[tex]K_{sp}[/tex] of the compound is found to be 5.04 ×[tex]10^{-10}[/tex].
Solubility :Solubility can be define as the amount of a substance that dissolves or mixes in a given amount of solvent at specific conditions.
Solubility equilibrium
Ksp = [tex][A^{+} ]^{a}[/tex] [tex][B^{-} ]^{b}[/tex]
Ksp = solubility product constant
A+ = cation in an aquious solution
B- = anion in an aqueous solution
a, b = relative concentrations of a and b
Given,
Solubility = s = 3.60 × [tex]10^{-2}[/tex] g/L
molar mass = 288 g/ mol
∴ s= 3.60 × [tex]10^{-2}[/tex] g/L ÷ 288 g/ mol = 1.25 ×[tex]10^{-4}[/tex] mol/ L
Reaction:
MX3 ⇄ M + 3X
s 3s
[tex]K_{sp}[/tex] =[ [tex]M^{+3}[/tex]] [ [tex]X^{-1}[/tex][tex]]^{3}[/tex] = solubility product
∴ [tex]K_{sp}[/tex] =[tex][s]^{} [3s]^{3}[/tex]
∴ [tex]K_{sp}[/tex] = 3 [tex]s^{4}[/tex]
∴ [tex]K_{sp}[/tex] = 3 × (3.60 × [tex]10^{-2}[/tex] [tex])^{4}[/tex]
∴ [tex]K_{sp}[/tex] = 503.8848 ×[tex]10^{-8}[/tex] = 5.04 ×[tex]10^{-10}[/tex]
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