# balton’s Law of Partial Pressures

This law describes the relation between the pressure of the mixture of non-reacting gases enclosed in a vessel to their individual pressures. The law was given by John Dalton in 1807. It states:

At constant temperature, the pressure exerted by a mixture of two or more non-reacting gases enclosed in a definite volume, is equal to the sum of the individual pressures which each gas would exert if present alone in the same volume at the same temperature.

The individual pressures of gases are known as partial pressures.

If P is the total pressure of the mixture of non-reacting gases at temperature T and volume V, and P1, P2, P3, …… represent the partial pressures of the gases, then

P = P1 + P2 + P3 + …… (T, V are constant)

The law can be illustrated by considering the following example:

Suppose we have three containers of capacity litre each; one containing x moles of nitrogen, the other y moles of oxygen and the third having a mixture of x moles of nitrogen and y moles oxygen. All the three containers, are kept at the same temperature.

Now, if the manometer, attached to first container shows a pressure P 1 and that attached to second container shows a pressure P2. Then the pressure in the third container is P1 +P2.

Utility of Dalton’s law. This law is useful in calculating the pressure of the gas collected by the displacement of water. The gas being collected over water also contains water vapours. The observed pressure of the moist gas is equal to the sum of the pressure of the dry gas and the pressure of the water vapours. The pressure of the water vapours is constant at a given temperature and is known as aqueous tension at that temperature.

Thus,

P observed = P gas + aqueous tension

P gas = P observed – aqueous tension

Aqueous tension of water at different temperatures is given in Table 15.2.

Table 15.2. Aqueous Tension (Vapour Pressure) of Water as a Function of Temperature

Temperature                Pressure           Temperature                Pressure

(K)                               x 102 kPa                  (K)                 x 101 I kPa

273.15                         0.0060                         295.15             0.0260

283.15                         0.0121                         297.15             0.0295

288.15                         0.0168                         299.15            0.0331

291.15                         0.0204                         301.15             0.0372

293.15                         0.0230                         303.15            0.0418

Partial Pressure in Terms of Mol Fraction

Mol fraction is one of the method of expressing concentration of a component in a mixture. Mole fraction is the ratio of the number of mol of the component to the total number of moles. If n 1 is the number of moles of any component present in a mixture and n is the total number of moles of all the components in a mixture, then, the mole fraction (x1) of the component is given as x1 = n1 / n

Now consider a mixture of two gases A and B with p A and p8 as their respective partial pressures in a vessel of volume V

PA = nART / v ; PB = nBRT

Total pressure of the mixture

P Total = P A + PB

P Total = PA + PB = (n A + n B) RTN / V

Now,                       PA / P Total = n A / ( n A + n B) x A

or                                        PA = x A  x P Total

Similarly                          PB= x B x P total

Thus, partial pressure of a gas in a mixture is equal to the product of its mol fraction and total pressure of the mixture.