91Ó°ÊÓ

Moles of oleic acid can be calculated by dividing its mass by its molar mass.

The surface area occupied by one molecule by dividing surface area by the moles of oleic acid.

Consider the given data as below.

The mass of oleic acid, $m=2.50\text{mg}=2.50\text{ }×{10}^{−3}\text{g}$

The molar mass of oleic acid,$M=283\raisebox{1ex}{${\displaystyle \text{g}}$}\!\left/ \!\raisebox{-1ex}{$\text{mol}$}\right.$

Determine the molecules of oleic acid as below.

$\begin{array}{rcl}\text{³¾´Ç±ô±ð²õ o´Ú o±ô±ð¾±³¦â€‰a³¦¾±»å}& =& \frac{\text{mass}}{\text{³¾´Ç±ô²¹°ù″¾²¹²õ²õ}}\\ & =& \frac{m}{M}\\ & =& \frac{2.50\text{ }×{10}^{−3}\text{g}}{283{\displaystyle \raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{mol}$}\right.}}\\ & =& 8.83×{10}^{−6}\text{mol}\end{array}$

One mole of substance is $6.022×{10}^{23}\text{molecules}$.

Hence, the number of oleic acid molecules is,

$(8.83×{10}^{−6}\text{mol})×\frac{6.022×{10}^{23}\text{molecules}}{1\text{mol}}=5.32×{10}^{18}\text{molecules}$

The diameter of circular monolayer, $d=38.6\text{cm}$

The radius is half of diameter, so it becomes,

$\begin{array}{rcl}r& =& \frac{38.6\text{cm}}{2}\\ & =& 19.3\text{cm}\end{array}$

Now, the surface area of molecules can be calculated by using following formula.

$\begin{array}{rcl}A& =& \mathrm{π}{r}^2\\ & =& 3.14×{\left(19.3\text{cm}\right)}^2\\ & =& 1169.61{\text{cm}}^2\end{array}$

Thus, it can find out the surface area occupied by one molecule by dividing above calculated surface area by the moles of oleic acid.

$\begin{array}{rcl}\text{²õ³Ü°ù´Ú²¹³¦±ð a°ù±ð²¹â€‰o³¦³¦³Ü±è¾±±ð»å b²â​â¶Ä‰o²Ô±ð″¾´Ç±ô±ð³¦³Ü±ô±ð}& =& \frac{1169.61{\text{cm}}^2}{5.32×{10}^{18}\text{molecule}}\\ & =& 2.19×{10}^{−16}\raisebox{1ex}{${\displaystyle {\text{cm}}^{\text{2}}}$}\!\left/ \!\raisebox{-1ex}{$\text{molecule}$}\right.\end{array}$

Hence, the surface area occupied by one molecule is $2.19×{10}^{−16}\raisebox{1ex}{${\displaystyle {\text{cm}}^{\text{2}}}$}\!\left/ \!\raisebox{-1ex}{$\text{molecule}$}\right.$.