Question

A solution of palmitic acid $(M=256gmo{l}^{-1})$ in benzene contains $4.24$ g of acid per litre. This solution on pouring on water surface forms a monomolecular level of palmitic acid as benzene gets evaporated. If $500c{m}^2$ area of water surface is to be covered by a monolayer, the volume of solution in benzene needed is $y\times {10}^{-6}L$. Find $y$ rounded to the nearest integer. Area covered by one molecule of palmitic acid is $0.21n{m}^2$.

Answer 1

Let $V$ litres be the volume of solution needed.

Mass of palmitic acid $=V\times d=V\times 4.24g$

Moles of palmitic acid $=\frac{V\times 4.24}{256}$

$\therefore$ Number of molecules of palmitic acid $=\frac{4.24\times V\times 6.023\times {10}^{23}}{256}$

$\therefore$ Total area covered $=\frac{4.24\times V\times 6.023\times {10}^{23}}{256}\times 0.21\times {10}^{-18}\times {10}^{4}c{m}^2$

or $500=\frac{4.24\times V\times 6.023\times {10}^{23}\times 0.21\times {10}^{-18}\times {10}^4}{256}$

$\therefore V=23.86\times {10}^{-6}L$

So, the nearest integer value of $y$ is $24$.