# The volume of a gas is 250 mL at 340.0 kPa pressure. With the temperature remaining constant what will the volume be when the pressure is reduced to 500.0 kPa?

Jul 3, 2018

The final volume will be $\text{170 mL}$.

#### Explanation:

According to the data in the question, the pressure is increased from $\text{340.0 kPa}$ to $\text{500.0 kPa}$.

This is an example of the pressure-volume law, or Boyle's law, which states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant. This means that if the pressure increases, the volume decreases and vice versa. The equation for this law is:

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

Known

${P}_{1} = \text{340.0 kPa}$

${V}_{1} = \text{250 mL}$

${P}_{2} = \text{500.0 kPa}$

Unknown

${V}_{2}$

Solution

Rearrange the equation to isolate ${V}_{2}$. Plug in the known values and solve.

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

V_2=(340.0color(red)cancel(color(black)("kPa"))xx"250 mL")/(500.0color(red)cancel(color(black)("kPa")))="170 mL"