Question

A cationic colloidal electrolyte forms micelles at ${10}^{-4}$ M concentration in water. If $1$ mm${}^3$ solution contains ${10}^{12}$ micelle structure, then the number of cations involved in one micelle is:

• A. $20$
• B. $40$
• C. $60$
• D. $80$

Answer 1

The correct option is C $60$

It is given that a cationic colloidal electrolyte forms micelles at ${10}^{-4}$ M concentration in water.

The number of particles of cationic colloidal electrolyte per litre before micelle formation $={10}^{-4}\times 6\times {10}^{23}=6\times {10}^{19}$

$\therefore$ The number of particles of cationic colloidal electrolyte per mm${}^3=6\times {10}^{19}\times {10}^{-6}=6\times {10}^{13}$

The number of micelles formed $={10}^{12}$ per mm${}^3$

$\therefore$ The number of cations in one micelle $=\frac{6\times {10}^{13}}{{10}^{12}}=60$

Hence, option C is the correct answer.