The partial pressures of individual gases can be written in terms of ideal gas equation as follows:
$\begin{aligned}P_1= & n_1\left(\frac{R T}{V}\right), P_2=n_2\left(\frac{R T}{V}\right), P_3=n_3\left(\frac{R T}{V}\right), \ldots \text { and so on .....(1) } \\\therefore \quad P_{\text {Total }} & =n_1\left(\frac{R T}{V}\right)+n_2\left(\frac{R T}{V}\right)+n_3\left(\frac{R T}{V}\right) \ldots \ldots. \\& =\left(\frac{R T}{V}\right)\left(n_1+n_2+n_3 \ldots\right)=\frac{R T}{V} n_{\text {Total }.........(2)}\end{aligned}$
Mole fraction of any individual gas in the mixture is given by the equation: $x_1=\frac{n_1}{n_1+n_2+n_3+\ldots}=\frac{n_1}{n_{\text {Total }}}$
From equation (1) and (2), we get $n _1=\frac{ P _1}{\left(\frac{ RT }{ V _{ }}\right)}.........(3)$and$n _{\text {Total }}=\frac{ P _{\text {Total }}}{\left(\frac{ RT }{ V }\right)}......(4)$
By combining equation (3) and (4), we get $\frac{ n _1}{ n _{\text {Total }}}=x_1=\frac{\frac{ P _1}{\left(\frac{ RT }{ V }\right)}}{\frac{ P _{\text {Total }}}{\left(\frac{ RT }{
V }\right)}}=\frac{ P _1}{ P _{\text {Total }}}.......(5)$$ \therefore \quad P _1=x_1 \cdot P _{\text {Total }} $
Similarly
$ P _2=x_2 \cdot P _{\text {Total }} $ $\qquad$ .....and so on.{.......(6)
Thus, partial pressure of a gas is obtained by multiplying the total pressure of mixture by mole fraction of that gas.$
Similarly
$
P _2=x_2 \cdot P _{\text {Total }}
$
$\qquad$ .....and so on.{.......(6)
Thus, partial pressure of a gas is obtained by multiplying the total pressure of mixture by mole fraction of that gas.