Acid-Base Equilibria and Buffer Solutions: Study Notes for Organic Chemistry

Acid-Base Equilibria

Ortho Phosphoric Acid and Dissociation Constants

Ortho phosphoric acid (H3PO4) is a triprotic acid, meaning it can donate three protons (H+) in aqueous solution. Each dissociation step has its own equilibrium constant:

• Ka1: $\mathrm{H_3PO_4 (aq) \rightleftharpoons H^+ (aq) + H_2PO_4^- (aq)}$

• Ka2: $\mathrm{H_2PO_4^- (aq) \rightleftharpoons H^+ (aq) + HPO_4^{2-} (aq)}$

• Ka3: $\mathrm{HPO_4^{2-} (aq) \rightleftharpoons H^+ (aq) + PO_4^{3-} (aq)}$

The order of acid strength is: $K_{a1} > K_{a2} > K_{a3}$, meaning the first proton is the easiest to remove.

Calculating Concentrations in Acid Solutions

Using Dissociation Constants

For a solution of 0.1 M H3PO4 with $K_{a1} = 10^{-2}$, the concentration of H+ ions can be estimated using the formula:

• $K_a = \frac{[H^+][A^-]}{[HA]}$

• Assume $[H^+] \approx [A^-]$ and $[HA] \approx$ initial concentration if dissociation is small.

For polyprotic acids, only the first dissociation is significant for calculating [H+] in dilute solutions.

Polyprotic Acids and Successive Ionization

Negligibility of Higher Ionizations

In aqueous solutions, the second and third ionizations of polyprotic acids are often negligible compared to the first, due to much smaller $K_a$ values.

• Key Point: The effect of OH- ions produced from higher ionizations is minimal.

• Example: For H3PO4, $K_{a1} \gg K_{a2} \gg K_{a3}$.

Buffer Solutions

Preparation and Calculation

Buffers are solutions that resist changes in pH upon addition of small amounts of acid or base. They are typically made from a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Henderson-Hasselbalch Equation:

$\mathrm{pH = pK_a + \log \left(\frac{[A^-]}{[HA]}\right)}$

• Example: Mixing 0.1 M acetic acid and 0.1 M sodium acetate forms a buffer with pH near the pKa of acetic acid.

Salt Hydrolysis and pH of Salt Solutions

Types of Salts and Their Hydrolysis

Salts can be classified based on the acid and base from which they are derived:

• Strong acid + strong base: Neutral solution

• Strong acid + weak base: Acidic solution

• Weak acid + strong base: Basic solution

• Weak acid + weak base: pH depends on relative strengths

Hydrolysis of salts can produce acidic or basic solutions depending on the ions present.

Dissociation Constants and Relationships

Acid and Base Dissociation

The dissociation constant of an acid ($K_a$) and its conjugate base ($K_b$) are related by:

$K_a \times K_b = K_w$

where $K_w$ is the ionic product of water ($1.0 \times 10^{-14}$ at 25°C).

Calculating pH and Ion Concentrations

Using $K_a$, $K_b$, and Concentrations

To calculate pH or ion concentrations in solutions:

• Use the appropriate equilibrium expression for the acid or base.

• For strong acids/bases, assume complete dissociation.

• For weak acids/bases, use $K_a$ or $K_b$ and initial concentration to solve for [H+] or [OH-].

Example: For a 0.01 M solution of BOH (a strong base), $[OH^-] = 0.01$ M, and $pOH = -\log[OH^-]$.

Tables: Dissociation Constants and pH Values

Comparison of $K_a$ and $K_b$ Values

Acid/Base	$K_a$ or $K_b$	pKa or pKb
Acetic Acid	$1.69 \times 10^{-5}$	4.77
H3PO4 (1st dissociation)	$7.2 \times 10^{-3}$	2.14
H2SO4 (1st dissociation)	Very large (strong acid)	~0
NH4OH	$1.8 \times 10^{-5}$	4.74

Additional info: Table values inferred from standard acid/base tables for common organic and inorganic acids/bases.

Summary of Key Equations

• $K_a = \frac{[H^+][A^-]}{[HA]}$

• $K_b = \frac{[OH^-][BH^+]}{[B]}$

• $K_a \times K_b = K_w$

• $\mathrm{pH = -\log[H^+]}$

• $\mathrm{pOH = -\log[OH^-]}$

• $\mathrm{pH + pOH = 14}$

• Henderson-Hasselbalch: $\mathrm{pH = pK_a + \log \left(\frac{[A^-]}{[HA]}\right)}$

Applications in Organic Chemistry

• Understanding acid-base equilibria is essential for predicting reaction outcomes, especially in synthesis and mechanism studies.

• Buffer solutions are crucial in maintaining pH during organic reactions and in biological systems.

• Salt hydrolysis explains the behavior of organic salts in water, affecting solubility and reactivity.