Acid-Base & Equilibrium

Acid-Base Chemistry & Equilibrium

Part 1 of 5 — pH, pOH, $K_w$, and Strong vs. Weak Acids/Bases

The pH Scale

$\text{pH} = -\log[\text{H}^+]$ $\text{pOH} = -\log[\text{OH}^-]$ $\text{pH} + \text{pOH} = 14 \quad (\text{at } 25°\text{C})$

Ion product of water: $K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \quad (\text{at } 25°\text{C})$

Estimation trick: Each 1 pH unit = 10-fold change in $[\text{H}^+]$.

Strong Acids and Bases — 100% Dissociation

For strong acids/bases, $[\text{H}^+]$ or $[\text{OH}^-]$ = initial concentration.

Strong acids (memorize these 7):

• HCl, HBr, HI
• $\text{HNO}_3$, $\text{H}_2\text{SO}_4$ (first proton), $\text{HClO}_4$, $\text{HClO}_3$

Strong bases:

• Group 1 hydroxides: NaOH, KOH, LiOH
• Heavy Group 2 hydroxides: $\text{Ca(OH)}_2$, $\text{Ba(OH)}_2$, $\text{Sr(OH)}_2$

Example — Strong acid: $[\text{HCl}] = 0.010\text{ M}$

$[\text{H}^+] = 0.010\text{ M} = 10^{-2}\text{ M} \Rightarrow \text{pH} = 2$

Example — Strong base: $[\text{NaOH}] = 0.0010\text{ M}$

$[\text{OH}^-] = 0.0010\text{ M} = 10^{-3}\text{ M} \Rightarrow \text{pOH} = 3 \Rightarrow \text{pH} = 11$

Weak Acids and Bases — Partial Dissociation

Weak acids partially dissociate: $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$ $K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$

Weak bases partially accept protons: $\text{B} + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^-$ $K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}$

Conjugate acid-base relationship: $K_a \times K_b = K_w = 1.0 \times 10^{-14}$ $\text{p}K_a + \text{p}K_b = 14$

Stronger acid → weaker conjugate base. If $K_a$ is large, the acid is strong; its conjugate base is weak.

Approximation for Weak Acid pH

For a weak acid with initial concentration $C$ and $K_a$:

$[\text{H}^+] \approx \sqrt{K_a \times C}$

(Valid when $[\text{H}^+]/C < 5\%$ — the "5% rule")

Example: $0.100$ M acetic acid ($K_a = 1.8 \times 10^{-5}$):

$[\text{H}^+] = \sqrt{1.8 \times 10^{-5} \times 0.100} = \sqrt{1.8 \times 10^{-6}} = 1.34 \times 10^{-3}\text{ M}$

$\text{pH} = -\log(1.34 \times 10^{-3}) = 3 - \log(1.34) \approx 2.87$

pH, Strong/Weak Acids — MCAT Questions 🎯

Key Takeaways — Part 1

• $\text{pH} = -\log[\text{H}^+]$; $\text{pH} + \text{pOH} = 14$ at 25°C
• $K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}$
• Strong acids/bases dissociate 100% — $[\text{H}^+]$ equals initial concentration
• Memorize 7 strong acids: HCl, HBr, HI, $\text{HNO}_3$, $\text{H}_2\text{SO}_4$, $\text{HClO}_4$, $\text{HClO}_3$
• Weak acid approximation: $[\text{H}^+] \approx \sqrt{K_a C}$
• Conjugate pairs: $K_a \times K_b = K_w$; stronger acid → weaker conjugate base

Acid-Base Chemistry & Equilibrium

Part 2 of 5 — $K_a$, $K_b$, Henderson-Hasselbalch & Percent Dissociation

The Acid Dissociation Constant $K_a$

A larger $K_a$ means a stronger acid (more dissociation at equilibrium).

$\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$

$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$

$\text{p}K_a = -\log K_a \quad \Rightarrow \quad \text{lower } \text{p}K_a = \text{stronger acid}$

Typical $\text{p}K_a$ values to know:

Percent Dissociation

$\% \text{ dissociation} = \frac{[\text{H}^+]_{\text{eq}}}{[\text{HA}]_0} \times 100\%$

Key pattern: As concentration decreases, percent dissociation increases. Diluting a weak acid solution makes it dissociate to a greater percent (though $[\text{H}^+]$ decreases).

