Atoms and Molecules : Moles

 

The Mole Concept                                                                                                                                                                

A chemical change involves atoms, molecules, ions and electrons. We will realise that depicting a chemical change on the basis of the number of particles (atoms, molecules, ions, electrons or any other elementary particles) is easier and at the same time of greater significance than doing so on the basis of their masses.

H2(g)  +   Cl2(g) \longrightarrow 2HCl(g)

2 atoms  2 atoms   2 molecules

Ag+(aq)  +   Cl– \longrightarrow Ag+Cl– (s) or AgCl

1 ion  1 ion                1 formula unit

Let us consider the first reaction in a little greater detail.

H2(g)               +        Cl2(g)  \longrightarrow           2HCl (g)

1 molecules               1 molecule           2 molecules

2 atoms                        2 atoms                 2 molecules

1 atom                          1 atom                   1 molecule

1 x N atoms               1 x N atoms          1 x N molecules

 

Since one atom of hydrogen reacts with one atom of chlorine to give one molecule of hydrogen chloride, one may say that, in terms of mass, 1 gram-atom of chlorine (35.5g) to give 1 gram-molecule of hydrogen chloride (36.5 g).

Thus, 1 g (i.e., 1 gram-atom) of hydrogen will contain the same number of atoms as 35.5 g (i.e., 1 gram-atom) of hydrogen will contain the same number of atoms as 35.5 g (1 gram-molecule) of hydrogen chloride.

Atomic and molecular masses are measured with respect to 12C, which is considered to have a mass of exactly 12. So, the number of atoms in 1 gram-atomic mass of element and that of molecules in 1 gram-molecular mass of a substance must be the same as the atoms in exactly 12 g of 12C. An assemblage of this number (N) of particles is known as a mole (mol when used as a unit), which may be defined as follows.

“A mole is the amount of a substance that contains the same number of particles – atoms, molecules, ions, electrons or any other elementary particles – as the number of atoms is exactly 12 g of carbon – 12.”

This number of particles (6.022 x 1023), previously called the Avogadro number, is of great fundamental significance. Nowadays, the term ‘Avogadro constant’ is preferred, which is simply the Avogadro number suffixed by the unit of mol–1.

Gram atomic mass and gram atom

So, the gram-atomic mass or the gram-atom or a mole of an element is definated as the mass in grams of the same number of atoms as contained in exactly 12 g of 12C. It is equal to the relative atomic mass expressed in grams.

We can easily arrive at the following important relationships.

1. 1 mole of atom of an element

= number of atoms in 1 gram-atom of the element

= 6.022 x 1023 atoms.

2. (a) The absolute mass of 1 atoms of an element

= \frac { gram-atomic\quad mass }{ 6.022\times { 10 }^{ 23 } } \quad g

= \frac { gram-atomic\quad mass }{ 6.022\times { 10 }^{ 23 } } \times { 10 }^{ -3 }\quad kg

(b) The absolute mass of 1 atom of an element

= relative atomic mass x 1.66 x 10-24 g.

3. In a given mass of element,

(a) the number of gram-atoms (mole) = \frac { mass\quad of\quad the\quad an\quad element }{ gram-atomic\quad mass } and,

(b) the total number of atoms = \frac { mass\quad of\quad the\quad element\quad in\quad gram }{ gram-atomic\quad mass } \times 6.022\times { 10 }^{ 23 }

4. No. of moles = \frac { No.\quad of\quad Particles }{ 6.022\times { 10 }^{ 23 } }

 

Illustration 2:         If you need 3.011 x 1023 atoms of Na for a chemical reactions, what is the mass of the metal required (relative atomic mass of Na = 23.0)?

Solution:                   The gram-atomic mass of Na = 23.0 g.

For 6.022 x 1023 atoms of Na, the mass of the metal required  = 23.0g

∴ for 3.011 x 1023 atoms of Na, the mass of the metal required

= \frac { 3.011\times { 10 }^{ 23 } }{ 6.022\times { 10 }^{ 23 } } \times \quad 23.0\quad g   = 11.5 gm

 

Exercise 1:    What masses of the following elements will contain 6.022 x 1023 atoms each?

