Atoms and Molecules : Density

 

Molecular mass from vapour density                                                                                                                      

The density of a gas relative to that of hydrogen at the same temperature and pressure is known as the vapour density or the hydrogen density of the gas.

 

Thus, the vapour density of a gas = \frac { Density\quad of\quad the\quad gas\quad at\quad a\quad given\quad p\quad an\quad T }{ Density\quad of\quad hydrogen\quad at\quad the\quad same\quad P\quad and\quad T }

                                    = \frac { Mass\quad of\quad given\quad volume\quad of\quad the\quad gas\quad at\quad a\quad given\quad P\quad and\quad T }{ Mass\quad of\quad the\quad same\quad volume\quad of\quad hydrogen\quad at\quad the\quad same\quad P\quad and\quad T }

                                    = \frac { Mass\quad of\quad 22.4\quad L\quad of\quad the\quad gas\quad at\quad STP }{ Mass\quad of\quad 22.4\quad L\quad of\quad hydrogen\quad at\quad STP }

                                    = \frac { 1\quad gram-molecules\quad mass\quad of\quad the\quad gas }{ 2 }

∴ the relative molecular mass of a gas = 2 x vapour density.

 

The vapour densities of gases can be determined experimentally. So can those of many other substance like methanol, ethanol and acetone, which can be completely volatilized. Thus, it is easy to calculate the relative molecular masses of such substances.

 

Substance Vapour density Relative molecular mass (= 2 x vapour density) Molecular formula
Nitrogen 14 28 N2
Oxygen 16 32 O2
Chlorine 35.5 71 Cl2
Methane 8 16 CH4
Ethane 15 30 C2H6
Carbon dioxide 22 44 CO2
Methanol 16 32 CH3OH
Ethanol 23 46 C2H5OH
Acetone 29 58 (CH3)2CO

 

Atomicity

The atomicity of a gaseous element can be easily calculated if we know its vapour density and atomic mass.

                                    Atomicity = \frac { Molecular\quad Mass }{ Atomic\quad Mass } =\frac { 2\quad \times \quad vapour\quad density }{ atomic\quad mass } .

For example, the vapour density of nitrogen is 14 and so its molecular mass = 2 x 14=28

As the atomic mass of nitrogen is 14, its atomicity = \frac { 28 }{ 14 } =2.

Hence the molecular formula N2.

 

Percentage Composition

The percentage composition of a compound in terms of the different elements constituting it can be easily calculated if we know the molecular or the empirical formula of the compound and the atomic masses of its constituents.

 

Illustration 6:         What is the percentage of Ca is CaCO3? (Ca = 40, C = 12, O =16)

Solution:                   The relative molecular mass of CaCO3 = 40 + 12 + 3 x 16 = 100.

                                    100 g of CaCO3 contain 40 g of Ca.

                                    ∴ the percentage of Ca in CaCO3 = 40.

 

Exercise 10: Calculate the percentages of H and O in H2O. (H = 1, O = 16)

Ans.    11.11 % of H,  88.89 % of O.

 

Exercise 11:  Calculate the percentage of Cu and water of crystallisation in blue vitriol CuSO4 . 5H2O).

                        (Cu = 63.5, S = 32, O = 16, H = 1)

Ans.    25.45 % of Cu, 76.07 % of H2O

 

Exercise 12: Calculate the percentage composition of ethanol (C2H5OH) in terms of all the elements present in the compound.

Ans.    52.17 % of C, 13.04 % of H,  34.78 % of O

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Atoms and Molecules : Percentage Composition