Henderson-Hasselbalch Equation

For a buffer (mixture of weak acid and its conjugate base):

$\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}$

Maximum buffering capacity occurs when $[\text{A}^-] = [\text{HA}]$, so $\text{pH} = \text{p}K_a$.

Practical range of a buffer: $\text{p}K_a \pm 1$ pH unit.

Worked Example

A buffer contains 0.100 M acetic acid and 0.200 M sodium acetate. $\text{p}K_a = 4.74$.

$\text{pH} = 4.74 + \log\frac{0.200}{0.100} = 4.74 + \log 2 = 4.74 + 0.30 = \mathbf{5.04}$

Since $[\text{A}^-] > [\text{HA}]$, pH > $\text{p}K_a$ — makes sense.

Polyprotic Acids

Polyprotic acids lose protons in steps; each step has a smaller $K_a$:

$K_{a1} \gg K_{a2} \gg K_{a3}$

Carbonic acid (physiologically relevant):

$\text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^- \quad K_{a1} = 4.3 \times 10^{-7}$ $\text{HCO}_3^- \rightleftharpoons \text{H}^+ + \text{CO}_3^{2-} \quad K_{a2} = 4.7 \times 10^{-11}$

For pH calculation, only $K_{a1}$ matters in practice (subsequent dissociations are negligible).

Amphiprotic Species

An amphiprotic species can act as either an acid or a base:

• $\text{H}_2\text{O}$ (acid/base of water)
• $\text{HCO}_3^-$ (acid: loses $H^{+}$ → $\text{CO}_3^{2-}$; base: gains $H^{+}$ → $\text{H}_2\text{CO}_3$)
• $\text{HPO}_4^{2-}$, $\text{H}_2\text{PO}_4^-$, amino acids

$K_a$, Henderson-Hasselbalch & Percent Dissociation 🎯

Key Takeaways — Part 2

• $K_a$ quantifies weak acid strength; $\text{p}K_a = -\log K_a$; lower $\text{p}K_a$ = stronger acid
• Henderson-Hasselbalch: $\text{pH} = \text{p}K_a + \log([\text{A}^-]/[\text{HA}])$
• Maximum buffering capacity at $\text{pH} = \text{p}K_a$ (equal acid and base concentrations)
• Diluting a weak acid: $[\text{H}^+]$ decreases, but percent dissociation increases
• Polyprotic acids: each successive $K_a$ is much smaller; only $K_{a1}$ governs pH
• Amphiprotic species can donate or accept protons (e.g., $\text{HCO}_3^-$, amino acids)

Acid-Base Chemistry & Equilibrium

Part 3 of 5 — Buffers: Mechanism, Capacity & Physiological Relevance

What Is a Buffer?

A buffer is a solution that resists changes in pH when small amounts of strong acid or strong base are added. It consists of:

• A weak acid (HA) and its conjugate base ($\text{A}^-$), OR
• A weak base (B) and its conjugate acid ($\text{BH}^+$)

How Buffers Work

When you add strong acid $(H^{+})$ to a buffer: $\text{H}^+ + \text{A}^- \to \text{HA}$

The added $H^{+}$ is consumed by the conjugate base — pH barely changes.

When you add strong base $(OH^{-})$ to a buffer: $\text{OH}^- + \text{HA} \to \text{A}^- + \text{H}_2\text{O}$

The added $OH^{-}$ is consumed by the weak acid — pH barely changes.

Buffer Capacity

Buffer capacity is the amount of acid or base the buffer can absorb before pH changes significantly.

Buffer capacity is highest when:

1. Concentrations of weak acid and conjugate base are large (more moles to react with added $H^{+}/OH^{-}$)
2. The ratio $[\text{A}^-]/[\text{HA}]$ is close to 1 (i.e., pH ≈ $pK_{a}$)

A buffer becomes ineffective when:

• The ratio $[\text{A}^-]/[\text{HA}]$ exceeds 10:1 or drops below 1:10
• This corresponds to the buffer range: $pK_{a}$ ± 1

Choosing a Buffer for a Target pH

Rule: Select a weak acid/base pair where $\text{p}K_a \approx$ target pH.

