Answer to Question #109319 in Physical Chemistry for DEEPAK SINGH

Question

State dalton's law of fartial pressure. Derive it's mathematical from.

Answer 1

Dalton's law states that in a mixture of non-reacting gases, the total partialpressure exerted is equal to the sum of the partial pressures of the individual gases.

Or, $P=P_1+P_2+P_3+.....+P_n$

Where $P$ is total pressure and $P_1,P_2,...,P_n$ are the partial pressure of individual component of gases.

Mathematical derivation:

By moles conservation,

$n=n_1+n_2+...+n_n$ ......(1)

And $PV=nRT,$

$P_1V=n_1RT$ and similarly for all others.

$n=\frac{PV}{RT};n_1=\frac{P_1V}{RT};...;n_n=\frac{P_nV}{RT}$

Substituting these values in equation (1),

$\frac{PV}{RT}=\frac{P_1V}{RT}+\frac{P_2V}{RT}+......+\frac{P_nV}{RT}$

$\implies P=P_1+P_2+...+P_n$