Question

Rate of diffusion of a gas having molecular weight just double of nitrogen gas is 56 ml per sec. the rate of diffusion of nitrogen gas will be:
A. 79.19 ml/sec
B. 112 ml/sec
C. 56 ml/sec
D. 90 ml/sec

Answer 1

Hint: Rate of diffusion depends on the difference in the concentration of gradient as diffusion takes place from high concentration to low concentration.

Complete answer:
As per Graham’s law that states “at constant pressure and temperature, the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight”.

Rate of diffusion$ \propto \dfrac{1}{{\sqrt m }}$

If $R_1$ and $R_2$ be two gases where $R_1$ is the rate of diffusion of nitrogen and $R_2$ be the rate of diffusion of another gas whose molecular weight is double that of nitrogen.
Therefore molecular weight of Nitrogen is $(m_1)$ = M g
Molecular weight of another gas $(m_2)$ = 2M g
According to Graham’s law of diffusion,
The diffusion of gas or effusion is inversely proportional to the square root of its molecular weight. Thus,
$\dfrac{{{R_1}}}{{{R_2}}} = \sqrt {\dfrac{{2 \times {M_1}}}{{{M_1}}}}$
By putting the values of molecular weight in the above equation,
=$\dfrac{{{R_1}}}{{56}} = \sqrt {\dfrac{{2M}}{M}} = 56\sqrt 2 = 79.19$ ml/sec

Hence the correct option is option A.

Additional information:
Rate of diffusion can be defined as:
a) Volume or number of moles of gas diffused per unit time.
b) Distance travelled by gas per unit time through a tube of uniform cross section.

Note: The phenomenon of rate of diffusion can occur even against gravity this mixing ability of two non reacting gases to form a homogeneous mixture.