Question

Rate of diffusion of a gas X is twice that of another gas with molecular weight 64 the molecular weight of gas X

Answer 1

Molecular weight of X is 16

Explanation:

According to Graham's Law, the rate of diffusion of gas is inversely proportional to square root of molecular weight.

$Rate of diffusion \alpha \frac{1}{\sqrt{Molecular weight}}$   or    $r\alpha\frac{1}{\sqrt{M. wt}}$

Suppose rate of diffusion of gas X = $r_{1}$

rate of diffusion of another gas = $r_{2}$

Molecular weight of gas X = ${M. wt_{1}}$

Molecular weight of another gas = ${M. wt_{2}}$

      $r\alpha\frac{1}{\sqrt{M. wt}}$

      $\frac{r_{1}}{r_{2}}=\sqrt{\frac{M. wt_{2}}{M. wt_{1}}}$

  Given        $r_{1}=2r_{2}$

       $\frac{2r_{2}}{r_{2}}=\sqrt{\frac{64}{M. wt_{1}}}$

         $2=\sqrt{\frac{64}{M. wt_{1}}}$

         $2^{2}=\frac{64}{M. wt_{1}}$

         $\frac{4}{64}=\frac{1}{M. wt_{1}}$

        ${M. wt_{1}}=16$

So, Molecular weight of gas X is 16.