Question

The solubility product of \[AgCl\]is${10^{ - 10}}{M^2}$. The minimum volume (in ${m^3}$) of water required to dissolve 14.35mg of AgCl is approximately:
(A)- 0.01
(B)- 0.1
(C)- 100
(D)- 10

Answer 1

Hint: Solubility products refer to a large group of sparingly soluble salts and hydroxides and some oxides. For some oxides, the solubility measurements showed quite low values even under a strongly acidic condition.

Complete step by step solution:
The above question is based on the concept of the solubility product constant. So, before proceeding further, let's get the basic knowledge about it.
The solubility product constant is the equilibrium constant for the dissolution of a solid compound into an aqueous solution. The solubility product is a kind of equilibrium constant whose values depend on temperature. It usually increases with an increase in temperature due to increased solubility. The solubility of ionic compounds in water varies to a great deal. Some compounds are highly soluble and may even absorb moisture from the atmosphere whereas others are highly insoluble. The solubility product could be measured at solubility equilibrium,
You might be thinking that what is solubility equilibrium. So, let's look at its definition.
Solubility equilibrium is a kind of dynamic equilibrium that exists when a chemical compound (in the solid-state) is in chemical equilibrium with a solution of that compound. Each solubility equilibrium is characterized by a solubility product which is temperature-dependent in nature and which functions like an equilibrium constant.
In our question, the solubility product of Silver chloride is given. So, it's solubility equation can be given as:
$\begin{gathered}
AgCl(s) \to A{g^ + }(aq) + C{l^ - }(aq) \\
{\text{ S S}} \\
\end{gathered} $
Now, by using the formula of solubility product, we can write that
$Ksp = {S^2}$
By putting the value of solubility product constant in the above equation, we get
${10^{ - 10}} = {S^2}$
$S = {10^{ - 5}}M$
Now, we know that the molecular weight of silver chloride is 143.5g
Therefore, the number of moles of silver chloride in the solution can be calculated as follows:
$n = \dfrac{{14.35 \times {{10}^{ - 3}}}}{{143.5}} = {10^{ - 4}}moles$
By further calculation, we get
\[Solubility{\text{ }} = \dfrac{{Moles{\text{ }}of{\text{ }}solute}}{{volume{\text{ }}of{\text{ }}solution}}{\text{ }}\]
${10^{ - 5}} = \dfrac{{{{10}^{ - 4}}}}{{V(in{\text{ liter)}}}}$
$V = 10liters$
Now, we are well aware of the fact that: 1 ${m^3}$ = 1000 liters
Therefore, 10 liters = 0.01 ${m^3}$

Hence, the correct answer is (A)- 0.01.

Note: Don't get confused between solubility and solubility products. The solubility of a substance in a solvent is the total amount of the solute that can be dissolved in it at equilibrium. On the other hand, the solubility product is an equilibrium constant that provides insight into the equilibrium between the solid solute and its constituent ions that are dissociated across the solution.