table.

Hence the symmetry operations for the px orbitals are as follow.

1. E: Symmetric hence character will be 1

2. C2:Anti-symmetric, hence character will be 1

3. σv(xz):Symmetric; character :1

4. σv(yz):Anti-symmetric, character: -1

Hence the character table for C2v point group.

C2v  E C2  σv(XZ)  σv(YZ)     
A1 1 1 1 z x2, y2,z2 
A2  -1  -1  Rz  xy 
B1  -1  -1  x, Ry  xz 
B2  -1  -1  y, Rx  yz 

 

Similarly character can be assigned for other symmetry species. The last two columns of character table make it easier to understand the symmetric nature. For example; x in second last column of Bsymmetry indicates that the x-axis has Bsymmetry in C2v point group and the Rx notation indicates the rotation around the x-axis. Similarly the character table for C3v point group will be

C3v  2C3  3σv    
A1 1 1 1 x2+y2, z2 
A2  -1  Iz  
-1  (x, y), (Ixy, Iz (x2-y2, xy), (xz, yz)

 

For doubly degenerate, the character for E will be 2 and for triply degenerate it will be 3, because in this case we have two and three orbitals respectively which are symmetric with respect to E. Some of the character tables with their point groups are as follow

a. Character table for Oh point group, for example Sulfur fluorine (SF6)

 

b. Character table Td point group, methane (CH4)

 

 

c. Character table for D3d point group, for example, staggered ethane

 

d. Character table for D6h point group, example Benzene (C6H6)

 

Symmetry Adapted Linear Combinations

In some molecules like water, ammonia, methane which have more than one symmetry equivalent atom, the combinations of the symmetry equivalent orbitals can transform according to a irreducible representations of the molecules point group which are refer as Symmetry Adapted Linear Combinations. For the formation of an n-dimensional representation a set of equivalent functions -f1, f2, …, fn- can be used. The representation can be expressed as a sum of irreducible representations with the use of calculation of characters for this representation and by the use of the great orthogonality theorem. The n-linear combinations of f1, …, fn which transform the irreducible representations is given by the projection operator which denoted as p^p^ Gi;

Here 

  • p^p^ = The operator which projects out of a set of equivalent functions the Gi Irreducible representation of the point group.
  • In n/g factor; n = dimension of the irreducible representation
  • g = the order of the group

The function fj can be chosen by any one of n which belongs to the equivalent set. For example, in the C3v character table; the 2C3^C3^ represents the class composed by C13^C31^ and C13^C31^operations. With Cclass, there are three different C3^C3^ operations would also perform separately on fj which produce different results. Let’s take an example of the O-H stretches along the ‘yz’ plane as molecular plane in water molecule; the formula can be apply to tabulate the characters of the irreducible representations and list the effect of O^O^R on one of the functions at the bottom of the table.

C2v  E C2(Z)  sv(XZ)  sv(YZ) 
A1 1 1 1
B1  -1  +1  -1
B2  -1  -1  +1 
OR(OH2 OHa  OHb OHb OHa 

 

After applying the projection operator for A1
p^p^ A1 (O-Ha) = ¼ (O-Ha + O-Hb + O-Hb + O-Ha) = 1/2 (O-Ha + O-Hb)

According to the orthogonality theorem; it shouldn’t be possible to obtain a B1 linear combination, and indeed the projection operator will be zero.
p^p^ B(O-Ha) = ¼ (O-Ha + O-Hb + O-Hb + O-Ha)=0

Application of the B2 projection operator gives
p^p^ B2 (O-Ha) = ¼ (O-Ha + O-Hb + O-Hb + O-Ha)

=1/2 (O-Ha + O-Hb)

 

These linear combinations relate to the symmetric (A1) and anti-symmetric (B2) stretches of water as given below.

When two equivalent real functions are involved, the correct linear combinations will be equals to the sum and difference functions. In case of degenerate representations like in case of N-H stretching vibrations in ammonia, it is more difficult to construct the symmetry adapted linear combinations. 

 

We can create symmetry-adapted linear combinations of atomic orbitals in exactly the same way. The point group is D2h with four carbon-hydrogen sigma bonds which are symmetry-equivalent and can make four carbon-hydrogen bonding symmetry-Adapted Linear Combinations ‘s. The character table will be as follow.

Result of symmetry operations on s1
  E C2(Z) C2(Y)  C2(X)  i s(XY)  s(XZ) s(YZ)
s1 s1  s3 s4  s2 s3 s1  s2 s4 

 

There are four non-zero symmetry-adapted linear combinations can be possible. 

 

Hybridization

 

HYBRIDIZATION

In the Valence Bond (VB) theory an atom may rearrange its atomic orbitals prior to the bond formation. Instead of using the atomic orbitals directly, mixture of them (hybrids) are formed. For carbon (and other elements of the second row) the hybridization is limited to mixing one 2s and three 2p orbitals, as appropriate.

