Solubility Product Constant — Revision Notes

⚡ 30-Second Revision

Equilibrium: — $A_x B_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$
$K_{sp}$ Expression: — $K_{sp} = [A^{y+}]^x [B^{x-}]^y$
$K_{sp}$ vs. $s$ (Molar Solubility):**

- AB type: $K_{sp} = s^2 implies s = sqrt{K_{sp}}$ - $AB_2$/$A_2B$ type: $K_{sp} = 4s^3 implies s = sqrt[3]{K_{sp}/4}$ - $A_x B_y$ type: $K_{sp} = x^x y^y s^{(x+y)}$

Ionic Product ($Q_{sp}$): — Same form as $K_{sp}$ but with non-equilibrium concentrations.
Precipitation Prediction:

- $Q_{sp} < K_{sp}$: Unsaturated, no precipitation. - $Q_{sp} = K_{sp}$: Saturated, equilibrium. - $Q_{sp} > K_{sp}$: Supersaturated, precipitation occurs.

Common Ion Effect: — Decreases solubility ($s$), but $K_{sp}$ remains constant.
pH Effect: — Affects solubility of hydroxides, carbonates, etc. (e.g., acidic pH increases $Mg(OH)_2$ solubility).
Temperature: — $K_{sp}$ is temperature-dependent.

2-Minute Revision

The Solubility Product Constant ($K_{sp}$) is a crucial concept for sparingly soluble ionic compounds, representing the equilibrium between the undissolved solid and its ions in a saturated solution. For a general salt $A_x B_y$, the equilibrium is $A_x B_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$, and $K_{sp} = [A^{y+}]^x [B^{x-}]^y$.

Molar solubility ($s$) is the concentration of the dissolved salt. The relationship between $K_{sp}$ and $s$ depends on stoichiometry: $s = sqrt{K_{sp}}$ for AB type, and $s = sqrt[3]{K_{sp}/4}$ for $AB_2$ or $A_2B$ type salts.

A key distinction for NEET is that a larger $K_{sp}$ doesn't always mean higher solubility if stoichiometries differ; always calculate $s$ for comparison. The Common Ion Effect significantly reduces the solubility of a sparingly soluble salt by shifting the equilibrium, but it does not change $K_{sp}$.

The Ionic Product ($Q_{sp}$) is used to predict precipitation: if $Q_{sp} > K_{sp}$, precipitation occurs. pH also affects the solubility of salts with acidic or basic ions. Remember that $K_{sp}$ is temperature-dependent.

5-Minute Revision

The Solubility Product Constant ($K_{sp}$) is an equilibrium constant specific to the dissolution of sparingly soluble ionic compounds. When a salt like $A_x B_y$ dissolves, it sets up a dynamic equilibrium: $A_x B_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$. The $K_{sp}$ is defined as the product of the molar concentrations of the ions, each raised to its stoichiometric coefficient: $K_{sp} = [A^{y+}]^x [B^{x-}]^y$. The solid reactant is omitted from the expression.

Molar solubility ($s$) is the concentration of the dissolved salt in a saturated solution. The relationship between $K_{sp}$ and $s$ is stoichiometry-dependent:

For $AB$ type salts (e.g., AgCl): $K_{sp} = s^2$. If $K_{sp} = 1.8 \times 10^{-10}$, then $s = sqrt{1.8 \times 10^{-10}} = 1.34 \times 10^{-5}$ M.
For $AB_2$ or $A_2B$ type salts (e.g., $CaF_2$, $Ag_2CrO_4$): $K_{sp} = 4s^3$. If $K_{sp} = 3.9 \times 10^{-11}$ for $CaF_2$, then $s = sqrt[3]{3.9 \times 10^{-11}/4} = 2.13 \times 10^{-4}$ M.

