Question

In an experiment it is found that at a constant temperature, rate of adsorption of gas on solid surface follows the relation
Rate $\infty$ ${\text{[surface area of solid]}}^1$
A solid is taken in form of cube that has side length 1 $cm$. The total surface area of this cube is $xc{m}^2$ and rate of adsorption of gas is $r1$. If this solid cube is divided equally into ${10}^{12}$ cubes then total surface area available for adsorption becomes $yc{m}^2$ and rate becomes $r^2$.

On the basis of above information, select correct statement(s).

• A. $r2/r1=6\times {10}^4$
• B. $r2/r1={10}^4$
• C. y is $6.0\times {10}^4$
• D. x is 6

Answer 1

Answer: (B), (C), (D)

x is 6

If edge length of cube is 1 cm
Surface area = $6c{m}^2$
If edge length of cube = 1 cm = ${10}^{-2}m$
Volume = ${10}^{-6}{m}^3$
After division let length become = $l$
So, volume = $l^3$
Total volume $\Rightarrow {10}^{12}\times l^3={10}^{-6}$
$l={10}^{-6}m$
Surface area of one divide cube = $6\times l^2$
$=6\times {10}^{-12}{m}^2$
Total area = $6\times {10}^{-12}\times {10}^{12}=6m^2=6\times {10}^{4}c{m}^2$