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# Solubility of salt ${A_2}{B_3}$, is $\;1 \times {10^{ - 4}}$its solubility product isOptionA.$\;1.08 \times {10^{ - 18}}$B.$\;1.08 \times {10^{ - 13}}$C.$\;1.08 \times {10^{ - 15}}$D.$\;1.08 \times {10^{ - 17}}$

Last updated date: 23rd Jul 2024
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Hint:The ability of a substance called a solute to dissolve in a solvent and form a solution is known as solubility. Ionic compounds (which dissociate to form cations and anions) have a wide range of solubility in water. Some compounds are very soluble and can also absorb moisture from the air, while others are extremely insoluble.

The solubility product is a type of equilibrium constant whose value is temperature dependent. Due to enhanced solubility, ${K_{sp}}$ typically rises as the temperature rises. The ability of a substance called a solute to dissolve in a solvent and form a solution is known as solubility.
Solubility product is represented as
${K_{sp}} = {\left[ {{A^ + }} \right]^a}{\left[ {{B^ - }} \right]^b}$
${A_2}{B_3} \Leftrightarrow 2{A^{3 + }} + \quad 3{B^{2 - }}$
$2S \,\,\,\,\,\,\,\,\,\,\,\,\,\,\ 3S$
Substituting the value in ${K_{sp}}$
${K_{sp}} = {(2S)^2}{(3S)^3}$
2 x 2 x 3 x 3 x 3 = 108
Hence,
${K_{sp}} = 108{S^5}$
${K_{sp}} = 108 \times {\left( {{{10}^{ - 3}}} \right)^5}$
${K_{sp}} = 108 \times {10^{ - 15}}$
${K_{sp}} = 1.08 \times {10^{ - 13}}$

Hence option B Is correct.