Question

(a) A vessel contains N molecules of oxygen at a certain temperature and pressure. How many molecules of sulphur dioxide can the vessel accommodate at the same temperature and pressure?
(b) Each of the two flasks contain 2.0 g of gas at the same temperature and pressure. One flask contains oxygen and the other hydrogen.
(i) Which sample contains the greater number of molecules?
(ii) If the hydrogen sample contains N molecules, how many molecules are present in oxygen sample?

Answer 1

(a) Under the conditions of same temperature, pressure and volume (as the vessel is same), the number of moles of oxygen and sulphur dioxide will be equal, as per Avogadro's law.
Also,
Number of molecules of oxygen gas = Number of molecules of sulphur dioxide gas
If n₁ is the number of moles of oxygen gas and n₂ is the number of moles of sulphur dioxide gas, then
n₁(N_A) = n₂(N_A),
where N_A = Avogadro's number
So, number of molecules of both the gases will also be equal. Hence, there will be N molecules of sulphur dioxide in the vessel.

(b)
(i) Number of molecules in 2 g of oxygen = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{oxygen}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{oxygen}}\times \mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{Number}=\frac{2}{16}\times 6.023\times {10}^{23}$
Number of molecules in 2 g of hydrogen = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{hydrogen}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{hydrogen}}\times \mathrm{Avogadro}\text{'}\mathrm{s}\mathrm{Number}=\frac{2}{1}\times 6.023\times {10}^{23}$
Hence, the vessel containing hydrogen gas has greater number of molecules.

(ii) As evident from the above solution, if hydrogen sample contains N molecules, then oxygen sample contains $\frac{N}{16}$ molecules.