Acids, Bases & Buffers

• The three acid-base theories have increasing scope: Arrhenius (aqueous only) $\rightarrow$ Brønsted-Lowry (aqueous + non-aqueous, single ions) $\rightarrow$ Lewis (electron pairs, broadest).
• Strong acids/bases dissociate completely ($\alpha = 1$, one-way $\rightarrow$, no equilibrium); weak acids/bases dissociate partially ($\alpha < 1$, reversible $\rightleftharpoons$, equilibrium exists).
• $pH + pOH = 14$ and $K_a \times K_b = K_w = 10^{-14}$ — both relationships are valid only at 25°C.
• Salt hydrolysis rule: SA + SB = neutral; SA + WB = acidic; WA + SB = basic; WA + WB = calculate.
• A buffer requires $HA \approx A^-$ in comparable amounts — a weak acid alone is NOT a buffer.

Three Acid-Base Theories — Master Comparison 🔬

⚠️ Exam Trap: All Arrhenius acids/bases are also Brønsted-Lowry, but not vice versa. $NH_3$ is Brønsted-Lowry and Lewis, but NOT Arrhenius. Brønsted-Lowry is contained within Lewis — Lewis is the most inclusive theory.

Strong vs Weak — Master Comparison 🔬

Salt Hydrolysis — pH Prediction Table 🧪

Constants Formula Reference ⚡

• Hydronium ion ($H_3O^+$) (a proton $H^+$ attached to a water molecule via a dative bond — both electrons come from oxygen)

  • VSEPR class: $AX_3E \rightarrow$ trigonal pyramidal shape
  • Charge: +1

• Hydroxide ion ($OH^-$) (a water molecule that has lost one $H^+$)

  • Charge: −1

• Key equivalence: $H^+ = H_3O^+ = \text{proton } (p^+)$ — all three are synonyms and used interchangeably in equations.

🧠 Mnemonic: "H-Three-O-Plus = Hydronium = $H^+$ in water" — whenever you see $H^+$ in an aqueous equation, the real species is $H_3O^+$.

To fully understand acid-base chemistry, you must understand how the definition of an acid and base expanded over time, from strict aqueous solutions (Arrhenius) to universal electron-pair transfers (Lewis).

1. Arrhenius Theory (Aqueous Only)

• Scope: Aqueous medium only; does not work for single ions.

• Arrhenius Acid (a molecular substance that increases $[H^+]$ in water through ionisation):

  • $HCl \rightarrow H^+_{(aq)} + Cl^-_{(aq)}$ (strong — complete)
  • $CH_3COOH \rightleftharpoons CH_3COO^-_{(aq)} + H^+_{(aq)}$ (weak — partial)

• Arrhenius Base (an ionic compound that increases $[OH^-]$ in water through dissociation):

  • $NaOH \rightarrow Na^+_{(aq)} + OH^-_{(aq)}$

Limitations:

• Applies only in aqueous medium.
• Cannot explain why $NH_3$ is a base (no $OH^-$ present).
• Cannot explain acid-base behaviour of single ions.

2. Brønsted-Lowry Theory (Proton Transfer)

• Scope: Aqueous AND non-aqueous media; works for single ions.

• Brønsted-Lowry Acid (a proton/$H^+$ donor — releases $H^+$).

• Brønsted-Lowry Base (a proton/$H^+$ acceptor — gains $H^+$).

Conjugated acid-base pair (two particles that interconvert by donation or acceptance of one $H^+$):

⚠️ Exam Trap: In the $HCl$ reaction with water, $H_2O$ acts as a Brønsted-Lowry base ($H^+$ acceptor). Water is amphoteric — it acts as acid or base depending on the reaction partner.

🧠 Mnemonic: "BL Acid = gives away $H^+$ (Blasts proton away). BL Base = grabs $H^+$ (Base Brings proton in)."

3. Lewis Theory (Electron Pair Transfer)

• Scope: Broadest — based on electron pairs, not proton transfer.

• Lewis Acid (an electron pair acceptor):

  • Every metal cation ($Al^{3+}, Cu^{2+}, Fe^{3+}$).
  • Central atoms of $AX_3$ molecules that violate the octet rule ($AlCl_3, BF_3$).
  • $H^+$ itself (empty 1s orbital — accepts electron pair).

• Lewis Base (an electron pair donor):

  • Molecules with lone pairs: $NH_3, H_2O, CO, O_2$.

