Dalton's law of partial Pressures

Dalton's law of partial Pressures

When two or more gases, which do not react chemically, are mixed together in a vessel, the total pressure of the mixture is given by Dalton's law of partial pressures which states that, 

"At constant temperature, the total pressure exerted by the gaseous mixture is equal to the sum of the individual pressures which each gas would exert if it occupies the same volume of mixture fully by itself. Partial pressure is the measure of the pressure of an individual gas in a mixture of same volume and temperature.

Thus, if p1, p2, p3 .... are the partial pressures of the various gases present in a mixture, then the total pressure P of the gaseous mixture is given by

P = p1 + p2 + p3 ..., provided the volume and temperature of mixture and that of the individual gases are the same.

Equation of state of a Gaseous mixture

Let a gaseous mixture consists of n_A, n_B and n_C moles of three ideal gases A, B and C respectively, subjected to constant T and V, then, according to ideal gas equation.

p_A      =       n_ART / V

p_B  =  n_B RT / V

pc      = n_c RT / V

where pA, pB, pC are the partial pressures of A,B,C gases respectively. Hence the total pressure of the mixture is given as

P       =       p_A + p_B + pc

P = n_ART/ V + n_BRT/V + n_CRT/V

PV =  (n_A + n_B + n_C) RT

This equation is known as equation of state of gaseous mixture.

Calculation of Partial Pressure

In order to calculate the pressure (p_A) of the individual component say A, in a mixture (A and B), which is equal to the partial pressure of A, according to the equation of state of gaseous mixture it is seen that,

P       =       Total pressure of the mixture

P   = (n_A + n_B) x (RT/V)

But p_A  = ( n_A /V ) RT   and   pB      = (n_B/V) x RT

The ratio is given by

p_A / P =  n_A / (n_A + n_B) . V/RT . RT/V

          x_A  =   mole fraction of A.

Or     p_A = X_AP

i.e:-   Partial pressure, p_A = mole fraction of A x total pressure. Similarly;

p_B  =  X_B P

Thus, the partial pressure of the individual component in the mixture can be calculated by the product of its mole fraction and total pressure.