Equilibrium (Chemical + Ionic)

This chapter introduces the concept of equilibrium, a state reached by reversible chemical reactions where the rates of the forward and reverse reactions become equal. You will learn to describe this dynamic state quantitatively using the Law of Mass Action to derive the equilibrium constant, expressed in terms of concentration (Kc) or partial pressure (Kp). The chapter covers the relationship between these constants and how to calculate them from reaction data.

A significant part of the chapter is dedicated to Le Chatelier's principle, which predicts how an equilibrium system responds to changes in concentration, temperature, or pressure. Mastering this principle is about applying logic to predict the direction in which a reaction will shift to counteract a disturbance. The effect of catalysts and inert gases on equilibrium is also explained.

The chapter then extends these principles to ionic equilibrium in solutions. This section covers theories of acids and bases, the pH scale, and the ionization of weak electrolytes. The most challenging topics are often the calculation of pH for buffer solutions and during salt hydrolysis, and problems involving the solubility product (Ksp) of sparingly soluble salts. A strong foundation in stoichiometry and the mole concept is necessary to handle the calculations in this chapter.

Formulas for Equilibrium (Chemical + Ionic)

Equilibrium Constant in terms of Concentration (Kc): $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ For the reaction aA + bB ⇌ cC + dD. [X] is the molar concentration of X at equilibrium.
Equilibrium Constant in terms of Partial Pressures (Kp): $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$ P_X represents the partial pressure of gas X at equilibrium.
Relationship between Kp and Kc: $K_p = K_c (RT)^{\Delta n_g}$ Δn_g is the change in the number of moles of gaseous products and reactants.
Ionic Product of Water (Kw): $K_w = [H^+][OH^-]$ At 298 K (25°C), Kw is 1.0 x 10⁻¹⁴.
Definition of pH: $pH = -\log_{10}[H^+]$ [H⁺] is the molar concentration of hydrogen ions.
Relationship between pH and pOH: $pH + pOH = pK_w$ At 298 K, pH + pOH = 14.
Acid Dissociation Constant (Ka): $K_a = \frac{[H^+][A^-]}{[HA]}$ For a weak acid HA.
Base Dissociation Constant (Kb): $K_b = \frac{[B^+][OH^-]}{[BOH]}$ For a weak base BOH.
Relationship between Ka and Kb for a Conjugate Pair: $K_a \times K_b = K_w$ Applies to a conjugate acid-base pair.
Henderson-Hasselbalch Equation (Acidic Buffer): $pH = pK_a + \log_{10}\frac{[\text{Salt}]}{[\text{Acid}]}$ Calculates the pH of an acidic buffer solution. [Salt] and [Acid] are concentrations.
Solubility Product (Ksp): $K_{sp} = [A^{y+}]^x [B^{x-}]^y$ For a sparingly soluble salt A_x B_y. Concentrations are in a saturated solution.