Question

a drop of olive oil of radius 0.30 mm spreads into a rectangular film of 30 cm ×15 cm on the water surface . estimate the molecular size of olive oil.

Answer 1

Answer: $5.83 \times 10^{-8} \ \mathrm{cm}$

Given:

Radius of oil drop = 0.30 mm = 0.3 cm

Solution:

Molecular size is defined as the measure of the area occupied by the molecules in a three-dimensional space.

$v=\frac{4 \pi r^{3}}{3}$

$v=4 \times \frac{22}{7} \times \frac{(0.03)^{3}}{3}$

$\begin{aligned} v &=\frac{88 \times 27 \times 10^{-6}}{3 \times 7} \\ v &=\frac{88 \times 9 \times 10^{-6}}{7} \end{aligned}$

$\begin{aligned} v &=113.14 \times 10^{-6} \\ v &=11314 \times 10^{-8} \mathrm{cm}^{3} \end{aligned}$

$\begin{array}{l}{1134 \times 10^{-8}=l \times b \times h} \\ {1134 \times 10^{-8} c m^{3}=13 c m \times 15 c m \times h}\end{array}$

$\begin{array}{l}{1134 \times 10^{-8} \mathrm{cm}^{3}=195 \mathrm{cm}^{2} \times h} \\ {\frac{1134 \times 10^{-8} \mathrm{cm}^{3}}{195 \mathrm{cm}^{2}}=h} \\ {5.83 \times 10^{-8} \mathrm{cm}=h}\end{array}$

Here, molecular size is equal to h of one molecule

So molecular size of olive oil is $5.83 \times 10^{-8} \ \mathrm{cm}$