                        (a) Hydrogen                       (b) Sodium

                        (c) Chlorine                         (d) Copper

Ans.             (a)       1 gm  

                       (b)       23 gm

                       (c)       35.5 gm

                       (d)       63.5 gms

Exercise 2:    Calculate the absolute masses of 1 atom of H, N, O and Na

Ans.    1.67 x 10-27 kg , 2.32 x 10 – 26 kg, 2.65 x 10 – 26 , 3.81 x 10 – 26

Exercise 3:    How many gram-atoms are there in 106.5g of chlorine (relative atomic mass of Cl =35.5)?

Ans.    3

Exercise 4:    How many atoms of Na are present in 46.0 g of metal (Ar of Na = 23.0)?

Ans.    1.2 x 1024

 

Gram  Molecular Mass (GMM)

“The gram-molecular mass or the mole of a substance is defined as the mass in grams of the same number of molecules or formula units of the substance as the number of atoms contained in exactly 12 g of 12C”. It is equal to the relative molecular mass (Mr) expressed in grams.

As we have said earlier, the formula mass of a substance like an ionic solid or an associated liquid is considered as the molecular mass for purposes of calculation.

The following important relationships may be easily derived.

1. 1 mole of molecules of a substance

= number of molecules in 1 gram-mole of the substance

= 6.022 x 1023 molecules

2. The absolute mass of 1 molecule of a substance

= \frac { gram-molecular\quad mass\quad of\quad the\quad substance }{ 6.022\times { 10 }^{ 23 } } (in grams)

= \frac { gram-molecular\quad mass\quad of\quad the\quad substance }{ 6.022\times { 10 }^{ 23 } } x 10-3 (in kilograms)

3. In a given mass of a substance,

(a) the number of gram-moles         = \frac { mass\quad of\quad the\quad substance\quad in\quad gram }{ gram-molecular\quad mass }

(b) the total number of molecules  = the number of gram-moles x 6.022 x 1023

= \frac { mass\quad of\quad the\quad substance\quad in\quad gram }{ gram-molecular\quad mass }  x 6.022 x 1023

(c) the number of atoms of a given element constituting the substance

= the number of gram-moles of the substance x the number of atoms of the element in 1 molecule of the substance x 6.022 x 1023

(d) the total number of atoms= the number of gram-moles of the substance x the total number of atoms in a molecule of the substance x 6.022 x 1023

 

Illustration 3:         How many moles of HCl molecules are there in 109.5 g of HCl? Calculate the number of molecules in the sample (Ar of H = 1.0, Cl = 35.5).

Solution:                   The relative molecular mass of HCl = 1 + 35.5 = 36.5

The number of moles of HCl molecules in 109.5 g

= \frac { mass\quad of\quad HCl\quad (in\quad gram) }{ gram-molecular\quad mass } k\quad =\quad \frac { 109.5\quad g }{ 36.5\quad g } =3.  

The number of HCl molecules in 109.5 g

= number of moles x 6.022 x 1023

= 3 x 6.022 x 1023

= 18.066 x 1023

= 1.8066 x 1024

 

Illustration 4:         How many moles of water are there in 1 L of water? Assume a density of 1.0g mL-1.

Solution:                   The mass of 1 L (i.e. 1000 mL) of water

= volume x density

= 1000 mL x \frac { 1.0g }{ mL }

= 1000 g.

The gram-molecular mass of water (H2O) = 2 x 1 + 16 = 18 g.

∴ the number of moles of water 1 L = \frac { 1000g }{ 18g } =55.55. 

Exercise 5:    For 196g of pure H2SO4, calculate

                        (a) the number of moles of H2SO4

                        (b) the total number of H2SO4 molecules,

                        (c) the total number of atoms,

                        (d) the number of atoms of each kind, and

                        (e) the absolute mass of an H2SO4 molecule. (Ar of H = 1, O = 16, S =32.)

Ans5.             (a)       2

                        (b)       1.2 x 1024

                        (c)       8.43 x 1024

                        (d)       H = 2.4 x 1024  ,  S = 1.2 x 1024 ,  O = 4.81 x 1024

                        (e)       1.62 x 10-23 kg

Exercise 6:    The mass of an atom of an element is 3.986 x 10-26 kg. Find the relative atomic mass of the ement and identify it.

