Question

Question #95169

Answer 1

The relative molecular mass of gas Z is 32

To get feasible result the volume of hydrogen gas diffused is considered `200cm^3`.

Explanation:

To solve this problem we are to apply Graham's law of diffusion which states that the rate of effusion or of diffusion (R)of a gas is inversely proportional to the square root of its molecular weight or relatve molecular mass (M) at constant temperature and pressure.

`color(red)("Symbolically, "R prop 1/sqrtM)`

Let

`M_Z->"Relative molecular mass of gas Z"=?`

`M_H->"Rel. molecular mass of Hydrogen"=2`

`R_Z->"Rate diffusion of gas Z"=100/10=10"cm"^3/s`

`R_H->"Rate diffusion of Hydrogen"=200/5=40"cm"^3/s`

Now by Graham's law

`R_H/R_Z=sqrt(M_Z/M_H)`

`=>40/10=sqrt(M_Z/2)`

`M_Z=4^2*2=32`

The relative molecular mass of gas Z is 32