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Acid-Base & Equilibrium

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Acid-Base & Equilibrium - Complete Interactive Lesson

Part 1: pH, pOH & Strong vs. Weak Acids

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

pH	Solution	$[\text{H}^+]$
< 7	Acidic	> $10^{-7}$ M
= 7	Neutral	M

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), ,

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: $\text{B} + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^-$

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

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

Part 2: Ka, Kb & Henderson-Hasselbalch

Acid-Base Chemistry & Equilibrium

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

The Acid Dissociation Constant $K_a$

Part 3: Buffers & Physiological Chemistry

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:

Part 4: Titrations & Indicators

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).

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

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

Part 5: Equilibrium, Ksp & Le Chatelier's Principle

Acid-Base Chemistry & Equilibrium

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

K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]}

\text{p}K_a + \text{p}K_b = 14

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

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:

Acid	$K_a$	$\text{p}K_a$	Strength
HF	$7.2 \times 10^{-4}$	3.14	Weak
Acetic acid ( $\text{CH}_3\text{COOH}$ )	$1.8 \times 10^{-5}$	4.74	Weak
$\text{NH}_4^+$	$5.6 \times 10^{-10}$	9.25	Very weak
$\text{HCO}_3^-$	$4.7 \times 10^{-11}$	10.3	Very weak

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.

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 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).

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)

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

Buffer capacity is highest when:

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

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: pKₐ ± 1

Choosing a Buffer for a Target pH

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

Target pH	Buffer system
~3.7	Formic acid / formate ( $\text{p}K_a = 3.74$ )
~4.7	Acetic acid / acetate ( $\text{p}K_a = 4.74$ )
~6.4	$\text{H}_2\text{CO}_3$ / $\text{HCO}_3^-$ ()
~7.4	$\text{H}_2\text{PO}_4^-$ / $\text{HPO}_4^{2-}$ ()
~9.25	$\text{NH}_4^+$ / $\text{NH}_3$ ( $\text{p}K_a = 9.25$ )

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.

Condition	pH	$\text{CO}_2$ / $\text{HCO}_3^-$	Compensation
Respiratory acidosis	↓	↑ $\text{CO}_2$	Kidney retains $\text{HCO}_3^-$
Respiratory alkalosis	↑	↓ $\text{CO}_2$	Kidney excretes $\text{HCO}_3^-$
Metabolic acidosis	↓	↓ $\text{HCO}_3^-$	Hyperventilation
Metabolic alkalosis	↑	↑ $\text{HCO}_3^-$	Hypoventilation

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 $[\text{HCO}_3^-]$

MbVb(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 ≈ pKₐ when halfway to equivalence ("half-equivalence point")
At half-equivalence: $[\text{HA}] = [\text{A}^-]$ → pH = pKₐ ← 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 = pKₐ of conjugate acid

Key Features of Titration Curves

Feature	Meaning
Endpoint (indicator changes)	Should be ≈ equivalence point
Equivalence point	Stoichiometrically equal moles acid and base
Half-equivalence point	pH = pKₐ (for weak acid titration)
Inflection point	Steepest part of curve; near equivalence
Buffer region	Shallow slope; brackets the half-equivalence point

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 ≈ pKₐ (indicator). The indicator transitions over ~pH = pKₐ ± 1.

Common indicators:

Indicator	Acid color	Base color	Transition range
Phenolphthalein	Colorless	Pink	pH 8.2–10.0
Methyl orange	Red	Yellow	pH 3.1–4.4
Litmus	Red	Blue	pH 6.0–8.0
Bromothymol blue	Yellow	Blue	pH 6.0–7.6

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 = pKₐ — most testable titration fact
Indicators change color over ~pKₐ ± 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

Equilibrium Constant Expressions

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

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

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

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 $\Delta n = 0$ .

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

Comparison	Direction of reaction
$Q < K$	Shifts right (toward products)
$Q = K$	At equilibrium
$Q > K$	Shifts left (toward reactants)

Le Chatelier's Principle

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

Disturbance	Shift direction	$K$ changes?
Add reactant	Right (toward products)	No
Remove product	Right (toward products)	No
Increase pressure (compress)	Toward fewer moles of gas	No
Increase temperature	Toward endothermic direction	Yes
Decrease temperature	Toward exothermic direction	Yes
Add inert gas (constant V)	No shift	No
Add catalyst	No shift (faster equilibrium)	No

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 $[\text{F}^-] = 2s$

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

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

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

\text{p}K_{a1} = 6.37

\text{p}K_{a2} = 7.21

Acid-Base & Equilibrium

Percent Dissociation

Henderson-Hasselbalch Equation

Worked Example

Polyprotic Acids

Amphiprotic Species

Key Takeaways — Part 2

Buffer Capacity

Choosing a Buffer for a Target pH

The Bicarbonate Buffer System (Blood)

Key Takeaways — Part 3

Titration Curve Shapes

Strong Acid + Strong Base

Weak Acid + Strong Base

Weak Base + Strong Acid

Key Features of Titration Curves

Acid-Base Indicators

Polyprotic Titrations

Key Takeaways — Part 4

Equilibrium Constant Expressions

$K_p$ vs $K_c$

Reaction Quotient Q

Le Chatelier's Principle

Solubility Product ( $K_{sp}$ )

Common Ion Effect

Precipitation Criterion

Acid-Base & Equilibrium — Complete Topic Summary

Most Tested MCAT Concepts

Acid-Base & Equilibrium

Acid-Base & Equilibrium - Complete Interactive Lesson

Part 1: pH, pOH & Strong vs. Weak Acids

Acid-Base Chemistry & Equilibrium

The pH Scale

Strong Acids and Bases — 100% Dissociation

Weak Acids and Bases — Partial Dissociation

Approximation for Weak Acid pH

Key Takeaways — Part 1

Part 2: Ka, Kb & Henderson-Hasselbalch

Acid-Base Chemistry & Equilibrium

The Acid Dissociation Constant KaK_a

Part 3: Buffers & Physiological Chemistry

Acid-Base Chemistry & Equilibrium

What Is a Buffer?

How Buffers Work

Part 4: Titrations & Indicators

Acid-Base Chemistry & Equilibrium

Titration Fundamentals

Part 5: Equilibrium, Ksp & Le Chatelier's Principle

Acid-Base Chemistry & Equilibrium

Percent Dissociation

Henderson-Hasselbalch Equation

Worked Example

Polyprotic Acids

Amphiprotic Species

Key Takeaways — Part 2

Buffer Capacity

Choosing a Buffer for a Target pH

The Bicarbonate Buffer System (Blood)

Key Takeaways — Part 3

Titration Curve Shapes

Strong Acid + Strong Base

Weak Acid + Strong Base

Weak Base + Strong Acid

Key Features of Titration Curves

Acid-Base Indicators

Polyprotic Titrations

Key Takeaways — Part 4

Equilibrium Constant Expressions

KpK_pKp​ vs KcK_cKc​

Reaction Quotient Q

Le Chatelier's Principle

Solubility Product (KspK_{sp}Ksp​)

Common Ion Effect

Precipitation Criterion

Acid-Base & Equilibrium — Complete Topic Summary

Most Tested MCAT Concepts

The Acid Dissociation Constant $K_a$

$K_p$ vs $K_c$

Solubility Product ( $K_{sp}$ )