Question

The ratio of moles of CH4 to SO2 after fifth diffusion steps is x: 1 and their initially mole ratio is 1:8, then the value of 'x' is : -​

Answer 1

The value of x is 1.32.

The ratio of moles of CH₄ to SO₂ after fifth diffusion steps is x : 1 and their initially mole ratio is 1 : 8.

We have to find the value of x.

Concepts :

• Graham's law of diffusion/effusion : It states that the rate of diffusion/effusion of a gas is inversely proportional to the square root of its density.

From Graham's law of diffusion we get,

The ratio of moles of two gas A and B after nth diffusion steps :

$\left(\frac{n_A}{n_B}\right)^n=\frac{n^{\circ}_A}{n^{\circ}_B}\left(\sqrt{\frac{M_B}{M_A}}\right)^n$

Here no of diffusion steps , n = 5

A = methane and B = sulphur dioxide

$n^{\circ}_{CH_4}:n^{\circ}_{SO_2}=1:8\\\\M_{SO_2}:M_{CH_4}=64:16=4:1$

$\implies\left(\frac{n_{CH_4}}{n_{SO_2}}\right)^5=\frac{1}{8}\left(\sqrt{\frac{4}{1}}\right)^5=\frac{1}{8}\times32=4\\\\\implies\frac{n_{CH_4}}{n_{SO_2}}=\sqrt[5]{4}\approx1.32:1$

Therefore the value of x is 1.32.

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