Question

A soap $\left( {{C_{17}}{H_{35}}COONa} \right)$ solution becomes a colloidal sol at a concentration of $1.2 \times {10^{ - 3}}M$. On the average, $2.4 \times {10^{13}}$ colloidal particles are present in $1{\text{ }}m{m^3}$ What is the average number of stearate ions (in multiples of ${10^6}$) in one colloidal particle (micelle)?
A. $30$
B. $40$
C. $50$
D. $60$

Answer 1

For solving this question, we first need to understand the concept behind the micelle formation. The process of cleaning action of soap is due to micelle formation and emulsion formation. After that we can see that inside water a unique orientation form of clusters of molecules are formed in which the hydrophobic tails are in the interior of the cluster and the ionic ends on the surface of the cluster. Thus, it results in the formation of micelle.

Complete step by step answer:
As we know, soap in the form of micelle aims in cleaning the dirt as the dirt will be collected at the centre of micelle.
Now, we note the given quantities.
Concentration of colloidal sol $= 1.2 \times {10^{ - 3}}M$
As mentioned in the question, $1{\text{ }}m{m^3}$ will contain $\dfrac{{1.2 \times {{10}^3}mol/d{m^3}}}{{{{10}^6}m{m^3}/d{m^3}}} = 1.2 \times {10^{ - 3}}$ moles of soap.
We know that, $1$ mole of soap is equal to $6.023 \times {10^{23}}$ molecules
Now, we will substitute the respective values of the quantities
$1.2 \times {10^{ - 3}}$ moles of soap $= 1.2 \times {10^{ - 3}} \times 6.023 \times {10^{23}} = 7.227 \times {10^{20}}$ stearate ions.
$\therefore$ The average number of stearate ions in one colloidal particle (micelle)
$\Rightarrow \dfrac{{7.227 \times {{10}^{20}}}}{{2.4 \times {{10}^{13}}}} = 3 \times {10^7} = 30$

$\therefore$ Option A is a correct answer.

Note:
After solving this question, we need to understand the purpose of micelle formation. Micelles help our body to absorb the lipid and fat soluble vitamins. It helps our small intestine in absorbing essential lipids and vitamins from the liver and gallbladder. Also, carries complex lipids such as lecithin and lipid soluble vitamins A, D, E and K to the small intestine.