Solubility And Solubility Product
Solubility is the ability of a substance to dissolve in a solvent, resulting in a solution.
Solubility refers to the amount of a substance that can be dissolved in a given volume of solvent at a specified temperature. The solubility of a substance is affected by the nature of the substance, the solvent, the temperature, and the presence of any common ions.
Substances with very low solubility such as AgCl and BaSO4 are sparingly soluble in water. Despite this, they can still form a saturated solution as they are ionic substances and the ions are in equilibrium with the undissolved solid.
\(\begin{array}{l}Ag^+Cl^- \rightleftharpoons AgCl\end{array} \)
(Undissolved) (Dissolved)
The equilibrium constant of dissociation, (K_c) is given by:
$$K_c = \frac{{[Ag^+]}}{{[Cl^-]}} \div {[AgCl]}$$
Silver chloride being solid, the concentration is assumed to be constant, thus allowing for the consideration of a new equilibrium constant.
(\begin{array}{l}\text{The solubility product, }K_{sp}\text{, is equal to the equilibrium constant, }K_c\text{, multiplied by the product of the concentration of the ions, }\left[ A{{g}^{+}} \right]\left[ C{{l}^{-}} \right]\text{, in the reaction }AgCl \rightarrow A{{g}^{+}} + C{{l}^{-}}\end{array})
For a salt with a low solubility of the general formula, AxBy
(\begin{array}{l}xA^y(aq) + yB^x-(aq) \rightleftharpoons AxBy(s)\end{array} )
(\begin{array}{l}Ksp=\left[xA^{y+}\right]\left[yB^{x-}\right]^{y}\end{array} )
The substance’s value remains constant and only fluctuates with temperature.
Significance of Solubility Product
The presence of a common ion may influence the equilibrium and, consequently, the concentration (solubility); however, it will not affect the solubility product.
When the ionic product exceeds the Ksp, the solutes precipitate.
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(\begin{array}{l}xA^{Y+}+yB^{x-}\rightleftharpoons AxBy\end{array} )
At Equilibrium: C, Cx, Cy
[Ksp] = [[xAY+]]$\times$[[yBx-]]$\times$[[Cx]]$\times$[[Cy]] = [[C]]$\times$[x]$\times$[[C]]$\times$[y]$\times$[x]$\times$[y]
Ksp = [C]x+y [x]x [y]y
Ksp = [C]x+y [x]x [y]y
where C is the solubility in mole/L
(\begin{array}{l}\text{Solubility}= [S]^{x+y}=\frac{K_{sp}}{x^{x}y^{y}}\end{array})
(\begin{array}{l}2Ag^{+}+CrO_{4}^{2-}\rightleftharpoons Ag_2CrO_4\end{array})
Ksp = $(2S)^2 \quad S = \frac{4S^3}{1}$
Also Read:
pH Change By Common-Ion Effect
Ionic Equilibrium - Degree of Ionization and Dissociation
Equilibrium Constant - Characteristics and Applications