We recognize three basis types of hybridization: sp3, sp2 and sp. These terms specifically refer to the hybridization of the atom and indicate the number of p orbitals used to form hybrids.

  • In sp3 hybridization all three p orbitals are mixed with the s orbital to generate four new hybrids (all will form σ type bonds or hold lone electron pairs).
  • If two p orbitals are utilized in making hybrids with the s orbital, we get three new hybrid orbitals that will form σ type bonds (or hold lone electron pairs), and  the “unused” p may participate in π type bonding.  We call such an arrangement sp2 hybridization.
  • If only one p orbital is mixed with the s orbital, in sp hybridization, we produce two hybrids that will participate in σ type bonding (or hold a lone electron pair). In this case, the remaining two p orbitals may be a part of two perpendicular π systems.

The most important rule is that the number of orbitals must be preserved

in the mixing process. The mixing principles can be illustrated on a simple

example of one s and one p orbital making two equivalent sp hybrids

(only one is shown here for clarity). The constructive interference of

http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/making-sp-hybrids.gif

the wavefunctions at the “right” half gives a large lobe of the hybrid

orbital, while the destructive interference on the left (opposite signs

of the s and p wavefunctions) yields a small “tail”.  The second hybrid

formed in this case is a 180°-rotated version of the one shown.  In

this case each of the two hybrids is constructed from ½ of s and ½ of p.

Within each type of hybridization, one can produce infinite number of different hybrids (mixtures). The hybrids are defined by the p to s ratio of the contributing orbitals.  Thus, an spm hybrid is composed of m+1 parts: one part of s and m parts of p, and the p/s ratio is equal m, called the hybridization index.  For example, an sp3 hybrid has ¼ (25%) of s and ¾ (75%) of p. This fraction is called an s (or p) character of the orbital. Thus, an sp3 hybrid has 25% s character.

http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/hybrid-orbitals.gif

The hybrids with larger s character have bigger front lobes (and smaller “tails”) than the hybrids with smaller s character, as illustrated above for an sp (left) and sp3 (right) hybrids.  The s/p ratio is, thus, responsible for the bonding properties of the hybrid.  Increased s contribution brings electrons closer to the nuclei, increasing stabilizing Coulomb interactions. The more s character the hybrid orbital has the lower its energy, the better its overlap (with bonding partners), and the stronger (and shorter) bonds it can form.

It is important not to confuse the hybridization type that applies to the atom (see above) with the individual hybrid character that is described by the hybridization index m. The first (indirectly) indicates the number of p orbitals set aside (for participation in π systems), the second precisely describes the specific mixture of s and p used to construct the given hybrid.

The mixing of s and p orbitals in different ratios also results in changes of the angle between the resulting hybrids.  Since the atomic p orbitals are 90° from each other, their various degree of participation in the mixing will yield hybrids separated by different angles, depending on their p character.  For two identical hybrids, in general, the more p character in the hybrids the smaller the angle between them. Thus, two pure p orbitals (100% p) are 90° apart, two sp3 hybrids are 109.5° apart,  two sp2 hybrids are 120° apart, and two sp hybrids are 180° apart.  More generally, the angle (α) between any two hybrids (spm and spn) is given by cosα = –1/(m·n)0.5.

An atom will adjust its hybridization in such a way as to form the strongest possible bonds and keep all its bonding and lone-pair electrons in as low-energy hybrids as possible, and as far from each other as possible (to minimize electron-electron repulsions).  This adjustment  is accomplished by varying s and p characters of individual mixtures, but “moving” s character between hybrids (to lower energy of some) also changes the angles between them (potentially increasing electron-electron repulsion).  Thus, it is all a compromise game.

Let us look at some examples. Something simple to start: methane. The carbon atom forms four identical bonds using four identical hybrid orbitals. These orbitals are the result of sp3 hybridization (here we talk about the hybridization type), i.e. one s and three p orbitals are mixed to form four sp3 hybrids (here we talk about the composition, or character, of each hybrid).  Each of these hybrids is composed of ¼ of s and ¾ of p (the p/s ratio is 3, i.e. m = 3). The angle between any two such hybrid orbitals is (yes…  that’s the cosine formula above) 109.5o.  The table below gives more examples of different hybrid orbitals involved in making C-H bonds. Note that for the same hybridization type (sp3 in our example) one can have quite different hybrids involved in making C-H bonds.

