Question

A gaseous mixture contains 410.0 Torr H₂ (g), 336.7 Torr N₂ (g), and 81.9 Torr Ar (g). Calculate the mole fraction of each of the gas

Answer 1

If the volume and temperature of a gas mixture is held constant, the pressure of a gas is directly proportional to the number of its molecules. The total pressure of the mixture is equal to the sum of pressures of each component.Therefore,

$\chi(H_2)=\frac{p(H_2)}{p(H_2)+p(N_2)+p(Ar)}=\frac{410.0torr}{410.0torr+336.7torr+81.9torr}=0.4948$

$\chi(N_2)=\frac{p(N_2)}{p(H_2)+p(N_2)+p(Ar)}=\frac{336.7torr}{410.0torr+336.7torr+81.9torr}=0.4063$

$\chi(Ar)=\frac{p(Ar)}{p(H_2)+p(N_2)+p(Ar)}=\frac{81.9torr}{410.0torr+336.7torr+81.9torr}=0.0988$

Answer:

$\chi(H_2)=0.4948$

$\chi(N_2)=0.4063$

$\chi(Ar)=0.0988$