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In a sautrated solution of the sparingly soluble strong electrolyte $\mathrm{AgIO}_3$ (Molecular mass $=283$) the equilibrium which sets in is
$\mathrm{AgIO}_{3(\mathrm{s})} \rightleftharpoons \mathrm{Ag}_{(\mathrm{aq})}^{+}+\mathrm{IO}_{3(\mathrm{aq})}^{-}$
If the solubility product constant $\mathrm{K}_{\mathrm{sp}}$ of $\mathrm{AgIO}_3$ at a given temperature is $1.0 \times 10^{-8}$, what is the mass of $\mathrm{AgIO}_3$ contained in $100 \mathrm{~ml}$ of its saturated solution?
Options:
$\mathrm{AgIO}_{3(\mathrm{s})} \rightleftharpoons \mathrm{Ag}_{(\mathrm{aq})}^{+}+\mathrm{IO}_{3(\mathrm{aq})}^{-}$
If the solubility product constant $\mathrm{K}_{\mathrm{sp}}$ of $\mathrm{AgIO}_3$ at a given temperature is $1.0 \times 10^{-8}$, what is the mass of $\mathrm{AgIO}_3$ contained in $100 \mathrm{~ml}$ of its saturated solution?
Solution:
2387 Upvotes
Verified Answer
The correct answer is:
$2.83 \times 10^{-3} \mathrm{~g}$
$2.83 \times 10^{-3} \mathrm{~g}$
$\mathrm{AgIO}_3(\mathrm{s}) \rightleftharpoons \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{IO}_3^{-}(\mathrm{aq})$
Let the solubility of $\mathrm{AgIO}_3$ be $\mathrm{s}$
$\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{IO}_3^{-}\right]$
$1.0 \times 10^{-8}=\mathrm{s}^2$
$\mathrm{s}=10^{-4} \mathrm{~mol} / \mathrm{litre}$
$=\frac{10^{-4} \times 283}{1000} \times 100$
$=283 \times 10^{-5}$
$=2.83 \times 10^{-3} \mathrm{~g} / 100 \mathrm{~ml}$
Hence, (B) is correct.
Let the solubility of $\mathrm{AgIO}_3$ be $\mathrm{s}$
$\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{IO}_3^{-}\right]$
$1.0 \times 10^{-8}=\mathrm{s}^2$
$\mathrm{s}=10^{-4} \mathrm{~mol} / \mathrm{litre}$
$=\frac{10^{-4} \times 283}{1000} \times 100$
$=283 \times 10^{-5}$
$=2.83 \times 10^{-3} \mathrm{~g} / 100 \mathrm{~ml}$
Hence, (B) is correct.
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