10 ml of 1 millimolar surfactant solution forms a monolayer covering `0.24cm^(2)` on a polar substrate.
If the polar head is approximated as a cube. Consider the surfactant is adsorbed only on one face of the cube. What is the edge length of cube? (Answer should be in pm and assume Avogadro's number `=6xx10^(23)` ).

Answer

2

Explanation

Number of milimoles `=10ml xx10^(-3)M=10^(-2)`
Number of moles `=10^(-5)`
Now, number of molecules `=10^(-5)xx6xx10^(23)=6xx10^(18)`
`because` Surface area occupied by `6xx10^(18)` molecules `=0.24" cm"^(2)`
`because` Surface area occupied by 1 molecule `=(0.24)/(6xx10^(18))" cm"^(2)=0.04xx10^(-18)cm^(2)`
As, it is given that polar head is a cube
So, surface area of cube `=a^(2)` (a = edge length)
`a^(2)=0.04xx10^(-18)cm^(2)`
`a=2xx10^(-10)cm=2` pm