Question

A detergent (${C_{12}}{H_{25}}SO_4^ - N{a^ + }$ ) solution becomes a colloidal sol at a concentration of ${10^{ - 3}}M$ . On an average, ${10^{13}}$ colloidal particles are present in $1m{m^3}$ . What is the average number of ions which are contained by one colloidal particle (micelle).
(Given: ${N_A} = 6 \times {10^{23}}mo{l^{ - 1}}$ )
A. $6 \times {10^7}$
B. $10$
C. $60$
D. $6$

Answer 1

Hint: Micelles are formed by self-assembly of amphiphilic molecules. The structures contain a hydrophilic/polar region (head) and hydrophobic/ non-polar region (tail). Micelles are formed in aqueous solution whereby the polar region faces the outside surface of the micelle and the non-polar region forms the core.

Complete step by step answer:
When a detergent is added to a solution consisting of the colloidal particles, the polar part of the detergent gets attracted towards the polar part of the colloidal particles and binds them together to form a coagulate or the micelle. The detergents clean poorly soluble lipophilic material (such as oils and waxes) that cannot be removed by water alone. Detergents clean also by lowering the surface tension of water, making it easier to remove material from a surface. The emulsifying property of surfactants is also the basis for emulsion polymerization.
As per the question, ${10^{13}}$ colloidal particles are present in $1m{m^3}$.
${10^{ - 3}}M$means one mole in $1000liter$ .
In $1m{m^3}$, number of moles = $({10^{ - 3}} \times 1 \times {10^{ - 6}})$ moles of detergent = ${10^{ - 9}}$ moles of detergent
One mole of detergent will consist of = $6 \times {10^{23}}$ molecules
${10^{ - 9}}$ moles of detergent will consist of = \[6 \times {10^{23}} \times {10^{ - 9}} = 6 \times {10^{14}}\] molecules/ particles
The average number of detergent ions in one colloidal particle (micelle) = $\dfrac{{6 \times {{10}^{14}}}}{{{{10}^{13}}}} = 60$
Thus, the correct option is C. $60$ .

So, the correct answer is “Option C”.

Note:
Micelles are approximately spherical in shape. Other phases, including shapes such as ellipsoids, cylinders, and bilayers, are also possible. The shape and size of a micelle are a function of the molecular geometry of its surfactant molecules and solution conditions such as surfactant concentration, temperature, pH, and ionic strength. The process of forming micelles is known as micellization and forms part of the phase behavior of many lipids according to their polymorphism.