Boyle’s Law
Boyle’s Law can be used to compare changing conditions for a gas. We use \begin{align*}P_1\end{align*}
\begin{align*}P_1 \times V_1=P_2 \times V_2\end{align*}
This equation can be used to calculate any one of the four quantities if the other three are known.
Sample Problem: Boyle’s Law
A sample of oxygen gas has a volume of 425 mL when the pressure is equal to 387 kPa. The gas is allowed to expand into a 1.75 L container. Calculate the new pressure of the gas.
Step 1: List the known quantities and plan the problem.
Known

\begin{align*} P_1=387 \ \text{kPa}\end{align*}
P1=387 kPa 
\begin{align*}V_1=425 \ \text{mL}\end{align*}
V1=425 mL 
\begin{align*}V_2=1.75 \ \text{L}=1750 \ \text{mL}\end{align*}
V2=1.75 L=1750 mL
Unknown

\begin{align*}P_2=? \ \text{kPa}\end{align*}
P2=? kPa
Use Boyle’s Law to solve for the unknown pressure \begin{align*}(P_2)\end{align*}
Step 2: Solve.
First, rearrange the equation algebraically to solve for \begin{align*}P_2\end{align*}
\begin{align*}P_2=\frac{P_1 \times V_1}{V_2}\end{align*}
Now substitute the known quantities into the equation and solve.
\begin{align*}P_2=\frac{387 \text{ kPa} \times 425 \text{ mL}}{1750 \text{ mL}}=94.0 \text{ kPa}\end{align*}
Step 3: Think about your result.
The volume has increased to slightly over 4 times its original value and so the pressure is decreased by about \begin{align*}\frac{1}{4}{th}\end{align*}
Summary
 The volume of a gas is inversely proportional to pressure.