Ideal Gas Example Problem: Partial Pressure

In any mixture of gases, each component gas exerts a partial pressure that contributes to the total pressure. At ordinary temperatures and pressure, you can apply the ideal gas law to calculate the partial pressure of each gas.

What Is Partial Pressure?

Let's start by reviewing the concept of partial pressure. In a mixture of gases, the partial pressure of each gas is the pressure that gas would exert if it was the only one occupying that volume of space. If you add up the partial pressure of each gas in a mixture, the value will be the total pressure of the gas. The law used to find partial pressure assumes the temperature of the system is constant and the gas behaves as an ideal gas, following the ideal gas law:

PV = nRT

where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

The total pressure is then the sum of all the partial pressures of component gases. For n components of a gas:

P_total = P₁ + P₂ + P₃ +... P_n

When written this way, this variation of the Ideal Gas Law is called Dalton's Law of Partial Pressures. Moving around terms, the law can be rewritten to relate moles of gas and total pressure to partial pressure:

P_x = P_total (n / n_total)

Partial Pressure Question

A balloon contains 0.1 moles of oxygen and 0.4 moles of nitrogen. If the balloon is at standard temperature and pressure, what is the partial pressure of the nitrogen?

Solution

Partial pressure is found by Dalton's Law:

P_x = P_Total ( n_x / n_Total )

where
P_x = partial pressure of gas x
P_Total = total pressure of all gases
n_x = number of moles of gas x
n_Total = number of moles of all gases

Step 1

Find P_Total

Although the problem does not explicitly state the pressure, it does tell you the balloon is at standard temperature and pressure. Standard pressure is 1 atm.

Step 2

Add up the number of moles of the component gases to find n_Total

n_Total = n_oxygen + n_nitrogen
n_Total = 0.1 mol + 0.4 mol
n_Total = 0.5 mol

Step 3

Now you have all the information needed to plug the values into the equation and solve for P_nitrogen

P_nitrogen = P_Total ( n_nitrogen / n_Total )
P_nitrogen = 1 atm ( 0.4 mol / 0.5 mol )
P_nitrogen = 0.8 atm

Answer

The partial pressure of the nitrogen is 0.8 atm.

Helpful Tip for Performing the Partial Pressure Calculation

• Be sure to report your units correctly! Typically, when using any form of the ideal gas law, you'll be dealing with mass in moles, temperature in Kelvin, volume in liters, and pressure is in atmospheres. If you have temperatures in Celsius or Fahrenheit, convert them to Kelvin before proceeding.
• Remember real gases are not ideal gases, so although the calculation will have very little error under ordinary conditions, it won't be precisely the true value. For most situations, the error is negligible. Error increases as pressure and temperature of a gas increase because the particles are interacting with each other more often.