Key Points

Equilibrium in physical and chemical processes is dynamic, meaning forward and reverse reactions occur at equal rates, resulting in no net change in the concentrations of reactants and products. This state is only achievable in a closed system.

For a general reversible reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant $K_c$ is given by the expression $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$, where concentrations are equilibrium values.

For reactions involving gases, the equilibrium constant $K_p$ is expressed in terms of partial pressures. It is related to $K_c$ by the equation $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gaseous products minus gaseous reactants.

In heterogeneous equilibria, which involve reactants and products in different phases, the concentrations of pure solids and pure liquids are considered constant and are omitted from the equilibrium constant expression.

The reaction quotient $Q_c$ has the same expression as $K_c$ but uses non-equilibrium concentrations. If $Q_c < K_c$, the reaction proceeds forward; if $Q_c > K_c$, it proceeds in reverse; if $Q_c = K_c$, the system is at equilibrium.

If a change in concentration, pressure, or temperature is applied to a system at equilibrium, the system will shift in a direction that counteracts the change to re-establish equilibrium.

Increasing temperature favors the endothermic direction of a reaction, changing the value of K. A catalyst increases the rates of both forward and reverse reactions equally, allowing equilibrium to be reached faster without changing the equilibrium constant.

Arrhenius acids produce $H^+$ ions in water. Brønsted-Lowry acids are proton donors, while bases are proton acceptors. Lewis acids are electron-pair acceptors, and Lewis bases are electron-pair donors.

A conjugate acid-base pair consists of two species that differ by a single proton ($H^+$). For a weak acid HA, its conjugate base is $A^-$. A strong acid has a weak conjugate base, and vice versa.

The strength of a weak acid (HA) or a weak base (B) is quantified by its ionization constant, $K_a = \frac{[H^+][A^-]}{[HA]}$ for acids, and $K_b = \frac{[BH^+][OH^-]}{[B]}$ for bases.

Water undergoes autoionization ($2H_2O \rightleftharpoons H_3O^+ + OH^-$). The ionic product of water, $K_w = [H_3O^+][OH^-]$, has a value of $1.0 \times 10^{-14}$ at 298 K.

The pH scale measures the acidity of a solution and is defined as $pH = -\log[H_3O^+]$. For any aqueous solution at 298 K, $pH + pOH = 14$. Acidic solutions have $pH < 7$, and basic solutions have $pH > 7$.

For any conjugate acid-base pair, the product of their ionization constants equals the ionic product of water: $K_a \times K_b = K_w$. This implies that $pK_a + pK_b = pK_w = 14$ at 298 K.

The dissociation of a weak electrolyte is suppressed by the addition of a strong electrolyte containing a common ion. This is an application of Le Chatelier's principle.

A buffer solution resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base (e.g., $CH_3COOH$ and $CH_3COONa$) or a weak base and its conjugate acid.

The pH of an acidic buffer solution is calculated using the Henderson-Hasselbalch equation: $pH = pK_a + \log \frac{[\text{Conjugate Base}]}{[\text{Acid}]}$.

For a sparingly soluble salt, the solubility product, $K_{sp}$, is the equilibrium constant for the dissolution process. For a salt $A_xB_y$, the equilibrium is $A_xB_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$, and $K_{sp} = [A^{y+}]^x[B^{x-}]^y$.

Precipitation occurs if the ionic product (Q) of the salt exceeds its solubility product ($K_{sp}$). If $Q < K_{sp}$, more salt can dissolve; if $Q = K_{sp}$, the solution is saturated.