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# In a saturated solution of the sparingly soluble strong electrolyte $AgI{O_3}$(molecular mass =283) the equilibrium which sets in is$AgI{O_3} \rightleftharpoons A{g^ + }(aq) + I{O_3}^ - (aq)$. If the solubility product constant ${K_{sp}}$ of $AgI{O_3}$ at a given temperature is $1.0 \times {10^{ - 8}}$, what is the mass of $AgI{O_3}$ contained in 100 ml of its saturated solution?A. $28.3 \times {10^{ - 2}}g$B. $2.83 \times {10^{ - 3}}g$C. $1.0 \times {10^{ - 7}}g$D. $1.0 \times {10^{ - 4}}g$

Last updated date: 13th Jun 2024
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Hint: Try to recall that solubility product is defined as the product of molar concentrations of ions in a saturated solution raised to their stoichiometric coefficients. Now, by using this you can easily find the correct option from the given ones.

It is known to you that $AgI{O_3}$ is a sparingly soluble salt and $AgI{O_3}$ ionizes completely in the solution as: $AgI{O_3} \to A{g^ + } + I{O_3}^ -$.

Calculation:
Given, ${K_{sp}}$= $1.0 \times {10^{ - 8}}$--------1
On complete ionization: $AgI{O_3} \to A{g^ + } + I{O_3}^ -$.

So, let the solubility of $\left[ {A{g^ + }} \right] = \left[ {I{O_3}^ - } \right] = s$.
$\begin{gathered} AgI{O_3} \to A{g^ + } + I{O_3}^ - \\ {\text{s 0 0}} \\ {\text{0 s s}} \\ \end{gathered}$.

Therefore, ${K_{sp}} = \left( s \right)\left( s \right) = {s^2}$---------2
Equating eq. 1 and 2 we get,
$\begin{gathered} {s^2} = 1.0 \times {10^{ - 8}} \\ or,s = {10^{ - 4}}mol/L \\ \end{gathered}$.
So, $\left[ {AgI{O_3}} \right] = s = {10^{ - 4}}mol/L$
Given, volume of solution =100 ml=0.1L

Let the number of moles of $AgI{O_3}$ be n.
$\begin{gathered} \dfrac{n}{{0.1}} = {10^{ - 4}} \\ or,n = {10^{ - 5}} \\ \end{gathered}$

Also, given molar mass of $AgI{O_3}$= 283
Let the mass of $AgI{O_3}$ be x.
$\begin{gathered} \dfrac{x}{{283}} = {10^{ - 5}} \\ or,x = 283 \times {10^{ - 5}} \\ or,x = 2.83 \times {10^{ - 3}}g \\ \end{gathered}$

Hence, from the above calculation we can easily conclude that option B is the correct option to the given question.

Note:It should be remembered to you that if to the solution of a weak electrolyte which ionizes to a small extent, a strong electrolyte having a common ion is added which ionizes almost completely, the ionization of weak electrolyte is further suppressed.Similarly, if the solution of a sparingly soluble salt if a soluble salt having a common ion is added, the solubility of the sparingly soluble salt further decreases.