# A gas has a volume of 300 mL at 300 mm Hg. What will its volume be if the pressure is changed to 500 mm Hg?

May 30, 2016

${V}_{2} = 180 m L$

#### Explanation:

For this question, we will issue that the change happens at constant temperature and that the gas behaves ideally.

Thus, we can use the ideal gas law: $P V = n R T$

Since the change is occurring at constant temperature and number of mole, we can modify the ideal gas law as follows:

$P V = k$ where, $k = n R T$.

For position 1: we have ${P}_{1}$ and ${V}_{1}$.

For position 2: we will have ${P}_{2}$ and ${V}_{2}$.

Since $P V = k$ we can write ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

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

$\implies {V}_{2} = \frac{300 \cancel{m m H g} \times 300 m L}{500 \cancel{m m H g}} = 180 m L$