Table 1. Hybrids Involved in Making C–H Bonds in Simple Hydrocarbons

Hydrocarbon Hybridization

Type

Bond angle Hybrid  involveda s characterb Bond length (A) BDEc
http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/hyb-m.gif sp3 109.5o sp3 25% 1.100 105  
http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/hyb-ea.gif sp3 107.3o sp3.36 23% 1.100 100  
http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/hyb-cp.gif sp3 115o sp2.37 30% 1.089 106 46
http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/hyb-ee.gif sp2 116.6o sp2.23 31% 1.076 106 45
http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/hyb-a.gif sp 180o sp(e) 50% 1.060 132 25

a. Hybrid orbitals on carbon involved in the formation of the indicated (in green) bonds with hydrogen atoms calculated from the formula: m = -1/cosα

b. Percent s character in the hybrid orbitals [(1/(m+1)) ×100]

c. Homolytic Bond Dissociation Energies (BDE). BDE’s depend to a much larger degree on the stability of the radicals formed than on the hybridization type of the bond broken (see below).

d. Acidity of the C–H bonds (the pKa values for methane and ethane are very approximate).

e. Strictly speaking, in this case the hybrid cannot be determined just from the bond angle. An angle between any two sp-type hybrids is always 180°, regardless of their specific s characters. In this case, the two hybrids made by mixing s and p orbitals are not equivalent, one makes bond to carbon, one to hydrogen.

When we say that bonds made out of hybrids containing more s character are stronger, we have to be very precise in our meaning. Bond strength are commonly measured by bond dissociation energies (BDE’s) that reflect enthalpies of homolysis (i.e. the energy required to break a bond, forming two radicals).  What counts in such considerations is the actual strength of the bond broken (that is related to the s character of the hybrid) and the stability of the radicals formed which is influenced strongly by other effects (such as hyperconjugation or resonance) that may not even be present in the molecule before homolysis.  In general, the stability of the radicals is a more important contribution to BDE’s than the hybridization effect (i.e. s character).

Similarly the s character of the orbital containing the lone electron pair will influence the stability of the anion, and therefore, the pKa value of the hydrocarbon precursors of this anion.  If the geometry of the hydrocarbon is similar to that of the anion, the more s character in the hybrid involved in making the “acidic” C-H bond, the lower the pKa value of the hydrocarbon (and the more stable the anion).  But, again caution is required in making comparisons:  the stability of the anion also strongly depends on other effects (such as inductive and resonance stabilization, ion pairing and solvation, i.e. interactions with solvent molecules). In particular, if the resonance stabilization is involved, the hybridization of the hydrocarbon and the anion derived from it are going to be quite different.

In general, very rarely all hybrids formed by an atom are exactly equal.  We may have an infinite number of combinations of mixtures.  For example, let us assume that carbon forms two sp2 hybrids (with an angle of 120°) to two identical substituents and additional two (equal to each other) spx hybrid orbitals that are going to be used to form two additional bonds, as shown in A below. How can we find x? It is very simple, just a little fraction arithmetic! Each of the two sp2 hybrids contains 1/3 of s (total of 2/3 s). The remaining 1/3 s must be divided between the two identical spx hybrids; i.e. 1/6 s per orbital. To make the “full” hybrid the “missing” 5/6 of the hybrid must be composed of p. So, the ratio of p/s = 5 (or x = 5) and we have our answer (sp5). If you do not believe it, you may check the math doing the balance for the p orbitals.   Here, how it goes: the two sp2 hybrids contain 2/3 of p each (total 4/3 p).  Since all three p orbitals participate in hybridization, we have 3 – 4/3 = 5/3 of p left to be used in the two spx orbitals. That leaves (5/3)/2, or 5/6 of p per hybrid; exactly the same answer we got doing the balance for the s orbital.

http://courses.chem.psu.edu/chem210/mol-gallery/hybridization/mixed-hybrids.gif

Now we can look at the hybridization of nitrogen in ammonia (B) or oxygen in water (C) with more precision. Since each of these central atoms has four electron pairs around, and no π bonds (that information is available from a simple Lewis structure) we may say that oxygen and nitrogen are sp3 hybridized. We mean that each atom uses three p’s and one s atomic orbitals to make four hybrids. But none of these hybrids is an sp3 hybrid! The angle between hydrogens in : NH3 is 107°  Since all the hydrogens are identical, we can calculate that the hybrids used to make N-H bonds are sp3.42 (cos(107°) = –1/m or m = 3.42); i.e they have 1/(1+3.42) = 22.6% s character each). That leaves 32.2% s character for the hybrid containing the lone pair, or the lone pair is an sp2.10 hybrid (the p character in the lone-pair hybrid must be 100 –-32.2 = 67.8%, or m/(m+1) = 0.678 from where m = 2.10). For a moment, forget the arithmetic! The point is that the lone pair hybrid has increased its s character in comparison to what it would be in the pure sp3 hybrid (32.2% vs 25% s) stabilizing the lone pair (more s character more stabilization). And the lone pair needs more stabilization: these are, by definition, unshared electrons! The price to be paid is the decrease in the H-N-H angle from the ideal tetrahedral 109.5o to 107o and the increased repulsion between the bonding pairs. The observed situation is the compromise between these two trends. You may recognize this concept as being equivalent to saying that the lone pair needs “more space” than the bonding pairs. Similar situation is found in H2O. Here, the H-O-H bond is 104.5°. Now, you do the math! The O-H bonds use sp4 hybrids and the lone pairs (two here) are sp2.3, or have about 30% s character each. Still, that is better than the 25% s of the pure sp3 hybrids.