Question

an unknown gas diffuses the rate of 0.5 time that of nitrogen at the same temperature and pressure . calculate the molar mass of the unknown gas.​

Answer 1

answer : 112g/mol

explanation : according to , Graham's law of diffusion, “the rate of diffusion or effusion of a gas is inversely proportional to square root of their molecular weight at same temperature and pressure.”

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

a/c to question,

an unknown gas diffuses the rate of 0.5 times of Nitrogen at the same temperature and pressure

molecular weight of nitrogen gas , N2 = 28g/mol

Let molecular weight of unknown gas is X.

given, $r_{X}=0.5r_{N_2}$

so, $\frac{r_X}{r_{N_2}}=0.5=\sqrt{\frac{28}{X}}$

or, (1/2)² = 28/X

or, X = 28 × 2² = 28 × 4 = 112g/mol

hence, molecular weight of gas is 112g/mol.