Question

Adsorption is the presence of excess concentration of any particular component at the surface of liquid or solid phase as compared to bulk. This is due to presence of residual forces at the surface of body. In the adsorption of hydrogen gas over a sample of charcoal, $1.12$ $c{m}^3$ of $H_2$(g) measured over S.T.P. was found to adsorb per gram of charcoal. Consider only monolayer adsorption. Density of $H_2$ is $0.07$ g/cc.
In another experiment, same $1$ gram charcoal adsorbs $100$ ml of $0.5$ M $C{H}_{3}COOH$ to form monolayer and thereby the molarity of $C{H}_{3}COOH$ reduces to $0.49$.

What is the radius of adsorbed hydrogen molecule?

• A. $2.24\times {10}^{-7}cm$
• B. $2.24\times {10}^{-8}cm$
• C. $2.24\times {10}^{-9}cm$
• D. $2.24\times {10}^{-10}cm$

Answer 1

The correct option is B $2.24\times {10}^{-8}cm$

Given that : density of $H_2=0.07$ gm/cc.

$0.07$ g $H_2$ has volume$=1$ ml.

$2$ g $H_2$ has volume$=\frac{1}{0.07}\times 2$ ml.

So, $N_A$ molecules of $H_2$ have volume$=\frac{1}{0.07}\times 2$ ml.

$1$ molecule of $H_2$ has volume$=\frac{2}{0.07\times 6.023\times {10}^{23}}$.

Assuming $H_2$ to be spherical molecule so, volume of molecule $=\left(\frac{4}{3}\right)\pi r^3$.
Therefore, $\frac{2}{0.07\times 6.023\times {10}^{23}}=\frac{4}{3}\pi r^3$
or $r^3=3\times 47.437\times {10}^{-24}$

Hence, $r=2.24\times {10}^{-8}cm$.

Therefore, the correct option is B.