Ans 6.           24, Magnesium

 

Exercise 7:    How many moles of carbon atoms are there in 540g of glucose(C6H12O6)?

                        (Ar of C = 12, H = 1, O = 16.)

Ans.             18 Moles

 

A  mole of ions

Ions are formed by the loss or gain of electron(s) from or by an atom. The mass of an electron is negligible in comparison to that of an atom. So, for all practical purposes, atoms have the same mass as do the ions derived from them.

A mole of ions is defined as the assemblage of the same number of ions as the number of atoms in exactly 12g of 12C.

In other words, mole ions is an assemblage of 6.022 x 1023 ions. Its mass, called the gram-ion, is the same as the gram-atom of the element from the which it is derived.

For example, a mole of Na+ ions is a collection of 6.022 x 1023 Na+ ion, which collectively weight 23 g. Similarly, a mole of Cl– ions is an assemblage of 6.022 x 1023 Cl– ions, which collectively weight 35.5 g. 1 mole of NaCl will furnish 1 mole of Na+and Cl– ions.

NaCl  → Na+  + Cl–

 

Exercise 8:    How many moles of Ca2+ ions and Cl– ions will be furnished by 444 g of CaCl2   (Ar of Ca = 40, Cl = 35.5)?

Ans.    4 Moles of Ca+2 and 8 Moles of Cl –

 

Mole of electrons:

Electrons have negligible mass and hence they are reckoned only by number and not by mass.

6.022 x 1023 electrons constitute a mole.

As you know, all electrons carry an electrical charge.

The charge carried by 1 electron                              = 1.602 x 10–19 C.

∴ the charge carried by 1 mole of electrons         = 1.602 x 10–19 c x 6.022 x 1023 ≈ 96,500 C.

The charge carried by 1 mol of electrons, i.e., 96,500 C, is called a faraday.

 

Molar Volume

The volume occupied by one mole i.e., one gram-molecular mass of a gas, at a given temperature and pressure is called the molar volume of the gas.

As the volume of a gas is dependent on temperature and pressure, they must be mentioned along with the molar volume. If the molar volume is taken at STP, it is called the standard molar volume or the molar volume at STP.

It has been found that one gram-mole of every gas occupies 22.4 L at STP. In other words, a collection of 6.022 x 1023 molecules of any gas occupies 22.4 L at STP.

So, the standard molar volume of a gas = 22.4 L.

Thus, as the molecular mass of H2 is 2, 2 g of H2 occupies 22.4 L at STP. Similarly 2 x 16 = 32 g of O2 will also occupy 22.4 L at STP. Some more examples are given below.

 

Gas Molecular Mass Gram–molecular mass Standard Molar volume
H2 2 x 1 = 2 2 g 22.4 L
N2 2 x 14 = 28 28 g 22.4 L
O2 2 x 16 = 32 32 g 22.4 L
Cl2 2 x 35.5 = 71 71 g 22.4 L
CO2 12 + 2 x 16 = 44 44 g 22.4 L
CH4 12 + 4 x 1 = 16 16 g 22.4 L
SO2 32 + 2 x 16 = 64 64 g 22.4 L

 

Illustration 5:         What is the volume occupied by 17.75 g of Cl2 at STP?

Solution:                   The relative molar mass of Cl2 = 2 x 35.5 = 71.

The number of moles of Cl2 in 17.75 g of the gas

= \frac { the\quad mass\quad of\quad { Cl }_{ 2 }\quad gas\quad in\quad atom }{ gram-molecular\quad mass } \frac { 17.75 }{ 71\quad g } =\frac { 1 }{ 4 }

The volume of 1 mol of Cl2 at STP = 22.4 L.

∴ the volume of ¼ mol of Cl2 at STP = ¼ x 22.4 = 5.6 L.

 

Exercise 9:    What will be the mass of 1.4 L of CO2 at STP?

Ans.    2.75 gm

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Atoms and Molecules : Density