Question

A gaseous mixture contains 412.0 Torr H 2 ( g ) , 335.9 Torr N 2 ( g ) , and 83.1 Torr Ar ( g ) . Calculate the mole fraction, χ , of each of these gases.

Answer 1

Answer: The mole fraction of $H_2$ , $N_2$  and $Ar$  are 0.4950 , 0.4040 and 0.100 respectively.

Explanation:

According to Dalton's law, the total pressure is the sum of individual pressures.

$p_{total}=p_1+p_2+p_3$

$p_{total}=p_{H_2}+p_{N_2}+p_{Ar}$

$p_{total}=412.0+335.9+83.1=831.0torr$

The partial pressure of a gas is given by Raoult's law, which is:

$p_A=p_T\times \chi_A$ ......(1)

where,

$p_A$ = partial pressure of substance A

$p_T$ = total pressure

$\chi_A$ = mole fraction of substance A

a) mole fraction of $H_2$

$412.0=\chi_{H_2}\times 831.0$

$\chi_{H_2}=0.4950$

b) mole fraction of $N_2$

$335.9=\chi_{N_2}\times 831.0$

$\chi_{N_2}=0.4040$

c) mole fraction of $Ar$

$83.1=\chi_{Ar}\times 831.0$

$\chi_{Ar}=0.100$