# If 16 L of a gas at room temperature exerts a pressure of 6 kPa on its container, what pressure will the gas exert if the container's volume changes to 2 L?

Mar 1, 2016

$48 k P a$

#### Explanation:

When dealing with pressure-volume questions, it is important to remember that the two are inversely related.

With this in mind, if the volume of the container is reduced (like in the problem when it is changed from $16 L$to $2 L$) the pressure of the system must increase (granted there is no exchange of mass or change in temperature in the system).

To solve this problem, you can use an adaptation of the ideal gas equation:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

Where ${P}_{1}$ and ${V}_{1}$ are the initial pressure and volume of the system, and ${P}_{2}$ and ${V}_{2}$ are the final pressure and volume of the system.

From here, just plug in:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

$\frac{{P}_{1} {V}_{1}}{V} _ 2 = {P}_{2}$

$\frac{6 k P a \cdot 16 L}{2 L} = {P}_{2}$

${P}_{2} = 6 k P a \cdot 8$

${P}_{2} = 48 k P a$