pH of weak acids — AP Chemistry
1. Core Concepts of Weak Acid Dissociation ★★☆☆☆ ⏱ 2 min
Unlike strong acids that dissociate completely in dilute solution, weak acids only partially dissociate, so equilibrium $[H_3O^+]$ cannot be directly equated to the initial weak acid concentration. This topic accounts for approximately 7-9% of total AP Chemistry exam points, and appears in both multiple-choice (MCQ) and free-response (FRQ) sections.
Standard AP exam notation: $[HA]_0$ = initial concentration of monoprotic weak acid before dissociation, $K_a$ = acid dissociation constant, and $x$ = equilibrium concentration of dissociated HA. For pure weak acid solutions, $[H_3O^+]_{eq} = [A^-]_{eq} = x$. A core tested concept: the pH of a weak acid is always higher than the pH of an equal concentration of strong acid, because less hydronium is produced from partial dissociation.
2. Acid Dissociation Constant ($K_a$) Expression ★★☆☆☆ ⏱ 3 min
For any monoprotic weak acid $HA$, dissociation in water follows the equilibrium:
HA(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq)
Liquid water is omitted from the equilibrium expression because its concentration is nearly constant in dilute solutions, and is absorbed into the equilibrium constant. The $K_a$ expression is defined as:
K_a = \frac{[H_3O^+]_{eq}[A^-]_{eq}}{[HA]_{eq}}
From dissociation stoichiometry and ICE tables, for a solution of pure weak acid: $[H_3O^+]_{eq} = [A^-]_{eq} = x$, and $[HA]_{eq} = [HA]_0 - x$. $K_a$ values are always small ($< 1$) for weak acids, with smaller $K_a$ corresponding to weaker acids.
Exam tip: When calculating $K_a$ from pH, always use the equilibrium concentration of $HA$, not just the initial concentration. Only simplify to initial concentration after confirming $x$ is negligible.
3. Approximation Method and 5% Validation Rule ★★★☆☆ ⏱ 4 min
Most weak acids have very small $K_a$ values, so $x = [H_3O^+]$ is much smaller than $[HA]_0$. This means $[HA]_0 - x \approx [HA]_0$, which simplifies the $K_a$ expression to:
K_a \approx \frac{x^2}{[HA]_0} \implies x = [H_3O^+] = \sqrt{K_a \times [HA]_0}
This approximation drastically reduces calculation time, valuable for both MCQ and FRQ. The AP Chemistry standard for validation is the 5% rule: if $\frac{x}{[HA]_0} \times 100\% \leq 5\%$, the approximation is acceptable. If greater than 5%, you must solve the full quadratic equation for an accurate result.
Exam tip: AP FRQ graders require explicit 5% rule validation when you use the approximation method. Always write out the validation step to earn full credit, even if the approximation is obviously valid.
4. Quadratic Solution for Non-Approximable Weak Acids ★★★★☆ ⏱ 3 min
When the 5% rule fails (usually when the weak acid has a relatively large $K_a$, or is very dilute), you must solve the exact form of the $K_a$ expression. Starting from the original relationship:
K_a = \frac{x^2}{[HA]_0 - x}
Rearrange this into standard quadratic form $ax^2 + bx + c = 0$:
x^2 + K_a x - K_a [HA]_0 = 0
Here, $a = 1$, $b = K_a$, $c = -K_a [HA]_0$. Solve using the quadratic formula:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Only the positive root is physically meaningful, since concentration cannot be negative. This method gives an exact value of $x$ with no approximation error.
Exam tip: Double-check the sign of the constant term $c$ when writing the quadratic; it is always negative for weak acid dissociation, which guarantees one positive and one negative root.
5. Percent Dissociation of Weak Acids ★★★☆☆ ⏱ 3 min
A key conceptual relationship frequently tested on the AP exam: for the same weak acid at the same temperature, percent dissociation increases as the acid is diluted. This follows Le Chatelier's principle: adding water (diluting) reduces the concentration of all species, so equilibrium shifts right to produce more moles of dissolved ions, increasing the fraction of dissociated acid. Unlike strong acids (100% dissociation, 10x dilution increases pH by 1 unit), 10x dilution of a weak acid increases pH by less than 1 unit because of increased percent dissociation.
Exam tip: For conceptual MCQ questions asking how percent dissociation changes with dilution, you do not need to calculate: remember *more dilute = higher percent dissociation* to answer instantly.
Common Pitfalls
Why: Students memorize the shortcut and forget to check if it applies, especially on time-pressured MCQ
Why: Students confuse strong vs weak acid behavior, especially for weak acids with large $K_a$ values
Why: Students rush through calculation and forget concentration cannot be negative
Why: Students apply strong acid dilution rules (100% dissociation always) to weak acids
Why: Students confuse general equilibrium expressions with acid dissociation constants that omit pure solvents
Why: Students forget that for most polyprotic acids, $K_{a1}$ is thousands of times larger than $K_{a2}$