# Dalton’s Law of Partial Pressure | Explanation and Application

PARTIAL PRESSURE
Partial pressure of component gas in the mixture is defined as the pressure exerted by non-reacting gases of the mixture if it is alone occupies entire volume of container under identical condition of temperature.

DALTON’S LAW OF PARTIAL PRESSURE
John Dalton in 1801 formulated mathematical as well as theoretical relationship between partial pressure and total pressure exerted by non-reacting gases in the mixture which is known as Dalton’s law of partial pressure. Also, Dalton’s law of partial pressure states that "the total pressure of the mixture of non-reacting gases is the sum of partial pressure of an individual component of gases under identical condition of temperature (constant temperature)".

Let Pa, Pb and Pc be the partial pressure of non-reacting gases of A, B, and C respectively. Let ‘P’ be the total pressure of the mixture of non-reacting gases A,B and C.Then,
P=  Pa+Pb + Pc

EXPLANATAION
Let na, nb and nc be the no. of moles of non-reacting gases A, B, and C respectively. So,
n= na + nb + nc -------------(i)

Again, we have ideal gas equation
PV = nRT
P= n RT / V  -----------(ii)
Where ‘P’ is total pressure and ‘V’ is total volume of the mixture.

So, partial pressure of A,B and C
Pa= na RT / V  --------(iii)
P= nb RT / V   ---------(iv)
P= nc RT / V   ---------(v)

Pa +Pb + P= (na RT / V T) + (nb RT / V) + (nc RT / V)
= RT (na+ nb+ nc) / V
= n RT / V  [From equation i]
P =  P+ Pb + Pc

Again, for gas A,
P= na  RT / V
= na * P/n  [ P=nRT/V i.e. P/n = RT/ V]
= (na/n) * P -------------(vi)

Similarly,
Pb= (nb/n) * P -----------------(vii)
PC= (nC/n) * P ----------------(viii)

So mathematically, partial pressure of gas is also defined as the product of mole fraction and total pressure.

Application of Dalton’s Law of partial pressure

1. Dalton’s law of partial pressure is used to calculate pressure of dry gas when gas is collected over water. When gas is collected over water, the gas also contains water vapour due to evaporation. So, the pressure exerted by dry air and pressure exerted by water vapour is known as aqueos tension. i.e; Pmoist = Pdry + f (aqueous tension)
2. It is used to calculate an equilibrium constant in terms of the partial pressure of the gas.
3. It is applicable during steam distillation.

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