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

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Last updated date: 23rd Jul 2024
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Answer
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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.

Complete answer:
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.

Additional information:
As a salt is dissolved in a solvent, the interactions between ions and the solvent must counteract the intense forces of attraction of the solute (lattice enthalpy of the ions).
Ions have a negative solvation enthalpy, which ensures that energy is released during the process.
The amount of energy released during solvation, known as solvation enthalpy, is determined by the composition of the solvent.

Note:
The solvation enthalpy of non-polar solvents is low, indicating that this energy is insufficient to resolve the lattice enthalpy. As a result, non-polar solvents cannot dissolve the salts. As a result, a salt's solvation enthalpy must be greater than its lattice enthalpy in order for it to dissolve in a solvent. Temperature affects solubility, and each salt has a unique value.