Chemical Equilibrium and Solubility Product Constants: Study Notes

Chemical Equilibrium

Introduction to Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant, K, quantifies the ratio of product and reactant concentrations at equilibrium.

• Dynamic Equilibrium: Both forward and reverse reactions continue, but concentrations remain unchanged.

• Equilibrium Constant (K): For a general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant is:

$K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Applications: Predicting reaction direction, calculating equilibrium concentrations, and understanding reaction yields.

Calculating Equilibrium Concentrations

To determine equilibrium concentrations, use initial concentrations and changes (often denoted as 'x') based on stoichiometry. The ICE (Initial, Change, Equilibrium) table is a common tool.

• ICE Table: Organizes initial concentrations, changes during reaction, and equilibrium concentrations.

• Example: For $I_2(aq) + I^-(aq) \rightleftharpoons I_3^-(aq)$, if initial concentrations and equilibrium values are given, set up the ICE table and solve for unknowns.

Sample Calculation:

• Initial: $[I_2] = 1.0 \times 10^{-3}$ M, $[I^-] = 1.0 \times 10^{-3}$ M, $[I_3^-] = 0$

• Change: $-x$, $-x$, $+x$

• Equilibrium: $[I_2] = 1.0 \times 10^{-3} - x$, $[I^-] = 1.0 \times 10^{-3} - x$, $[I_3^-] = x$

• Use equilibrium concentrations to solve for $K$:

$K = \frac{[I_3^-]}{[I_2][I^-]}$

Equilibrium with Gaseous Reactions

For reactions involving gases, equilibrium constants can be expressed in terms of concentration ($K_c$) or pressure ($K_p$).

• Example: $N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$

• Given $K_c$ and equilibrium concentrations of $N_2$ and $O_2$, calculate $[NO]$:

$K_c = \frac{[NO]^2}{[N_2][O_2]}$

Weak Acid Equilibrium

Weak acids partially dissociate in water, and their equilibrium is described by the acid dissociation constant, $K_a$.

• Example: $HCN(aq) \rightleftharpoons H^+(aq) + CN^-(aq)$

• Set up ICE table with initial concentration of HCN, and solve for equilibrium concentrations using $K_a$:

$K_a = \frac{[H^+][CN^-]}{[HCN]}$

• For small $K_a$, the change $x$ is often much less than the initial concentration, allowing the 5% approximation: $[HCN]_{eq} \approx [HCN]_{initial}$

Solubility Equilibria

Dissolution and Precipitation

Dissolution: An ionic compound dissolves in water to form ions. Precipitation: Formation of a solid ionic compound from its ions in solution.

• Example Dissolution: $AgCl(s) \rightarrow Ag^+(aq) + Cl^-(aq)$

• Example Precipitation: $Mg^{2+}(aq) + PO_4^{3-}(aq) \rightarrow Mg_3(PO_4)_2(s)$

Solubility Product Constant (Ksp)

The solubility product constant, $K_{sp}$, is the equilibrium constant for the dissolution of a sparingly soluble ionic compound.

• General Form: For $A_mB_n(s) \rightleftharpoons mA^{n+}(aq) + nB^{m-}(aq)$:

$K_{sp} = [A^{n+}]^m [B^{m-}]^n$

• Application: Predicting solubility, calculating ion concentrations, and determining if precipitation will occur.

Writing Dissolution Equations and Ksp Expressions

• Example: For $Ag_2CrO_4$:

Dissolution: $Ag_2CrO_4(s) \rightleftharpoons 2Ag^+(aq) + CrO_4^{2-}(aq)$ $K_{sp} = [Ag^+]^2 [CrO_4^{2-}]$

• Example: For $Mg(NH_4)PO_4$:

Dissolution: $Mg(NH_4)PO_4(s) \rightleftharpoons Mg^{2+}(aq) + NH_4^+(aq) + PO_4^{3-}(aq)$ $K_{sp} = [Mg^{2+}][NH_4^+][PO_4^{3-}]$

Calculating Ksp from Molar Solubility

Given the molar solubility of a compound, use stoichiometry to determine ion concentrations and calculate $K_{sp}$.

• Example: For $Ag_2SO_4$ with molar solubility $s$:

$Ag_2SO_4(s) \rightleftharpoons 2Ag^+(aq) + SO_4^{2-}(aq)$ $[Ag^+] = 2s$, $[SO_4^{2-}] = s$ $K_{sp} = [Ag^+]^2 [SO_4^{2-}] = (2s)^2 (s) = 4s^3$

Summary Table: Key Equilibrium Expressions

Reaction	Equilibrium Expression
$I_2(aq) + I^-(aq) \rightleftharpoons I_3^-(aq)$	$K = \frac{[I_3^-]}{[I_2][I^-]}$
$N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$	$K_c = \frac{[NO]^2}{[N_2][O_2]}$
$HCN(aq) \rightleftharpoons H^+(aq) + CN^-(aq)$	$K_a = \frac{[H^+][CN^-]}{[HCN]}$
$Ag_2CrO_4(s) \rightleftharpoons 2Ag^+(aq) + CrO_4^{2-}(aq)$	$K_{sp} = [Ag^+]^2 [CrO_4^{2-}]$
$Mg(NH_4)PO_4(s) \rightleftharpoons Mg^{2+}(aq) + NH_4^+(aq) + PO_4^{3-}(aq)$	$K_{sp} = [Mg^{2+}][NH_4^+][PO_4^{3-}]$

Key Terms and Concepts

• Equilibrium Constant (K, Kc, Kp): Quantifies the ratio of product to reactant concentrations at equilibrium.

• ICE Table: Tool for organizing initial, change, and equilibrium concentrations.

• Solubility Product Constant (Ksp): Equilibrium constant for the dissolution of sparingly soluble salts.

• 5% Approximation: Used when the change in concentration is much less than the initial concentration, simplifying calculations.

Example Problems

• Calculate the equilibrium constant for a reaction given initial and equilibrium concentrations.

• Determine equilibrium concentrations using ICE tables and equilibrium expressions.

• Write dissolution equations and $K_{sp}$ expressions for ionic compounds.

• Calculate $K_{sp}$ from molar solubility data.

Additional info: These notes expand on handwritten examples and problems, providing context and formulas for equilibrium and solubility calculations relevant to General Chemistry chapters on chemical equilibrium and solubility equilibria.