Question

Solubility product of $AgCl$is $1\times {{10}^{-6}}$at $298K$. Its solubility in $mole\,litr{{e}^{-1}}$ would be
A. $1\times {{10}^{-6}}$ mole/litre
B. $1\times {{10}^{-3}}$mole/litre
C. $1\times {{10}^{-12}}$mole/litre
D. None of these

Answer 1

Hint: Solubility product is a type of equilibrium constant whose value depends on the temperature. It is denoted by ${{K}_{sp}}$. It usually increases with the increase in temperature because of the increased solubility.

Complete Step by Step Answer:
We know most ionic compounds which are insoluble in water still dissolve in water to some extent. For example silver chloride dissociates to small extent in the silver ions and the chloride ions.
$AgCl\rightleftharpoons A{{g}^{+}}+C{{l}^{-}}$
It is shown by the equilibrium. As the solid silver chloride does not have a variable concentration and is therefore not included in the above expression. This is the solubility product principle.
${{K}_{sp}}$= $\left[ A{{g}^{+}} \right]\left[ C{{l}^{-}} \right]$
Let x be the solubility of $\left[ A{{g}^{+}} \right]\,\,and\,\,\left[ C{{l}^{-}} \right]$
We can written the above equation as
${{K}_{sp}}=[x][x]$
By multiplying the above equation, we get
Then ${{K}_{sp}}={{x}^{2}}$
Hence $x=\sqrt{{{K}_{sp}}}$
We know value of ${{K}_{sp}}=1\times {{10}^{-6}}$
Then $x=\sqrt{1\times {{10}^{-6}}}$
Hence $x=1\times {{10}^{-3}}mol/litre$
Hence the value of solubility is $1\times {{10}^{-3}}mol/litre$
Thus, Option (B) is correct.

Note: Remember that solubility and the solubility product are different from each other. Solubility of a substance in a solvent is the highest amount of solute that can be dissolved in a solvent whereas the solubility product is an equilibrium constant that gives the equilibrium between the solid solute and its ions that are dissolved in the solution. Both the quantities are dependable upon the temperature. If we increase the temperature, both the solubility and the solubility product increases.