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.

Step-by-step 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* \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)* 831.0`

`\chi_(H_2)=0.4950`

b) mole fraction of
`N_2`

`335.9=\chi_(N_2)* 831.0`

`\chi_(N_2)=0.4040`

c) mole fraction of
`Ar`

`83.1=\chi_(Ar)* 831.0`

`\chi_(Ar)=0.100`