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When dealing with the composition of gases like air, understanding volume ratio is crucial. In this exercise, the volume ratio of \(\text{N}_2\) to \(\text{O}_2\) is given as 4:1. This implies that for every 4 volumes of nitrogen gas, there is 1 volume of oxygen gas. Volume ratio helps us understand the proportion of each gas in a mixture. This ratio is crucial for calculating other properties of the mixture, such as its average molecular mass.

Calculating molecular mass is the next important step. The molecular mass of a compound is found by adding together the atomic masses of all the atoms in its molecules. For nitrogen gas \(\text{N}_2\), each nitrogen atom has a mass of 14. Therefore, the molecular mass of \(\text{N}_2\) is 28 (14 + 14). For oxygen gas \(\text{O}_2\), each oxygen atom has a mass of 16. Consequently, the molecular mass of \(\text{O}_2\) is 32 (16 + 16). These molecular masses are necessary for further calculations, such as finding the weighted average molecular mass.

To find the average molecular mass of the air mixture, we use the concept of the weighted average. This accounts for the different proportions of nitrogen and oxygen in the air. The formula for the weighted average molecular mass, given the 4:1 ratio, is:
\[ \text{Average Molecular Mass} = \frac{(4 \times 28) + (1 \times 32)}{4 + 1} \]
Using this formula:
- Multiply the molecular mass of \(\text{N}_2\) by 4 (since there are 4 volumes of \(\text{N}_2\)): \(4 \times 28 = 112\)
- Multiply the molecular mass of \(\text{O}_2\) by 1 (since there is 1 volume of \(\text{O}_2\)): \(1 \times 32 = 32\)
- Add these results: \(112 + 32 = 144\)
- Divide by the total number of volumes (5): \( \frac{144}{5} = 28.8 \)
Thus, the average molecular mass of the air mixture is 28.8.

Finally, let's understand vapour density. Vapour density is defined as half of the molecular mass. Knowing the average molecular mass of the air mixture (which we calculated to be 28.8), we can find the vapour density:
\[\text{Vapour Density} = \frac{28.8}{2} = 14.4 \]
Therefore, the vapour density of air is 14.4. This property is useful in various scientific and industrial applications, including calculating the behaviour of air in different conditions.