Boyle's Law Example Problem

Boyle's gas law states the volume of a gas is inversely proportional to the pressure of the gas when temperature is held constant. This example problem uses Boyle's law to find the volume of a gas when pressure changes.

Problem:

A balloon with a volume of 2.0 L is filled with a gas at 3 atmospheres. If the pressure is reduced to 0.5 atmospheres without a change in temperature, what would be the volume of the balloon?

Solution:

Since the temperature does not change, Boyle's law can be used. Boyle's gas law can be expressed as:

P_iV_i = P_fV_f

where
P_i = initial pressure
V_i = initial volume
P_f = final pressure
V_f = final volume

To find the final volume, solve the equation for V_f:

V_f = P_iV_i/P_f

V_i = 2.0 L
P_i = 3 atm
P_f = 0.5 atm

V_f = (2.0 L)(3 atm)/(0.5 atm)
V_f = 6 L/0.5
V_f = 12 L

Answer:

The volume of the balloon will expand to 12 L.