Question

What is the molecular weight of a gas which diffuses 1/50 times as fast as hydrogen gas?​

Answer 1

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Answer 2

Answer:

The molecular weight of gas is 5000g/mol

Explanation:

Let the rate of diffusion of hydrogen gas is x.

The rate of diffusion of a gas is $\frac{1}{50}$ times of hydrogen gas.

Therefore, the rate of diffusion of a gas is  $\frac{x}{50}$.

According to Graham's law of  diffusion:

The rate of diffusion is inversely proportional to the square root of the molecular weight of the gas.

Therefore,

$\[R \propto \sqrt {\frac{1}{M}} \]$

Now,

$\[\begin{gathered} \frac{{{R_{{H_2}}}}}{{{R_{Gas}}}} = \frac{{\sqrt {\frac{1}{{{M_{{H_2}}}}}} }}{{\sqrt {\frac{1}{{{M_{Gas}}}}} }} \hfill \\ \frac{x}{{\frac{x}{{50}}}} = \frac{{\sqrt {\frac{1}{2}} }}{{\sqrt {\frac{1}{{{M_{Gas}}}}} }} \hfill \\ 50 = \sqrt {\frac{{{M_{Gas}}}}{2}} \hfill \\ {50^2} = \frac{{{M_{Gas}}}}{2} \hfill \\ 2500 \times 2 = {M_{Gas}} \hfill \\ {M_{Gas}} = 5000g/mol \hfill \\ \end{gathered} \]$

Therefore, the molecular weight of gas is 5000g/mol