Question

At $298K$ how many milligrams of silver bromide can be dissolved in $20$ litres of water [ ${{K}_{sp\left( AgBr \right)}}=5\times {{10}^{-13}}$ ; Atomic weight of silver and bromine is $108$ and $80$ respectively]
(A) $2.66$
(B) $3.66$
(C) $4.66$
(D) None of these.

Answer 1

We know that the solubility product constant ${{K}_{sp}}$ is the equilibrium constant for a solid substance dissolving in an aqueous solution. It represents the level at which a solute dissolves in solution. The more soluble substance means it has a higher solubility product value. Solubility products were only applicable for sparingly soluble ionic compounds.

Complete answer:
Solubility products cannot be used for normally soluble compounds like sodium chloride, silver nitrate, etc. interactions between the ions in the solution interfere with the simple equilibrium. The solubility product is a value that you get when the solution is saturated. If there is any solid present, it cannot dissolve any more solid than there is in a saturated solution.
Given the value solubility product of silver bromide is, ${{K}_{sp}}\left[ AgBr \right]=\left[ A{{g}^{+}} \right]\left[ B{{r}^{-}} \right]=5\times {{10}^{-13}}$
Thus, ${{K}_{sp}}\left( AgBr \right)={{S}^{2}}=5\times {{10}^{13}}=7.1\times {{10}^{7}}\text{ }M$
Silver nitrate is completely dissociated into silver ions and nitrate ions because it is a completely soluble substance. i.e., the concentration of silver nitrate is equal to concentration of silver ions usually; Thus, Mole in $20\text{ }L=7.1\times {{10}^{7}}\times 20=1.42\times {{10}^{5}}$
$Mass~=\text{ }1.42\times {{10}^{5}}\times \left( 108+80 \right)$
$=\text{ }2.66.96\times {{10}^{5}}\text{ }gm=2.66mgm$
Therefore the correct answer is option A.

Note:
Remember that as we know that Solubility products are a type of equilibrium constant and it is found that its value depends on temperature. As the temperature increases, the value of Solubility products increases, due to increased solubility. We should not get confused between the terms solubility and solubility product. As solubility is the total amount of solute that can be dissolved in the solvent.