Answer to Question #128152 in Chemistry for Henry king .S

Question

1. (a) State Graham’s law of diffusion
(b) Arrange the following gases He,CH4,and N2 in order of increasing rates of diffusion, give reasons for your answers. [H = 1,He = 4,C = 12,N = 14]
2. 60cm3 of hydrogen diffused through a porous membrane in 10 minutes. The same volume of a
gas G diffuses through the same membrane in 37.4 minutes. Determine the relative molecular
mass of G. [H = 1]

Answer 1

1. (a) According to Graham's law, the rate of diffusion or of effusion of a gas $r$ is inversely proportional to the square root of its molecular mass $M$:

$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}$ .

(b) In order to arrange the gases in order of increasing rates of diffusion, we must calculate their molecular masses.

He: 4

CH₄: 12+1·4 = 16

N₂: 14·2 = 28.

The molecular masses of the gases increase in a row: He<CH₄<N₂. Therefore, the rate of diffusion increases in a row: N₂<CH₄<He.

2. The rate of the diffusion can be defines as an amount of gas passing through the area per unit of time: $r = V/t$. Making use of the analytical expression of Graham's law given in p.1 of the Question, the relative molecular mass of the gas G is:

$M_G = M_{H_2}·\frac{r_{H_2}^2}{r_G^2} = M_{H_2}·\frac{t_G^2}{t_{H_2}^2}$

$M_G = 1·2·\frac{37.4^2}{10^2} = 28$ g/mol.

With a high probability, the gas G is N₂, nitrogen.