Question

A soap $({{C}_ {17}} {{H}_ {35}} COONa) $ 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 $1m{{m}^ {3}} $. What is the average number of stearate ions in one colloidal particle (micelle)?
(A) 30
(B) 40
(C) 50
(D) 60

Answer 1

Hint: A colloid is a mixture that has particles ranging between 1 and 1000 nanometres in diameter, yet are still able to remain evenly distributed throughout the solution. These are also known as colloidal dispersions because the substances remain dispersed and do not settle to the bottom of the container.

Complete step by step solution:
We have been provided the concentration of soap solution: $1.2\times {{10} ^ {-3}} moles/d{{m}^ {3}} $ or $1.2\times {{10} ^ {-9}} moles/m{{m}^ {3}} $,
We need to find out the average number of stearate ions in one colloidal particles,
 A colloid is a mixture that has particles ranging between 1 and 1000 nanometres in diameter, yet are still able to remain evenly distributed throughout the solution,
So, this corresponds the concentration: $6.022\times {{10} ^ {23}} \times 1.2\times {{10} ^ {-9}} =7.2\times {{10} ^ {14}} molecules/m{{m}^ {3}} $,
According to the question, we have been given that total number of colloidal particles in $1m{{m}^ {3}} $: $2.4\times {{10} ^ {13}} $,
Colloidal particles are microscopic solid particles suspended in a fluid. Colloidal suspensions are a powerful model system for the study of other phenomena in condensed matter physics, where the collective phase behaviour of the solid particles mimics that of other condensed systems.
So, the number of stearate ions in one particle are: $\dfrac {7.2\times {{10} ^ {14}}} {2.4\times {{10} ^ {13}}} =30$,
So, we can say that the number of stearate ions in one particle comes out to be 30.

Therefore, we can conclude that option (A) is correct.

Note: Stearic acid is a great addition to soap recipes if you'd like to create an extra firm bar of soap. It's usually used as a thickening agent in lotion. It's a vegetable derived waxy substance that can be used at a 0.5% of your oils in cold process soap.