Adsorption is the presence of excess concentration of any particular component at the surface of liquid a 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, `1.12cm^3` of `H_2(g)` measured over S.T.P was found to absorb per gram of charcoal.Consider only monolayer adsorption.Density of `H_2` is 0.07gm/cc. In another experiment same 1 gm charcoal adsorbs 100 ml of 0.5M `CH_3COOH` to form monolayer and thereby the molarity of `CH_3COOH` reduces to 0.49.
`((3xx47.43)/(4pi))^(1//3)=2.24`
`(2.24)^2=5`
What is the radius of adsorb hydrogen molecule-

Options

A. `2.24xx10^(-7) cm`
B. `2.24xx10^(-8) cm`
C. `2.24xx10^(-9) cm`
D. `2.24xx10^(-10) cm`

Answer

B

Explanation

Density of `H_2=0.07 gm//c c`
0.07 gm `H_2` has volume = 1ml
2gm `H_2` has volume`=1/0.07xx2` ml
So`N_A` molecules of `H_2` have volume `=1/0.07xx2`ml
1 molecules of `H_2` has volume`=2/(0.07xx6.023xx10^23)`
assuming `H_2` to be spherical molecule
`=2/(0.07xx6.023xx10^23)=4/3pir^3 implies r_3=(3xx47.437xx10^(-24))/(4pi)implies r=2.24xx10^(-8) cm`