Question

Let the solubilities of AgCl in ${{H}_{2}}O$ , 0.01 M$CaC{{l}_{2}}$, 0.01 M NaCl, and 0.05 M $AgN{{O}_{3}}$be ${{s}_{1}},{{s}_{2}},{{s}_{3}}$ and ${{s}_{4}}$ respectively. What is the correct relationship between these quantities?
(A)- ${{s}_{1}}>{{s}_{2}}={{s}_{3}}>{{s}_{4}}$
(B)- ${{s}_{1}}>{{s}_{2}}>{{s}_{3}}>{{s}_{4}}$
(C)- ${{s}_{4}}>{{s}_{2}}>{{s}_{3}}>{{s}_{3}}$
(D)- ${{s}_{1}}>{{s}_{3}}>{{s}_{2}}>{{s}_{4}}$

Answer 1

Hint: As a thumb rule of solubility, polar solutes tend to dissolve best in polar solvents and non-polar solutes tend to dissolve best in a nonpolar solvent.

Complete answer:
-The property of the ability of solute to dissolve itself uniformly in the solvent is known as solubility. Solubility is measured in terms of the maximum amount of solute dissolved in a solvent at equilibrium.

-The equilibrium constant for the dissolution of a solid substance into an aqueous solution is known as the solubility product and is denoted by ${{K}_{sp}}$. The solubility constant depends on temperature. As there is increment in the temperature, there will be increased solubility.

-Let us assume the following general reaction with the salt being a saturated aqueous solution.
${{M}_{p}}{{X}_{q}}\rightleftharpoons p{{M}^{m+}}(aq)+q{{X}^{n-}}(aq)$

So the equilibrium constant for the above reaction will be
$K=\dfrac{[p{{M}^{m+}}][q{{X}^{n-}}]}{[{{M}_{p}}{{X}_{q}}]}$

In case of pure solid substances, the concentration remains constant and so we can say,
${{K}_{sp}}=k[{{M}_{p}}{{X}_{q}}]=[p{{M}^{m+}}][q{{X}^{n-}}]$

-Let the solubility of AgCl be x.

-Therefore,
 The solubility of AgCl in water $=\sqrt{{{K}_{sp}}}={{s}_{1}}$
The solubility of AgCl in 0.01 M $CaC{{l}_{2}}$$={{K}_{sp}}=s\times (0.01\times 2+s)(\because {{s}_{2}}=\dfrac{{{K}_{sp}}}{0.02})$
The solubility of AgCl in 0.01 M NaCl $={{K}_{sp}}=s\times (0.01+s)(\because {{s}_{2}}=\dfrac{{{K}_{sp}}}{0.02})$
The solubility of AgCl in 0.05 M $AgN{{O}_{3}}={{K}_{sp}}=s\times (0.05+s)(\because {{s}_{4}}=\dfrac{{{K}_{sp}}}{0.05})$

-Now the solubilities are derived by neglecting s in comparison to 0.02, 0.01, and 0.05.

So, the order of solubilities is ${{s}_{1}}>{{s}_{3}}>{{s}_{2}}>{{s}_{4}}$ , i.e option D.

Additional information:
-When a solute is mixed with a solvent, the solute may either dissolve fully giving a clear homogeneous mixture or the solute may remain undissolved giving an unclear heterogeneous mixture.
-Depending on the solubility of a solute, there are three possible results: if the solution has less solute than the maximum solubility ability of the solvent, it will form a dilute solution; if the solution has the same amount of solute as the maximum solubility ability of the solvent, it will form a saturated solution; if there is more than solute than the maximum solubility ability of the solvent, it will form a supersaturated solution.
- In a supersaturated solution, the excess of solute separates from the solution and crystallizes at the bottom forming a precipitate.

Note:
The solubility rule helps us to determine which substances are soluble in a given solvent and to what extent. solute-solvent interactions also affect solubility. The stronger the solute-solvent interactions, the greater will be the solubility. The weaker the solute-solvent interactions, the lesser will be the solubility.