Unless they chemically react with each other, the individual gases in a mixture of gases do not affect each other’s pressure. Each individual gas in a mixture exerts the same pressure that it would exert if it were present alone in the container (
[link] ). The pressure exerted by each individual gas in a mixture is called its
partial pressure . This observation is summarized by
Dalton’s law of partial pressures :
The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the component gases :
In the equation
P
Total is the total pressure of a mixture of gases,
P
A is the partial pressure of gas A;
P
B is the partial pressure of gas B;
P
C is the partial pressure of gas C; and so on.
The partial pressure of gas A is related to the total pressure of the gas mixture via its
mole fraction (
X ) , a unit of concentration defined as the number of moles of a component of a solution divided by the total number of moles of all components:
where
P
A ,
X
A , and
n
A are the partial pressure, mole fraction, and number of moles of gas A, respectively, and
n
Total is the number of moles of all components in the mixture.
The pressure of a mixture of gases
A 10.0-L vessel contains 2.50
10
−3 mol of H
2 , 1.00
10
−3 mol of He, and 3.00
10
−4 mol of Ne at 35 °C.
(a) What are the partial pressures of each of the gases?
(b) What is the total pressure in atmospheres?
Solution
The gases behave independently, so the partial pressure of each gas can be determined from the ideal gas equation, using
:
The total pressure is given by the sum of the partial pressures:
Check your learning
A 5.73-L flask at 25 °C contains 0.0388 mol of N
2 , 0.147 mol of CO, and 0.0803 mol of H
2 . What is the total pressure in the flask in atmospheres?