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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 Pt 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:

Pt = 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 

The ratio n1/nt is called the mole fraction of gas 1, which we denote X1.

If we rearrange the equation above we get:

P1 =X1Pt

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

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