Question

The solubility product of silver chloride is $ 1.5625 \times {10^{ - 10}} $ at $ {25^ \circ }C $ . Find its solubility in $ g{L^{ - 1}} $ .

Answer 1

Hint: Solubility product is defined as the solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. It is represented by the symbol $ {K_{sp}} $ . Its value depends on temperature.
Formula used
 $ \text{Solubility in }g{L^{ - 1}} = M \times {K_{sp}} $
Where, $ M $ represents the molar mass of solute and $ {K_{sp}} $ is the solubility product constant of silver chloride.

Complete step by step solution
In the given question it is given that the solubility product of silver chloride is $ 1.5625 \times {10^{ - 10}} $ at $ {25^ \circ }C $ . We have asked to find its solubility in $ g{L^{ - 1}} $ .
Now, from the reaction,
  $ AgCl \rightleftharpoons A{g^ + } + C{l^ - } $
Let, S be the solubility of $ A{g^ + } $ and $ C{l^ - } $ .
Hence, we have given $ {S^2} $ which is equal to $ 1.5625 \times {10^{ - 10}} $ at $ {25^ \circ }C $ .
 $ {S^2} = 1.5625 \times {10^{ - 10}} $
 $ \Rightarrow $ $ S = \sqrt {1.5625 \times {{10}^{ - 10}}} $
 $ S = 1.25 \times {10^{ - 5}}mol{L^{ - 1}} $
Now, we can calculate the solubility of silver chloride in $ g{L^{ - 1}} $ by using above formula,
 $ \text{Solubility in }g{L^{ - 1}} = M \times {K_{sp}} $
By putting the value of known quantity, we get the solubility of silver chloride in $ g{L^{ - 1}} $ .
 $\text {Solubility in }g{L^{ - 1}} = 143.5 \times 1.25 \times {10^{ - 5}} $
 $ \text{Solubility in }g{L^{ - 1}} = 1.79 \times {10^{ - 3}}g{L^{ - 1}} $ .

Note
It is to be noted that the value solubility product constant depends on temperature, when we increase the temperature solubility product also increases due to increase in solubility.
Solubility and solubility are different from each other solubility of a solute or substance in a solvent is the maximum amount of solute that can be dissolved in a solvent whereas the solubility product constant is an equilibrium constant that provides insight into the equilibrium between the solid solute and its ions that are dissociated across the solution.
Solubility and solubility products depend on temperature i.e. if we increase the temperature the value of solubility and solubility product also increase. There is no effect of pressure on solubility of solid but solubility of gases increase with increase in temperature.