Question

Under the same conditions of temperature and pressure you collect 2 litres of carbon dioxide, 3 litres of chlorine, 5 litres of hydrogen, 4 litres of nitrogen and 1 litre of sulphur dioxide. In which gas sample will there be:
(a) The greatest number of molecules.
(b) The least number of molecules.
Justify your answer.

Answer 1

(a) According to Avogadro's law, at same temperature and pressure conditions, equal number of molecules of any gas occupy equal volumes.
Hence, higher the volume of a gas, larger will be the number of molecules of the gas. Therefore, five litres of hydrogen gas will have the greatest number of molecules.
Alternatively,
Number of molecules of a gas = $\frac{\mathrm{Volume}\mathrm{of}\mathrm{gas}}{\mathrm{Molar}\mathrm{volume}\mathrm{of}\mathrm{gas}}\times \mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{number}$
= $\frac{\mathrm{Volume}\mathrm{of}\mathrm{gas}\left(\mathrm{L}\right)}{22.4\mathrm{L}}\times 6.023\times {10}^{23}$

Volume of different gas	Number of molecules
2 L of CO2	$\frac{2}{22.4\mathrm{L}}\times 6.023\times {10}^{23}=0.54\times {10}^{23}$
3 L of Cl2	$\frac{3}{22.4\mathrm{L}}\times 6.023\times {10}^{23}=0.81\times {10}^{23}$
5 L of H2	$\frac{5}{22.4\mathrm{L}}\times 6.023\times {10}^{23}=1.34\times {10}^{23}$
4 L of N2	$\frac{4}{22.4\mathrm{L}}\times 6.023\times {10}^{23}=1.07\times {10}^{23}$
1 L of SO2	$\frac{1}{22.4\mathrm{L}}\times 6.023\times {10}^{23}=0.27\times {10}^{23}$

It is evident from the table that five litres of H₂ has largest number of molecules, which is 1.34$\times$10²³.

(b) As can be seen in the table above, the gas having the lowest volume will contain least number of molecules. So, one litre of SO₂ will have the least number of molecules, which is 0.26$\times$10²³.