Question

The rate of diffusion of hydrogen is three times than
that of an unknown gas at same temperature and
pressure, the molar mass of unknown gas is:
(a) 18gmol
(b) 16g mol
(c) 32gmol-'
(d) 27gmol'

explain plz​

Answer 1

answer : option (a) 18g/mol

explanation: according to Graham's law of diffusion or effusion, under similar conditions of temperature and pressure, rate of diffusion or effusion of gas is inversely proportional to square root of molar mass.

e.g., $r\propto\frac{1}{\sqrt{M}}$

a/c to question, rate of diffusion of hydrogen gas is three times of unknown gas.

so, $r_{H_2}=3r_{X}$

or, $\frac{r_{H_2}}{r_{X}}=3$

or, $3=\frac{r_{H_2}}{r_{X}}=\sqrt{\frac{M_X}{M_{H_2}}}$

molar mass of Hydrogen gas= 2 g/mol

so, $3=\sqrt{\frac{M_{X}}{2}}$

or, $9=\frac{M_{X}}{2}$

hence, $M_{X}=18$

hence, molar mass of unknown gas is 18g/mol