Key Factors Affecting Solubility:

1
Common Ion Effect: — Adding a soluble salt with a common ion to a saturated solution of a sparingly soluble salt decreases the solubility of the latter. For example, adding NaCl to AgCl solution reduces AgCl solubility. The $K_{sp}$ value itself remains constant.
2
pH: — The solubility of salts with basic anions (like $OH^-$, $CO_3^{2-}$, $S^{2-}$) increases in acidic solutions because $H^+$ ions react with the basic anions, shifting the equilibrium towards dissolution. For $Mg(OH)_2$, $Mg(OH)_2(s) \rightleftharpoons Mg^{2+}(aq) + 2OH^-(aq)$. In acid, $H^+$ consumes $OH^-$, increasing solubility.
3
Complex Ion Formation: — If one of the ions can form a stable complex with another species, solubility can increase (e.g., AgCl dissolves in $NH_3$ due to $[Ag(NH_3)_2]^+$ formation).

Predicting Precipitation: The Ionic Product ($Q_{sp}$) is calculated using current ion concentrations.

If $Q_{sp} < K_{sp}$: Solution is unsaturated, no precipitation.
If $Q_{sp} = K_{sp}$: Solution is saturated, at equilibrium.
If $Q_{sp} > K_{sp}$: Solution is supersaturated, precipitation occurs until $Q_{sp} = K_{sp}$.

NEET Tip: Always calculate molar solubility ($s$) when comparing the solubilities of salts with different stoichiometries, as a higher $K_{sp}$ does not always imply higher solubility. Be meticulous with dilution calculations when predicting precipitation.

Prelims Revision Notes

The Solubility Product Constant ($K_{sp}$) is an equilibrium constant for sparingly soluble ionic compounds. For $A_x B_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$, $K_{sp} = [A^{y+}]^x [B^{x-}]^y$. The solid is excluded. $K_{sp}$ is temperature-dependent.

Molar Solubility ($s$) vs. $K_{sp}$:

AB type (e.g., AgCl, BaSO$_4$): — $K_{sp} = s^2$. $s = sqrt{K_{sp}}$.
$AB_2$ type (e.g., $CaF_2$, $PbCl_2$): — $K_{sp} = s(2s)^2 = 4s^3$. $s = sqrt[3]{K_{sp}/4}$.
$A_2B$ type (e.g., $Ag_2CrO_4$, $Cu_2S$): — $K_{sp} = (2s)^2s = 4s^3$. $s = sqrt[3]{K_{sp}/4}$.
$A_x B_y$ general type: — $K_{sp} = x^x y^y s^{(x+y)}$. $s = sqrt[x+y]{\frac{K_{sp}}{x^x y^y}}$.

Common Ion Effect: The solubility ($s$) of a sparingly soluble salt decreases in the presence of a common ion. $K_{sp}$ remains constant. Example: $PbCl_2$ solubility decreases in NaCl solution. When calculating, approximate the common ion concentration from the strong electrolyte if its concentration is much higher than $s$.

**Ionic Product ($Q_{sp}$):** Calculated using current ion concentrations. Used to predict precipitation:

$Q_{sp} < K_{sp}$: Unsaturated, no precipitate.
$Q_{sp} = K_{sp}$: Saturated, equilibrium.
$Q_{sp} > K_{sp}$: Supersaturated, precipitation occurs.

Effect of pH: Solubility of metal hydroxides ($M(OH)_n$) increases in acidic solutions (lower pH) because $H^+$ consumes $OH^-$, shifting equilibrium to the right. Solubility of salts with basic anions (e.g., $CO_3^{2-}$, $S^{2-}$) also increases in acidic solutions.

Comparing Solubilities: Only compare $K_{sp}$ values directly for salts of the *same* stoichiometric type. For different stoichiometries, calculate and compare their molar solubilities ($s$).

Calculations: Be proficient with roots and exponents. Remember to account for dilution when mixing solutions to calculate initial ion concentrations for $Q_{sp}$.

Vyyuha Quick Recall

KSP: Keep Solubility Predictions.

K is for Konstant (at a given T). S is for Stoichiometry (affects $s$ vs $K_{sp}$ relation). P is for Precipitation (compare $Q_{sp}$ with $K_{sp}$).

And remember Common Ion Effect: CIE = Causes Ion Excess, Equilibrium shifts left, Solubility Decreases (SD).