Lewis acid-base reaction $\rightarrow$ ADDUCT (product formed by a dative bond between Lewis acid and Lewis base):

• $BF_3 + F^- \rightarrow BF_4^-$ (boron tetrafluoride)
• $H^+ + NH_3 \rightarrow NH_4^+$

If a metal cation is at the centre $\rightarrow$ complex ion:

• $[CuCl_4]^{2-}$ : chloro complex of copper
• $[Cu(H_2O)_6]^{2+}$ : aqua complex of copper

⚠️ Exam Trap: The Lewis acid-base product is called an adduct, not a salt. The bond formed is always a dative (coordinate covalent) bond — both electrons come from the Lewis base. If a metal cation is central, the adduct is called a complex ion.

Neutralisation (Arrhenius and Brønsted-Lowry)

• General: Acid + Base $\rightarrow$ Salt + $H_2O$ (in aqueous medium)

Three levels of the same reaction:

1. Molecular equation: $HCl_{(aq)} + NaOH_{(aq)} \rightarrow NaCl_{(aq)} + H_2O_{(l)}$
2. Ionic equation: $H^+ + Cl^- + Na^+ + OH^- \rightarrow Na^+ + Cl^- + H_2O$
3. Net ionic equation: $H^+_{(aq)} + OH^-_{(aq)} \rightarrow H_2O_{(l)}$

• Spectator ions (ions that appear unchanged on both sides — they play no role in the reaction) — $Na^+$ and $Cl^-$ above.
• The net ionic equation $H^+ + OH^- \rightarrow H_2O$ is the universal equation for all aqueous neutralisation reactions.

Lewis Theory Product

• Lewis acid + Lewis base $\rightarrow$ adduct (dative bond)
• Example: $[Al(H_2O)_6]^{3+} + H_2O \rightleftharpoons [Al(H_2O)_5OH]^{2+} + H_3O^+$ $\rightarrow$ acidic ($Al^{3+}$ is a strong Lewis acid).

By Strength

Strong acids (memorise all 7):

• $HCl$, $HBr$, $HI$, $HNO_3$, $HClO_3$, $HClO_4$, $H_2SO_4$

Strong bases:

• Group IA hydroxides: $LiOH, NaOH, KOH, RbOH, CsOH$
• Group IIA hydroxides: $Mg(OH)_2, Ca(OH)_2, Sr(OH)_2, Ba(OH)_2$ (some textbooks classify as weak due to solubility)

Weak acids:

• $HF$, $HNO_2$, $H_2SO_3$, $H_2CO_3$, $H_3PO_4$, $CH_3COOH$, $HCOOH$

Weak bases:

• $NH_3$, $Al(OH)_3$, $CH_3NH_2$, $(CH_3)_3NH$, aniline ($C_6H_5NH_2$)

⚠️ Exam Trap: HF is a weak acid despite F being the most electronegative element. The H–F bond is so strong that ionisation is incomplete. Electronegativity does not determine acid strength.

🧠 Mnemonic: "The 7 strong acids: $HCl, HBr, HI$ — the three halogen acids — plus $HNO_3, HClO_3, HClO_4, H_2SO_4$. Everything else is weak."

By Proticity

Polyprotic acids — stepwise hydrolysis:

• Each $H^+$ released in a separate step, each with its own $K_a$ value.
• $K_{a1} > K_{a2} > K_{a3}$ always (each successive step harder).
• Example — $H_2CO_3$:
  • Step 1: $H_2CO_3 + H_2O \rightleftharpoons HCO_3^- + H_3O^+ \rightarrow K_{a1} = 4.5 \times 10^{-7}$
  • Step 2: $HCO_3^- + H_2O \rightleftharpoons CO_3^{2-} + H_3O^+ \rightarrow K_{a2} = 4.7 \times 10^{-11}$

⚠️ Exam Trap: For polyprotic acids, $K_{a1} \gg K_{a2}$ always. The second ionisation is far harder because removing $H^+$ from an already-negative ion requires overcoming electrostatic repulsion. This pattern is guaranteed on exams.

• Amphoteric (general term: a substance that can act as both an acid and a base)
• Amphiprotic (Brønsted-Lowry specific: a particle that can both accept (+$H^+$) and donate (−$H^+$) a proton)

Key amphoteric/amphiprotic species:

• Self-ionisation of water (autoprotolysis): $H_2O + H_2O \rightleftharpoons OH^- + H_3O^+$

⚠️ Exam Trap: Amphiprotic is a Brønsted-Lowry term only — it specifically refers to $H^+$ transfer. Amphoteric is broader (includes Lewis theory). $HCO_3^-$ is amphiprotic because it is the anion of a polyprotic acid that still retains one ionisable $H^+$.

