Question

A container has a volume of `14 L` and holds `9 mol` of gas. If the container is compressed such that its new volume is `4 L`, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Answer 1

`PV = nRT`

Rewriting, we can say

`\frac{n}V = \frac{P}{RT}`

According to your problem, the right side is constant, since the temperature and pressure - both remain constant during the entire process. This means that `n/V` is constant during the whole process. Again, this means

`\frac{n_{i nitial}}{V_{i nitial}}= \frac{n_{fi nal}}{V_{fi nal}}`

`\Rightarrow n_{fi nal} = \frac{V_{fi nal}}{V_{i nitial}} n_{i nitial} = \frac{18}7 \text{mol}`

The number of moles that have escaped is given by `n_{f i nal} - n_{i nitial}= \frac{45}7 \text{mol}`.