# A 300*mL volume gas at 0.500*atm in a piston, is compressed to 0.750*atm. What is the new volume?

Aug 3, 2017

${V}_{2} = 200 \cdot m L$

#### Explanation:

Old $\text{Boyle's Law}$ holds that for a given quantity of gas, at constant temperature, $P \propto \frac{1}{V}$, and thus $P V = k$, where $k$ is some constant........

And it follows that ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$, and.........

${V}_{2} = \frac{{P}_{1} {V}_{1}}{P} _ 2$, which clearly has the units of volume as required.....

Here ${V}_{2} = \frac{300 \cdot m L \times 0.500 \cdot a t m}{0.750 \cdot a t m}$

$= 200 \cdot m L$, volume is reduced as expected..........