# A sample of a gas has a volume of of 2.0 liters at a pressure of 1.0 atmosphere. When the volume increases to 40 liters, at constant temperature, what will the pressure be?

Dec 16, 2016

The final pressure will be 0.05 atm.

#### Explanation:

This is an example of Boyle's law which states that the volume of a gas varies inversely with pressure, when mass and temperature are kept constant.

Equation
${V}_{1} {P}_{1} = {V}_{2} {P}_{2}$, where $V$ is volume and $P$ is pressure.

Known
${V}_{1} = \text{2.0 L}$
${P}_{1} = \text{1.0 atm}$
${V}_{2} = \text{40 L}$

Unknown
${P}_{2}$

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

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

P_2=((2.0cancel"L")xx(1.0"atm"))/(40cancel"L")="0.05 atm"