Dalton's Law of Partial Pressure

While studying the properties of air, John Dalton observed that the total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.  The  pressure exerted by a particular component of a mixture of gases is called the partial pressure of that gas, and Dalton's observation is known as Dalton's law of partial pressures.

If we let P_t be the total pressure of the mixture, and P₁, P₂, P₃, etc, be the partial pressures of the gases in a mixture, we can write Dalton's law in the following manner:

P_t = P₁ + P₂ + P₃ + ...

Partial Pressure and Mole Fractions

Since each gas in a mixture behaves independently, we can relate the amount of a given gas in a mixture to its partial pressure.  For an ideal gas P = nRT/V, so we can write

P1     n1RT/V        P1    n1 
--- = -------   or  --- = --- = X1
Pt     ntRT/V        Pt    nt 

If we rearrange the equation above we get:

P₁ =X₁P_t

The partial pressure of gas 1, P₁ is equal to its mole fraction, X₁ times the total pressure, P_t.