# A sample of oxygen gas occupies a volume of 250. mL at 100 kPa pressure. What volume will it occupy at 200 kPa pressure?

May 2, 2016

The new volume of $\text{O"_2}$ is $\text{125 mL}$.

#### Explanation:

This is an example of Boyle's law, which states that the volume of a gas varies inversely with pressure, as long as temperature and amount are kept constant. The equation to use for this law is ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$, where ${P}_{1}$ is the initial pressure, ${V}_{1}$ is the initial volume, ${P}_{2}$ is the final pressure, and ${V}_{2}$ is the final volume.

Known
${P}_{1} = \text{100 kPa O"_2}$
${V}_{1} = \text{250 mL O"_2}$
${P}_{2} = \text{200 kPa O"_2}$

Unknown
${V}_{2} = \text{???}$

Solution
Rearrange the equation to isolate ${V}_{2}$. Substitute the known values into the equation and solve.

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

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

V_2=(100 cancel"kPa"xx250 "mL")/(200 cancel"kPa")="125 mL O"_2"