The Bicarbonate Buffer System (Blood)

The most important buffer in human physiology:

$\text{CO}_2(\text{aq}) + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$

Normal blood values: $\text{pH} = 7.40$; $[\text{HCO}_3^-] = 24\text{ mM}$; $P_{\text{CO}_2} = 40\text{ mmHg}$

Respiratory compensation: Changing breathing rate alters $\text{CO}_2$ levels:

• Hyperventilation → ↓$\text{CO}_2$ → ↑pH (alkalosis)
• Hypoventilation → ↑$\text{CO}_2$ → ↓pH (acidosis)

Metabolic disturbances: Change $[\text{HCO}_3^-]$ directly.

Buffers & Physiological Chemistry 🎯

Key Takeaways — Part 3

• Buffers resist pH change by consuming added $H^{+}$ $(via A^{-})$ or $OH^{-}$ (via HA)
• HH equation: $\text{pH} = \text{p}K_a + \log([\text{A}^-]/[\text{HA}])$
• Best buffering: $\text{pH} \approx \text{p}K_a$; effective range: $\text{p}K_a \pm 1$
• Buffer capacity increases with higher concentrations of buffer components
• Bicarbonate buffer controls blood pH 7.35-7.45; lungs control $\text{CO}_2$, kidneys control $\text{HCO}_3^-$
• Respiratory acidosis/alkalosis: problem with breathing; metabolic: problem with $[\text{HCO}_3^-]$

Acid-Base Chemistry & Equilibrium

Part 4 of 5 — Acid-Base Titrations

Titration Fundamentals

A titration adds a standard solution (titrant) of known concentration to an unknown solution until the reaction is complete (equivalence point).

$\text{moles acid} = \text{moles base at equivalence point}$

$M_a V_a = M_b V_b \quad (\text{for 1:1 reactions})$

For polyprotic acids, account for the proton-to-hydroxide ratio: $n_a M_a V_a = n_b M_b V_b$

Titration Curve Shapes

Strong Acid + Strong Base

• Before equivalence: pH calculated from excess strong acid
• At equivalence: pH = 7.00 (neutral salt, no hydrolysis)
• After equivalence: pH calculated from excess strong base
• Sharp endpoint; almost any indicator works

Weak Acid + Strong Base

• Initially: pH > 0 (weak acid partially dissociates)
• Buffer region: pH ≈ $pK_{a}$ when halfway to equivalence ("half-equivalence point")
• At half-equivalence: $[\text{HA}] = [\text{A}^-]$ → pH = $pK_{a}$ ← MCAT key fact
• At equivalence: pH > 7 (conjugate base hydrolyzes: $\text{A}^- + \text{H}_2\text{O} \rightleftharpoons \text{HA} + \text{OH}^-$)
• After equivalence: pH from excess strong base

Weak Base + Strong Acid

• At equivalence: pH < 7 (conjugate acid hydrolyzes)
• At half-equivalence: pOH = pKb, or equivalently pH = 14 − pKb = $pK_{a}$ of conjugate acid

Key Features of Titration Curves

Acid-Base Indicators

Indicators are weak acids (HIn) where HIn and $In^{-}$ are different colors:

$\text{HIn} \rightleftharpoons \text{H}^+ + \text{In}^-$

Color changes at pH ≈ $pK_{a}$ (indicator). The indicator transitions over ~pH = $pK_{a}$ ± 1.

Common indicators:

Choosing the right indicator: Pick one whose transition range includes the equivalence point pH.

• Strong acid + strong base: any indicator (equiv. point pH = 7)
• Weak acid + strong base: equivalence point pH > 7 → use phenolphthalein

Polyprotic Titrations

Titrating $\text{H}_2\text{CO}_3$ or $\text{H}_3\text{PO}_4$ with NaOH gives multiple equivalence points. The number of equivalence points = number of ionizable protons.

