Question

A detergent $\left( {{C_{12}}{H_{25}}S{O_4}^ - N{a^ + }} \right)$ solution becomes a colloidal solution at concentrated of ${10^{ - 3}}M$. On average ${10^{13}}$ colloidal particles present in $1m{m^3}$.What is the average number of ions contained in one colloidal particle micelle.
1)$6 \times {10^{ - 7}}$
2)$10$
3)$60$
4) $4 \times {10^5}$

Answer 1

Hint:We know that the molar mass is the mass of one mole of the substance. The unit of molar mass is ${\text{g/mol}}{\text{.}}$ A mole of a substance is equal to Avogadro’s number of that substance $6.022 \times {10^{23}}{\text{molecules}}$.

Complete step by step answer:
Given,
The concentration of colloidal solution is ${10^{ - 3}}M$.
Before formation of colloid ${10^{ - 3}}M$ were present in one liter of solution.
We know that $1d{m^3} = {10^6}m{m^3}$, $1m{m^3} = {10^ - }^6d{m^3}$
The number of moles present in $1m{m^3}$ solution before formation of colloid $ = {10^{ - 3}} \times {10^{ - 6}} = {10^{ - 9}}moles$
The number of molecules in ${10^{ - 9}}moles$$ = {10^{ - 9}} \times 6.023 \times {10^{23}}$
The number of molecules in ${10^{ - 9}}moles$$ = 6.023 \times {10^{14}}molecules$
After the formation of colloids, the numbers of colloidal particles are${10^{13}}$.
Thus each colloidal particles contains$ = \dfrac{{6.023 \times {{10}^{14}}}}{{{{10}^{13}}}} = 60.23 \simeq 60$
Therefore, option 3 is correct.

Additional Note:
We know that bathing soaps are the potassium salts of long-chain fatty acids whereas washing soaps which are also called detergents are sodium salts of long-chain fatty acids.
Bathing soaps are potassium salts of long-chain fatty acid and the anionic group present in soap is $ - COO.$ Detergents are sodium salts are long-chain fatty acids and the anionic group present is ${\text{ - S}}{{\text{O}}_{\text{3}}}$,${\text{ - OS}}{{\text{O}}_{\text{3}}}$ based on the nature of the alkali used in soap production, soaps have different properties. Sodium hydroxide gives hard soap which is used for washing while potassium hydroxide gives soft soap that is used for bathing.
The main difference between soap and detergents are:
-Soaps are prepared from vegetable oil and animal fats whereas detergents are prepared from coal and petroleum.
-Soaps are biodegradable while detergents are non-biodegradable.
-Soaps do not easily form lather in hard water but detergents easily form lather in hard water.
-Soaps show weak cleansing action so they cannot be used in acidic water on the other hand detergents show strong cleansing action so they can be used in acidic water.

Note:
We must remember that the soaps are made from the materials found in nature whereas detergents are synthetic. Detergents soaps were first manufactured at the time of World War II when oils required to produce were scarce.