Combined Gas Law

$\genfrac{}{}{0.1ex}{}{P_1{V}_1}{T_1}=\genfrac{}{}{0.1ex}{}{P_2{V}_2}{T_2}$

Math Skills

The Combined Gas Law

A cylinder that contains air at a pressure of 100 kPa has a volume of 0.75 L. The pressure is increased to 300 kPa. The temperature does not change. Find the new volume of air.

1. Read and Understand

   What information are you given?

   $P1=100kPa P2=300kPa V1=0.75L$

2. Plan and Solve

   What unknown are you trying to calculate?

   

   What expression can you use?

   $\genfrac{}{}{0.1ex}{}{P_1{V}_1}{T_1}=\genfrac{}{}{0.1ex}{}{P_2{V}_2}{T_2}$

   Cancel out the variable that does not change and rearrange the expression to solve for V₂.

   $P_1{V}_1=P_2{V}_2{V}_2=\genfrac{}{}{0.1ex}{}{P_1{V}_1}{P_2}$

   Replace each variable with its known value.

   $V_2=100k\cancel{P}a\times \frac{0.75 L}{300k\cancel{p}a}=0.25L$

3. Look Back and Check

   Is your answer reasonable?

   Volume should decrease as pressure increases. The pressure tripled from 100 kPa to 300 kPa. The answer, 0.25 L, is one third the original volume, 0.75 L.