JEE Chemistry Ionic Equilibrium Notes Set 02

Electrolytes and Degree of Dissociation

An electrolyte is a substance that conducts electricity in solution because it splits into free ions. Strong electrolytes (strong acids, strong bases and most salts) ionise almost completely. Weak electrolytes (acetic acid, ammonia, most organic acids and bases) ionise only partly, and an equilibrium exists between the ions and the unionised molecules.

The degree of dissociation \( \alpha \) is the fraction of the dissolved electrolyte that has ionised. It rises with dilution, rises with temperature, and falls when a common ion is present.

Ostwald's Dilution Law

For a weak monobasic acid HA of concentration C, \( K_a = \dfrac{C\alpha^2}{1-\alpha} \). If \( \alpha \) is small, \( K_a \approx C\alpha^2 \), so \( \alpha = \sqrt{K_a/C} \) and \( [H^+] = C\alpha = \sqrt{K_a C} \). The same holds for a weak base with \( K_b \) and \( [OH^-] \). If the degree of dissociation is not small (above about 5 percent), solve the quadratic instead.

Acids and Bases

A conjugate acid-base pair differs by one proton, as in NH4+ and NH3. The stronger the acid, the weaker its conjugate base, and \( K_a \times K_b = K_w \) for a conjugate pair. Species that can both give and take a proton, such as H2O, HCO3- and H2PO4-, are called amphiprotic.

Water, pH and pOH

1. Water ionises slightly: \( 2H_2O \rightleftharpoons H_3O^+ + OH^- \). The ionic product \( K_w = [H^+][OH^-] \) is \( 10^{-14} \) at 25 C and rises with temperature (about \( 10^{-12} \) at 90 C).
2. \( pH = -\log[H^+] \), \( pOH = -\log[OH^-] \) and \( pH + pOH = pK_w \) (14 at 25 C).
3. Neutral water has \( [H^+] = [OH^-] \). Its pH is 7 only at 25 C, and it is lower at higher temperatures.
4. A pH change of one unit means a tenfold change in [H+].
5. If the acid concentration is near \( 10^{-7} \) M, include the H+ from water: for a strong acid of concentration c, \( [H^+] = \dfrac{c + \sqrt{c^2 + 4K_w}}{2} \). A strong acid can never give a pH above 7.

Strong and Weak Acid or Base Solutions

When equal volumes of two strong acids are mixed, add the moles of H+ and divide by the total volume. To mix an acid and a base, subtract the moles, then find the excess.

Polyprotic Acids and Bases

A polyprotic acid ionises in steps, with \( K_1 \gg K_2 \gg K_3 \). For H2A the [H+] comes almost entirely from the first step. The concentration of the dianion is nearly equal to \( K_2 \) when [H+] and [HA-] are almost equal. For the whole reaction \( H_2A \rightleftharpoons 2H^+ + A^{2-} \), \( K = K_1 K_2 \). When extra H+ is present, \( [A^{2-}] = \dfrac{K_1K_2[H_2A]}{[H^+]^2} \), which is how the sulphide concentration is controlled in qualitative analysis.

Worked Examples

1. pH of 0.1 M acetic acid, \( K_a = 1.8\times10^{-5} \): \( [H^+] = \sqrt{1.8\times10^{-6}} = 1.34\times10^{-3} \) M, so pH = 2.87.
2. [H+] in 0.01 M HCl plus 0.01 M acetic acid is almost 0.01 M, because HCl suppresses the ionisation of acetic acid.
3. pH of a solution containing 0.1 M HA (\( K_a = 10^{-5} \)) and 0.1 M HCl: \( [H^+] \approx 0.1 \) M, so pH = 1.