Acids and Bases

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Acids and Bases — Key Facts for MDCAT

Arrhenius Definition:

• Acid: produces $H^+$ ions in aqueous solution (e.g., $HCl \rightarrow H^+ + Cl^-$)
• Base: produces $OH^-$ ions in aqueous solution (e.g., $NaOH \rightarrow Na^+ + OH^-$)

Bronsted-Lowry Definition (most important for MDCAT):

• Acid: proton ($H^+$) donor
• Base: proton ($H^+$) acceptor
• Conjugate acid-base pair: related by the transfer of one proton
  • HCl (acid) donates proton → Cl$^-$ (conjugate base)
  • NH$_3$ (base) accepts proton → NH$_4^+$ (conjugate acid)

Strong vs Weak Acids:

Strong Acids (complete dissociation)	Weak Acids (partial dissociation)
HCl, HBr, HI, HNO$_3$, H$_2$SO$_4$ (1st proton), HClO$_4$	CH$_3$COOH$, H_2CO_3, H_3PO$_4$, HF, H$_2$S

pH and pOH: $$pH = -\log[H^+]$$ $$pOH = -\log[OH^-]$$ $$pH + pOH = 14 \text{ (at } 25^\circ C\text{)}$$ $$K_w = [H^+][OH^-] = 10^{-14} \text{ at } 25^\circ C$$

pH of weak acids: $[H^+] = \sqrt{K_a \times C}$ where $K_a$ is the acid dissociation constant and $C$ is concentration.

⚡ Exam tip: Memorise strong acids and strong bases — they dissociate completely in water. Common mistake: thinking $H_2SO_4$ is always strong (only the first proton dissociates completely; the second is weak). MDCAT frequently tests pH calculations of weak acids using the $\sqrt{K_a C}$ formula.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students who want genuine understanding.

Acids and Bases — Complete Study Guide

Lewis Definition:

• Acid: electron pair acceptor
• Base: electron pair donor
• Broader than Bronsted — includes reactions with no proton transfer (e.g., BF$_3$ + NH$_3 \rightarrow$ BF$_3$NH$_3$)

Acid-Base Strength and $K_a$/$K_b$: $$K_a = \frac{[H^+][A^-]}{[HA]} \text{ (weak acid)}$$ $$K_b = \frac{[OH^-][BH^+]}{[B]} \text{ (weak base)}$$ $$K_a \times K_b = K_w = 10^{-14}$$

For conjugate pairs: $K_a \times K_b = K_w$, so $pK_a + pK_b = 14$

Percent Dissociation: $$% \text{ dissociation} = \frac{[H^+]}{C} \times 100%$$ A higher $K_a$ means a stronger acid. For weak acids, dilution increases percent dissociation but decreases $[H^+]$.

Salt Hydrolysis: Salts of strong acid + weak base → acidic solution (e.g., NH$_4$Cl) Salts of weak acid + strong base → basic solution (e.g., CH$_3$COONa) Salts of strong acid + strong base → neutral solution (e.g., NaCl) Salts of weak acid + weak base → depends on $K_a$ and $K_b$ values

Buffer Solutions: A buffer resists changes in pH upon addition of small amounts of acid or base.

• Acidic buffer: weak acid + its salt (e.g., CH$_3$COOH/CH$_3$COONa)
• Henderson-Hasselbalch equation: $pH = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]}$

Indicators:

Indicator	pH Range	Colour Change
Methyl orange	3.1 – 4.4	Red → Yellow
Bromothymol blue	6.0 – 7.6	Yellow → Blue
Phenolphthalein	8.2 – 10.0	Colourless → Pink

⚡ Common mistakes: Confusing $K_a$ with $K_c$ — they are the same for acid dissociation in aqueous solution. Forgetting that $K_w$ changes with temperature (at $25^\circ C$, $K_w = 10^{-14}$; at $100^\circ C$, $K_w \approx 10^{-12}$). Students often use the wrong concentration in the Henderson-Hasselbalch equation (must be the ratio of salt to acid, not the absolute concentrations).

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Acids and Bases — Advanced Chemistry Notes

Thermodynamic Approach to Acid Strength: The strength of an acid HA in water depends on:

1. Bond dissociation energy of H-A: lower bond energy → easier proton release → stronger acid
2. Electron density on the conjugate base A$^-$: more stable A$^-$ (delocalised negative charge) → stronger acid
3. Solvation of the conjugate base: better solvation → more stable A$^-$ → stronger acid

Trends in Periodic Table: Across a period (left to right): Acidic strength of hydrides increases (e.g., $CH_4 < NH_3 < H_2O < HF$) Down a group: Oxyacid strength increases (e.g., $HClO < HBrO < HIO$) — because electronegativity of central atom decreases, reducing the pull on oxygen electrons and making the O-H bond more acidic.

Polyprotic Acids: Example: H$3$PO$4$ (phosphoric acid) has three dissociable protons: $$K{a1} = 7.5 \times 10^{-3}, \quad K{a2} = 6.2 \times 10^{-8}, \quad K_{a3} = 4.8 \times 10^{-13}$$ Each successive $K_a$ is much smaller because it is harder to remove a positively charged proton from an already negatively charged anion.

Lewis Acid-Base Reactions: Lewis acids (electron pair acceptors): metal cations (Al$^{3+}$, Fe$^{3+}$), electron-deficient molecules (BF$_3$, AlCl$_3$), molecules with polar double bonds. Lewis bases (electron pair donors): anions, molecules with lone pairs (NH$_3$, H$_2$O, alcohols).

Non-aqueous Solvents:

• Amphoteric solvents: can act as both acid and base (water, alcohols)
• Protic solvents: contain acidic hydrogen (water, liquid ammonia)
• Aprotic solvents: no acidic hydrogen (benzene, CCl$_4$)

Neutralisation Reactions and Enthalpy: All strong acid-strong base neutralisations have $\Delta H \approx -57.3$ kJ/mol (enthalpy of neutralisation of strong acid and strong base). This is because the net ionic reaction is always: $$H^+(aq) + OH^-(aq) \rightarrow H_2O(l)$$ The value is less exothermic when weak acids or weak bases are involved because some energy is used to dissociate the weak electrolyte.

Buffer Capacity: Buffer capacity = number of moles of strong acid or base needed to change pH of 1 litre of buffer by 1 unit. Maximum buffer capacity occurs when $[salt] = [acid]$, i.e., $pH = pK_a$.

MDCAT Question Patterns: Common MDCAT Pakistan questions include: (1) identifying conjugate acid-base pairs, (2) pH calculations for weak acids using $\sqrt{K_a C}$, (3) buffer pH using Henderson-Hasselbalch, (4) predicting whether salt solutions are acidic, basic, or neutral, (5) selecting appropriate indicators for titrations. Strong acid-strong base titrations use phenolphthalein; strong acid-weak base titrations use methyl orange.

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