Ka — Acid Ionisation Constant

• Equilibrium: $HA + H_2O \rightleftharpoons A^- + H_3O^+$ $K_a = \frac{[A^-][H^+]}{[HA]}$
• $[H_2O]$ excluded — water's molarity (55.56 M) is effectively constant and absorbed into $K_a$.
• Greater $K_a \rightarrow$ stronger acid; $K_a < 10^{-3} \rightarrow$ weak acid.

Kb — Base Ionisation Constant

• Equilibrium: $B + H_2O \rightleftharpoons BH^+ + OH^-$ $K_b = \frac{[BH^+][OH^-]}{[B]}$
• Greater $K_b \rightarrow$ stronger base; $K_b < 10^{-3} \rightarrow$ weak base.

Ka and Kb of Conjugate Pairs

• For any conjugate acid-base pair: $K_a \times K_b = K_w = 10^{-14}$ (at 25°C)

• Worked example — $H_2CO_3$ / $HCO_3^-$:

  • $K_{a1}(H_2CO_3) = 4.5 \times 10^{-7}$
  • $K_b(HCO_3^-) = \frac{10^{-14}}{4.5 \times 10^{-7}} = 2.2 \times 10^{-8}$

• Stronger acid $\rightarrow$ weaker conjugate base (and vice versa)

Kw — Ion Product of Water

• $H_2O + H_2O \rightleftharpoons OH^- + H_3O^+$ $K_w = [H^+][OH^-] = 10^{-14} \text{ at 25°C}$
• In pure water: $[H^+] = [OH^-] = 10^{-7} \text{ M}$
• $K_a, K_b, K_w$ all depend on temperature.

⚠️ Exam Trap: $K_w = 10^{-14}$ only at 25°C. At higher temperatures, $K_w$ increases (self-ionisation is endothermic). Therefore neutral pH < 7 above 25°C. "pH 7 = neutral" is only valid at exactly 25°C.

pKa and pKb

$pKa = -\log_{10}(K_a)$ $pKb = -\log_{10}(K_b)$

• Greater pKa/pKb = weaker acid/base (inverse of $K_a/K_b$ relationship).
• $K_a < 10^{-3} \rightarrow pKa > 3 \rightarrow$ weak.

Comparing strength using pKa:

• $K_a(HCOOH) = 1.8 \times 10^{-4} \rightarrow pKa = 3.79$
• $K_a(CH_3COOH) = 1.75 \times 10^{-5} \rightarrow pKa = 4.76$
• $pKa(HCOOH) < pKa(CH_3COOH) \rightarrow HCOOH$ is the stronger acid.

Conjugate pairs: $pKa + pKb = 14$ (at 25°C).

🧠 Mnemonic: "Bigger $K_a$ = smaller $pKa$ = stronger acid. Bigger $pKa$ = weaker acid. $K_a$ and $pKa$ are always opposites."

pH and pOH

$pH = -\log_{10}[H^+]$ $pOH = -\log_{10}[OH^-]$ $pH + pOH = 14 \text{ (at 25°C)}$

Biological pH values:

pH calculation rules:

• 10× dilution of a strong acid $\rightarrow$ pH increases by 1
• 10× dilution of a strong base $\rightarrow$ pH decreases by 1

• Electrolytes (substances that produce ions in water and therefore conduct electricity)

Three ion-producing processes:

• Ionisation (a molecular compound forms new ions in water) — e.g., $HCl \rightarrow H^+ + Cl^-$
• Dissociation (an ionic compound separates into its pre-existing ions in water) — e.g., $KCl \rightarrow K^+ + Cl^-$
• Hydrolysis (reaction with water that produces ions) — e.g., $HCOOH + H_2O \rightleftharpoons HCOO^- + H_3O^+$

⚠️ Exam Trap: Dissociation applies to ionic compounds (ions already exist, just separate). Ionisation applies to molecular compounds (ions must be newly formed).

• Salts (ionic compounds formed as products of neutralisation; dissociate 100% in water — they are always strong electrolytes)
• Only conjugates of weak acids/bases hydrolyse — conjugates of strong acids/bases do not.

