# If 32 L of a gas at room temperature exerts a pressure of 8 kPa on its container, what pressure will the gas exert if the container's volume changes to 8 L?

Jul 11, 2016

The pressure is 32kPa.

#### Explanation:

Let's identify our known and unknown variables.

The first volume we have is $32$ L, the first pressure is $8 k P a$, and the second volume is $8 L$. Our only unknown is the second pressure.

We can obtain the answer using Boyle's Law which shows that there is an inverse relationship between pressure and volume as long as the temperature and number of moles remain constant.
We will use this equation:

All we have to do is rearrange the equation to solve for ${P}_{2}$

We do this by dividing both sides by ${V}_{2}$ in order to get ${P}_{2}$ by itself:
${P}_{2} = \frac{{P}_{1} \times {V}_{1}}{V} _ 2$

Now all we have to do is plug in the given values:
${P}_{2} = \left(32 \setminus k P a \times 8 \setminus \cancel{\text{L")/(8\cancel"L}}\right)$ = $32 k P a$