Question

If `2/5` `L` of a gas at room temperature exerts a pressure of `15` `kPa` on its container, what pressure will the gas exert if the container's volume changes to `7/3` `L`?

Answer 1

Before starting the calculation, it's worth thinking about what we expect the answer to be. We have the same amount of gas, in a container that is getting a lot bigger: from `2/5` (40%) of a liter to `7/3` (233%) of a liter.

With the same amount of gas in a larger container, we expect the pressure to be lower than the initial `15` `kPa`.

There are a number of possible approaches to doing the calculation. My own favourite way is to use the Combined Gas Law and then remove the one that we're not using:

`(P_1V_1)/T_1 = (P_2V_2)/T_2`

In this case, we are not changing temperatures, so we can remove that:

`P_1V_1 = P_2V_2`

Rearranging to make `P_2` the subject:

`P_2 = (P_1V_1)/V_2`

Now we can substitute in the values from the question:

`P_2 = (15 xx (2/5))/(7/3) = 2.6` `kPa`