# A gas a volume of 2.50 L at a pressure of of 350.0 kPa. If the temperature remains constant, what volume would the gas occupy at 1750 kPa?

May 2, 2016

The new volume of the gas is $\text{0.500 L}$.

#### Explanation:

This is an example of Boyle's law, which states that at constant temperature and mass, the volume of a gas will vary inversely with the pressure. The equation to use for solving your question is ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$, where ${P}_{1}$ is initial pressure, ${V}_{1}$ is initial volume, ${P}_{2}$ is the final pressure, and $V$ is the final volume.

Known
${P}_{1} = \text{350.0 kPa}$
${V}_{1} = \text{2.50 L}$
${P}_{2} = \text{1750 kPa}$

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=(350.0cancel"kPa"xx2.50"L")/(1750 cancel"kPa")="0.500 L"