1. Bronsted-Lowry Theory, pH & Conjugate Pairs
In quantitative chemistry, acid-base behavior is governed by proton transfer:
- Acid: A proton (H+) donor.
- Base: A proton (H+) acceptor.
- Conjugate Acid-Base Pair: Two species that transform into each other by the gain or loss of a single proton.
Example: In CH3COOH + H2O <=> CH3COO- + H3O+, CH3COOH is the acid and CH3COO- is its conjugate base; H2O is the base and H3O+ is its conjugate acid.
pH = -log10[H+]
[H+] = 10^(-pH)
2. The Ionic Product of Water (Kw) & High-Temperature Neutrality
Water undergoes a slight self-ionisation (autoprotolysis):
H2O(l) <=> H+(aq) + OH-(aq) [delta H > 0, endothermic]
Because the concentration of undissociated water is immense (~55.5 mol dm-3) and effectively constant, it is incorporated into the equilibrium constant to give the ionic product of water (Kw):
Kw = [H+] [OH-]
At standard temperature (298 K / 25 degrees C):
Kw = 1.00 x 10^-14 mol2 dm-6 => pKw = -log10(Kw) = 14.00
Because the dissociation of water is endothermic (delta H > 0), increasing temperature shifts the equilibrium to the right according to Le Chatelier's principle. Consequently, Kw increases:
- At 25 degrees C: Kw = 1.00 x 10^-14 mol2 dm-6; [H+] = 1.00 x 10^-7 mol dm-3; pH = 7.00.
- At 50 degrees C: Kw rises to 5.48 x 10^-14 mol2 dm-6; [H+] = sqrt(Kw) = 2.34 x 10^-7 mol dm-3; pH = 6.63.
Crucial Examination Point: Even though the pH drops below 7 at 50 degrees C, water remains strictly neutral because [H+] is strictly equal to [OH-]. Neutrality does NOT mean pH = 7; neutrality means [H+] = [OH-]!
3. Weak Acids, Ka & pKa Calculations
Strong acids (HCl, HNO3, H2SO4) dissociate completely in aqueous solution, so [H+] = [acid]. Weak acids (CH3COOH, HCOOH, HCN) dissociate only partially:
HA(aq) <=> H+(aq) + A-(aq)
The acid dissociation constant (Ka) is:
Ka = ([H+] [A-]) / [HA] and pKa = -log10(Ka)
A higher Ka (or lower pKa) indicates a stronger weak acid that dissociates to a greater extent.
Standard Approximations for Weak Acid pH Calculations
- Equimolar dissociation: We assume all H+ ions come solely from the weak acid (ignoring the negligible contribution from water dissociation): [H+] = [A-].
- Negligible dissociation: Because the acid is weak, the amount dissociated is tiny compared to starting concentration: [HA]_eq = [HA]_initial.
Substituting these approximations gives:
Ka = [H+]^2 / [HA] => [H+] = sqrt(Ka * [HA])
4. Buffer Solutions & Mechanism of Action
A buffer solution is a chemical system that resists changes in pH when small amounts of acid (H+) or base (OH-) are added.
- Acidic Buffer (pH < 7): Formed from a weak acid and a salt of its conjugate base (e.g. ethanoic acid, CH3COOH, and sodium ethanoate, CH3COONa).
- Basic Buffer (pH > 7): Formed from a weak base and a salt of its conjugate acid (e.g. ammonia, NH3, and ammonium chloride, NH4Cl).
Mechanism of Acidic Buffer Action
An acidic buffer contains a large reservoir of undissociated weak acid (HA) and a large reservoir of conjugate base ions (A-):
- When a small amount of H+ is added: The added protons react with the large reservoir of conjugate base ions: A- + H+ -> HA. The position of equilibrium shifts to the left, removing added H+ and keeping pH almost constant.
- When a small amount of OH- is added: The added hydroxide reacts with the large reservoir of undissociated acid: HA + OH- -> A- + H2O. Protons are donated to neutralise OH-, keeping pH almost constant.
