Question

Two gases P and Q having ratio of rate of diffusion
is 1:2 and the ratio of their masses present in the
mixture is 1:3 then the ratio of their mole fraction
would be
(1) 2:5
(2) 1:(6)
(3) 5:9
14) 1: (12)​

Answer 1

Answer:

(4) 1 : 12

Explanation:

Given,

$R_P:R_Q=1:2$

$W_P:W_Q=1:3$

To Find :-

$n_A:n_B=?$

Solution :-

The rate of diffusion is inversely proportional to the square root of molar mass :-

$\implies \dfrac{R_P}{R_Q}=\sqrt{\dfrac{M_Q}{M_P}}$

$\dfrac{1}{2}=\sqrt{\dfrac{M_Q}{M_P}}$

Squaring on both sides :-

$\left(\dfrac{1}{2}\right)^2=\left(\sqrt{\dfrac{M_Q}{M_P}}\right)^2$

$\dfrac{1}{4}=\dfrac{M_Q}{M_P}$

Taking Reciprocal on both sides :-

$\implies \dfrac{M_P}{M_Q}=\dfrac{4}{1}$

[ Let it be equation - 1]

Given,

$\dfrac{W_P}{W_Q}=\dfrac{1}{3}$

[Let it be equation - 2]

Formula Required :-

$\dfrac{n_P}{n_Q}=\dfrac{\dfrac{W_P}{W_Q}}{\dfrac{M_P}{M_Q}}$

$\implies \dfrac{n_P}{n_Q}=\dfrac{equation-2}{equation-1}$

$\dfrac{n_P}{n_Q}=\dfrac{\dfrac{1}{3}}{\dfrac{4}{1}}$

$=\dfrac{1}{3}\times \dfrac{1}{4}$

$\dfrac{n_P}{n_Q}=\dfrac{1}{12}$

$\implies n_P:n_Q=1:12$

∴ Option (4) 1 : 12