Worked example — SA + WB ($NH_4Cl$):

1. $NH_4Cl \rightarrow NH_4^+ + Cl^-$
2. $Cl^-$ = conjugate of strong acid $HCl \rightarrow$ no hydrolysis.
3. $NH_4^+ + H_2O \rightleftharpoons NH_3 + H_3O^+$ $\rightarrow$ produces $H_3O^+$ $\rightarrow$ pH < 7

Worked example — WA + SB ($HCOONa$):

1. $HCOONa \rightarrow Na^+ + HCOO^-$
2. $Na^+$ = conjugate of strong base $NaOH \rightarrow$ no hydrolysis.
3. $HCOO^- + H_2O \rightleftharpoons HCOOH + OH^-$ $\rightarrow$ produces $OH^-$ $\rightarrow$ pH > 7

Al³⁺ — small, highly charged cation (special case):

• True form in water: $[Al(H_2O)_6]^{3+}$ (aqua complex — Lewis acid)
• $[Al(H_2O)_6]^{3+} + H_2O \rightleftharpoons [Al(H_2O)_5OH]^{2+} + H_3O^+ \rightarrow$ acidic solution

⚠️ Exam Trap: $NaCl$ dissolves to give pH = 7. $NH_4Cl$ gives pH < 7. $CH_3COONa$ gives pH > 7. The pH of a salt solution is never automatically 7 — always check whether the parent acid and base were strong or weak.

• Titration (an analytical technique using a neutralisation reaction and precise volume measurement to determine an unknown concentration).

Indicators:

• Must be used in small amounts so as not to shift the titration equilibrium.

Choosing the correct indicator:

• SA + SB $\rightarrow$ either indicator (sharp jump at equivalence point, pH = 7)

• WA + SB $\rightarrow$ phenolphthalein (equivalence point pH > 7)

• SA + WB $\rightarrow$ methyl orange (equivalence point pH < 7)

• Equivalence point (stoichiometric point where moles of acid = moles of base)

• End point (experimental observation of indicator colour change — ideally matches equivalence point)

⚠️ Exam Trap: The equivalence point and end point are NOT the same. The equivalence point is theoretical; the end point is experimental. A correctly chosen indicator minimises the gap between them.

• Buffer system (a solution that resists pH changes when small amounts of acid or base are added).

Two types:

Condition for buffer formation:

• $HA \approx A^-$ — both must be present in comparable amounts (ratio between 1:10 and 10:1).
• Salt must be from a Group IA or IIA metal (complete dissociation assured).

Common Ion Effect

• Common ion effect (when an ion that is common to two equilibria is present, it suppresses both equilibria simultaneously).
• In a buffer: $A^-$ from the salt appears in both the acid ionisation equilibrium and the conjugate base equilibrium. This creates buffering capacity.

Buffering Effect — Mechanism

When acid ($H^+$) is added:

• $H^+ + A^- \rightarrow HA$
• The conjugate base $A^-$ neutralises the added $H^+ \rightarrow$ pH barely changes.

When base ($OH^-$) is added:

• $OH^- + HA \rightarrow H_2O + A^-$
• The weak acid $HA$ neutralises the added $OH^- \rightarrow$ pH barely changes.

⚠️ Exam Trap: The buffering effect is maintained only when small amounts of acid or base are added. If a large amount exceeds the buffer capacity, the buffer components are depleted and pH changes dramatically.

🧠 Mnemonic: "A buffer = Weak Acid AND its Salt together — $HA$ and $A^-$ must coexist in comparable amounts. One alone = no buffer."

• HF is a weak acid — the H–F bond is too strong for complete ionisation despite F being the most electronegative element. This is the single most common strong/weak acid trap.

• All Arrhenius acids/bases are Brønsted-Lowry, but not vice versa — $NH_3$ is Brønsted-Lowry and Lewis base but NOT Arrhenius. Lewis is the most inclusive theory of the three.

• Salt hydrolysis: SA + SB = pH 7; SA + WB = pH < 7; WA + SB = pH > 7; WA + WB = compare $K_a$ vs $K_b$. The ion that hydrolyses is always the conjugate of the weak acid or base.

• $K_a \times K_b = K_w = 10^{-14}$ and $pKa + pKb = 14$ — only at 25°C. Bigger $K_a$ = stronger acid = smaller $pKa$.

• A weak acid alone is NOT a buffer. A buffer requires $HA \approx A^-$ in comparable amounts. Adding the conjugate base salt via the common ion effect achieves this balance.

• Equivalence point $\neq$ end point. Equivalence point is stoichiometric (theoretical); end point is the colour change (experimental). Choose phenolphthalein for WA + SB titrations; methyl orange for SA + WB titrations.