Avogadro's gas law states the volume of a gas is proportional to the number of moles of gas present when temperature and pressure are held constant. This example problem demonstrates how to use Avogadro's law to determine the volume of a gas when more gas is added to the system.
Problem:
A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas?
Solution:
Avogadro's law can be expressed by the formula:
Vi/ni = Vf/nf
where
Vi = initial volume
ni = initial number of moles
Vf = final volume
nf = final number of moles
For this example, Vi = 6.0 L and ni = 0.5 moles.
When 0.25 moles are added
nf = ni + 0.25 moles
nf = 0.5 moles = 0.25 moles
nf = 0.75 moles
The only variable remaining is the final volume.
Vi/ni = Vf/nf
Solve for Vf
Vf = Vinf/ni
Vf = (6.0 L x 0.75 moles)/0.5 moles
Vf = 4.5 L/0.5 Vf = 9 L
Check to see if the answer makes sense. You would expect the volume to increase if more gas is added. Is the final volume is greater than the initial volume? Yes. This check is useful since it is easy to put the initial number of moles in the numerator and the final number of moles in the denominator. If this happened, the final volume answer would be smaller than the initial volume. Answer:
The final volume of the gas is 9.0 L.