The Henderson-Hasselbalch Equation
pH = pKa + log10([A-] / [HA]) = pKa + log10(moles of salt / moles of acid)
5. pH Titration Curves
Plotting solution pH against the volume of alkali added produces characteristic titration curves:
| Titration Combination | Initial pH | Vertical Inflection Range | pH at Equivalence | Suitable Indicator |
|---|---|---|---|---|
| Strong Acid - Strong Base (HCl + NaOH) | ~1 | pH 3.0 to 11.0 (long vertical section) | 7.0 | Both Methyl Orange & Phenolphthalein |
| Weak Acid - Strong Base (CH3COOH + NaOH) | ~3 | pH 7.0 to 11.0 (vertical in alkaline region) | > 7.0 (~8.9) | Phenolphthalein ONLY |
| Strong Acid - Weak Base (HCl + NH3) | ~1 | pH 3.0 to 7.0 (vertical in acidic region) | < 7.0 (~5.1) | Methyl Orange ONLY |
| Weak Acid - Weak Base (CH3COOH + NH3) | ~3 | No vertical section (inflection point only) | ~7.0 | No standard indicator (use pH meter) |
6. Indicator Selection & Half-Neutralisation Determination of Ka
Determining Ka from the Half-Neutralisation Point
During a weak acid titration, at the half-neutralisation point (halfway to equivalence volume, e.g. at 12.5 cm3 if equivalence is 25.0 cm3):
[HA] = [A-]
Substituting into Ka = ([H+][A-]) / [HA]:
Ka = [H+] => pH = pKa
Therefore, reading the pH at exactly half the equivalence volume directly gives the pKa of the weak acid!
7. Worked Calculations
Step 1: Apply weak acid approximation:
[H+] = sqrt(Ka * [HA])
[H+] = sqrt((1.74 x 10^-5) * 0.150) = sqrt(2.61 x 10^-6) = 1.616 x 10^-3 mol dm-3
Step 2: Calculate pH:
pH = -log10(1.616 x 10^-3) = 2.79
Calculate the pH of this buffer solution.
Step 1: Calculate moles of acid and salt:
Moles of HCOOH = 0.500 dm3 * 0.200 mol dm-3 = 0.100 mol
Moles of HCOO- = 0.500 dm3 * 0.100 mol dm-3 = 0.050 mol
Step 2: Calculate pKa:
pKa = -log10(1.78 x 10^-4) = 3.75
Step 3: Apply Henderson-Hasselbalch equation:
pH = pKa + log10(moles of salt / moles of acid)
pH = 3.75 + log10(0.050 / 0.100) = 3.75 + log10(0.50) = 3.75 + (-0.301) = 3.45
Exam-Style Practice Questions
Test your understanding of these core syllabus concepts with targeted questions and detailed explanations.
Question 1: At 60 degrees C, Kw is 9.60 x 10^-14 mol2 dm-6. What is the pH of pure water at this temperature, and is the water acidic, basic, or neutral?
Show Answer & Explanation
Correct Answer: C
[H+] = sqrt(Kw) = sqrt(9.60 x 10^-14) = 3.10 x 10^-7 mol dm-3. pH = -log10(3.10 x 10^-7) = 6.51. The water remains neutral because [H+] = [OH-].
Question 2: Which indicator is most suitable for titrating ethanoic acid (weak acid) with sodium hydroxide (strong base)?
Show Answer & Explanation
Correct Answer: C
A weak acid - strong base titration curve has its vertical inflection in the alkaline region (pH 7 to 11). Phenolphthalein's working range (8.3 to 10.0) lies entirely within this vertical section.
Question 3: In a titration of 25.0 cm3 of a weak monoprotic acid with 0.10 M NaOH, equivalence is reached at 30.0 cm3. At what volume of added NaOH does the solution pH equal the pKa of the acid?
Show Answer & Explanation
Correct Answer: C
pH equals pKa at the half-neutralisation point. Halfway to the 30.0 cm3 equivalence point is 15.0 cm3.
Question 4: What happens to the pH of an acidic buffer when a small volume of hydrochloric acid is added?
Show Answer & Explanation
Correct Answer: C
The large reservoir of conjugate base ions (A-) reacts with added protons (A- + H+ -> HA), preventing any major change in [H+] and keeping pH virtually constant.