For $\text{H}_3\text{PO}_4$ + NaOH:

• 1st equiv. point: $\text{H}_3\text{PO}_4 \to \text{NaH}_2\text{PO}_4$
• 2nd equiv. point: $\text{NaH}_2\text{PO}_4 \to \text{Na}_2\text{HPO}_4$
• 3rd equiv. point: $\text{Na}_2\text{HPO}_4 \to \text{Na}_3\text{PO}_4$

Titrations & Indicators 🎯

Key Takeaways — Part 4

• At equivalence: moles acid = moles base; $M_aV_a = M_bV_b$ (for 1:1)
• Strong acid + strong base → equivalence pH = 7.00
• Weak acid + strong base → equivalence pH > 7 (conjugate base hydrolysis)
• Half-equivalence point: $[\text{HA}] = [\text{A}^-]$ → pH = $pK_{a}$ — most testable titration fact
• Indicators change color over ~$pK_{a}$ ± 1; choose so that transition includes equivalence pH
• Phenolphthalein: pH 8.2–10, good for weak acid titrations (equiv. pH > 7)
• Polyprotic acids give multiple equivalence points on the titration curve

Acid-Base Chemistry & Equilibrium

Part 5 of 5 — Equilibrium: $K_c$, $K_p$, Le Chatelier's Principle & $K_{sp}$

Equilibrium Constant Expressions

For a reaction: $a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$

$K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$

Rules:

• Pure solids and liquids: NOT included in $K$ expression
• Only gases and aqueous species are included
• $K > 1$: products favored; $K < 1$: reactants favored

$K_p$ vs $K_c$

For reactions involving gases: $K_p = K_c (RT)^{\Delta n}$

where $\Delta n = \text{moles gaseous products} - \text{moles gaseous reactants}$.

At constant temperature, $K_p = K_c$ when $\Delta n = 0$.

Reaction Quotient Q

$Q = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b} \quad (\text{at any point, not just equilibrium})$

Le Chatelier's Principle

If a system at equilibrium is disturbed, it shifts to partially counteract the disturbance.

Key distinction: Adding or removing species, changing pressure all shift equilibrium but do not change $K$. Only temperature changes $K$.

Solubility Product ($K_{sp}$)

For a sparingly soluble salt: $\text{MX}(s) \rightleftharpoons \text{M}^+(aq) + \text{X}^-(aq)$

$K_{sp} = [\text{M}^+][\text{X}^-]$

For $\text{CaF}_2(s) \rightleftharpoons \text{Ca}^{2+} + 2\text{F}^-$:

$K_{sp} = [\text{Ca}^{2+}][\text{F}^-]^2$

Molar solubility: If $s$ = moles dissolved per liter, then for $\text{CaF}_2$: $[\text{Ca}^{2+}] = s$ and $[\text{F}^-] = 2s$

$K_{sp} = (s)(2s)^2 = 4s^3$

Common Ion Effect

Adding a common ion (e.g., adding NaF to a $\text{CaF}_2$ solution) shifts equilibrium left, decreasing solubility.

Precipitation Criterion

• If $Q_{sp} > K_{sp}$: precipitation occurs (solution is supersaturated)
• If $Q_{sp} < K_{sp}$: no precipitate (solution is unsaturated)
• If $Q_{sp} = K_{sp}$: saturated, at equilibrium

Equilibrium, Le Chatelier & $K_{sp}$ 🎯

Acid-Base & Equilibrium — Complete Topic Summary

Part 1: pH, pOH, Kw, strong vs weak acids/bases, pH calculation methods.

Part 2: Ka, Kb, pKa, Henderson-Hasselbalch equation, percent dissociation, polyprotic acids, amphiprotic species.

Part 3: Buffer mechanism (HA consumes $OH^{-}$; $A^{-}$ consumes $H^{+}$), buffer capacity, buffer range (pKa ± 1), bicarbonate buffer in blood, acid-base disturbances.

Part 4: Titration curves, equivalence vs half-equivalence point (pH = pKa), indicators, strong/weak acid titration differences, polyprotic titrations.

Part 5: Kc, Kp, Δn, reaction quotient Q, Le Chatelier's principle (only T changes K), Ksp, molar solubility, common ion effect, precipitation criterion (Q vs Ksp).

Most Tested MCAT Concepts

1. Half-equivalence point: pH = pKa (titrations)
2. Le Chatelier shifts vs. K changes (only T changes K)
3. Common ion effect reduces solubility
4. Henderson-Hasselbalch for buffer pH
5. pH > 7 at equivalence for weak acid + strong base titration
6. Ksp → molar solubility (account for stoichiometric coefficients)