Question

Samples of the gases O₂, N₂, CO₂ and CO under the same conditions of temperature and pressure contain the same number of molecules represented by X. The molecules of oxygen [O₂], occupy V litres and have a mass of 8 g. Under the same conditions of temperature and pressure:
(a) What is the volume occupied by:
(i) X molecules of N₂?
(ii) 3X molecules of CO? [C = 12, N = 14, O = 16]
(b) What is the mass of CO₂ in g?
(c) In answering the above questions, which law have you used?

Answer 1

(a)
(i) At same temperature and pressure conditions, equal number of molecules contain equal volumes. Hence, X molecules of N₂ occupy V litres.

(ii) For 3X molecules of CO, number of moles is three times the number of moles of oxygen gas. Hence, volume occupied by 3X molecules of CO is also three times the volume occupied by oxygen gas at same temperature and pressure conditions, which is 3V litres.

(b) Number of moles of oxygen in 8 g = $\frac{8}{32}=0.25\mathrm{mol}$
Number of molecules of oxygen = (0.25 mol $\times$ 6.023 $\times$ 10²³) ......(i)
As number of molecules of oxygen and carbon dioxide is same.
Number of molecules of carbon dioxide = (0.25 mol $\times$ 6.023 $\times$ 10²³)
Number of molecules of carbon dioxide = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{carbon}\mathrm{dioxide}}{\mathrm{Molecular}\mathrm{weight}\mathrm{of}\mathrm{carbon}\mathrm{dioxide}}\times 6.023\times {10}^{23}$
= $\frac{\mathrm{Mass}\mathrm{of}\mathrm{Carbon}\mathrm{dioxide}}{44}\times 6.023\times {10}^{23}$ ........(ii)
Equating equations (i) and (ii), we get:
0.25 mol $\times$ 6.023 $\times$ 10²³ = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{Carbon}\mathrm{dioxide}}{44}\times 6.023\times {10}^{23}$
Mass of carbon dioxide = 11 g

(c) Above questions were answered using Avogadro's law, which states that under same temperature and pressure conditions same number of molecules occupy same volume.