JEE Chemistry Ionic Equilibrium Notes Set 04

Acid-Base Concepts

An Arrhenius acid gives H\(^+\) from its own molecule in water, and an Arrhenius base gives OH\(^-\). A Bronsted-Lowry acid is a proton donor and a base is a proton acceptor; removing H\(^+\) from an acid gives its conjugate base, and adding H\(^+\) to a base gives its conjugate acid. Species that can both give and take a proton (HCO\(_3^-\), H\(_2\)PO\(_4^-\), H\(_2\)O, HS\(^-\)) are amphiprotic. A Lewis acid accepts an electron pair (BF\(_3\), AlCl\(_3\), H\(^+\), Fe\(^{3+}\)) and a Lewis base donates one (NH\(_3\), F\(^-\), H\(_2\)O). Boric acid is not an Arrhenius acid; it behaves as a Lewis acid: \( \ce{B(OH)3 + 2H2O <=> B(OH)4^- + H3O^+} \).

The stronger an acid, the weaker its conjugate base: \( K_a \times K_b = K_w \) and \( pK_a + pK_b = 14 \) at 25 degrees C for a conjugate pair.

Water and the pH Scale

Water ionises slightly: \( K_w = [H^+][OH^-] = 10^{-14} \) at 25 degrees C. Since ionisation is endothermic, \( K_w \) rises with temperature, and both pH and pOH of pure water fall below 7 while the water stays neutral because \( [H^+] = [OH^-] \). Always use \( pH + pOH = pK_w \), and \( pH = -\log[H^+] \).

When \( \alpha \) is larger than 10 percent, solve the quadratic \( K = C\alpha^2/(1 - \alpha) \). A strong acid diluted so that its concentration approaches \( 10^{-7} \) M gives a pH close to, but never above, 7, because water supplies its own H\(^+\).

Salt Hydrolysis

Salts of a strong acid and strong base (NaCl) give neutral solutions. For the salt of a weak acid and a strong base, \( K_h = K_w/K_a \), \( h = \sqrt{K_h/C} \) and \( pH = \frac12(pK_w + pK_a + \log C) \). For the salt of a strong acid and a weak base, \( pH = \frac12(pK_w - pK_b - \log C) \). For the salt of a weak acid and a weak base, \( pH = \frac12(pK_w + pK_a - pK_b) \), independent of concentration, and the degree of hydrolysis is also independent of concentration.

Buffer Solutions

A buffer resists a change in pH when small amounts of acid or base are added. It contains a weak acid with its conjugate base (or a weak base with its conjugate acid). It can be made directly by mixing the two forms, or by partly neutralising the weak acid with a strong base (acid in excess), or the weak base with a strong acid (base in excess).

Acidic buffer: \( pH = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]} \). Basic buffer: \( pOH = pK_b + \log\frac{[\text{salt}]}{[\text{base}]} \). When the two forms are equal, pH equals \( pK_a \) (or pOH equals \( pK_b \)), and the buffer works best within one pH unit of this value.

Solubility Product

For a sparingly soluble salt \( A_xB_y \) with molar solubility s, \( K_{sp} = (xs)^x (ys)^y \), so \( K_{sp} = s^2 \) for AB, \( 4s^3 \) for AB\(_2\) or A\(_2\)B, \( 27s^4 \) for AB\(_3\) and \( 108s^5 \) for A\(_3\)B\(_2\). Precipitation begins when the ionic product exceeds \( K_{sp} \). A common ion lowers the solubility, found from \( K_{sp} \) with the common ion at its added concentration. Salts of weak acids (carbonates, sulphides, hydroxides) dissolve more in acidic solution, and complex formation (for example Ag\(^+\) with NH\(_3\)) also increases solubility.

When several anions compete for the same cation, the one needing the smaller cation concentration, \( K_{sp}/C \) (adjusted for the formula type), precipitates first. Only compare \( K_{sp} \) values directly for salts of the same formula type.