Difficulty: Intermediate to Advanced | Prerequisites: Acid-base definitions (Part 1), pH and equilibrium (Part 2), logarithms
Titration lets you find the concentration of an unknown acid or base by adding a solution of known concentration until the equivalence point, where acid and base equivalents are equal. Buffers are mixtures of a weak acid (or base) and its salt that resist pH changes; the Henderson-Hasselbalch equation calculates their pH. Polyvalent acids donate more than one proton, giving multiple equivalence points and introducing normality as a measure of total acidic or basic capacity.
Titration
A laboratory technique for determining the concentration of a known reactant in solution by adding measured amounts of a reagent of known concentration.
Titrant
The solution of known concentration that is added (usually from a burette).
Titrand (analyte)
The solution of unknown concentration being analysed (usually in a flask).
Equivalence point
The point at which the number of acid equivalents in solution equals the number of base equivalents added. Think of it as the moment when the acid and base have completely reacted with each other.
Endpoint
The point at which the indicator changes to its final colour. This is the observable signal that you are at (or near) the equivalence point.
Indicator
A weak acid or base that changes colour at a specific pH range. It must be weaker than the acid or base being titrated, otherwise the indicator would be consumed first.
Buffer solution
A mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid) that resists changes in pH when small amounts of acid or base are added.
Buffering capacity
The amount of acid or base a buffer can absorb before the pH changes significantly. Doubling the concentrations of both the weak acid and its conjugate base doubles the capacity without changing the pH.
Half-equivalence point
The point during a titration at which half of the original acid (or base) has been neutralised. At this point [HA] = [A⁻], so pH = pKa. This is the centre of the buffer region.
Henderson-Hasselbalch equation
The equation pH = pKa + log([A⁻]/[HA]) used to estimate the pH of a buffer solution. In simple terms, it rearranges the Ka expression into logarithmic form so you can read off the pH directly.
Polyvalent (polyprotic)
An acid or base that can donate or accept more than one proton (or equivalent) per molecule. H₂SO₄ and H₃PO₄ are common examples.
Acid equivalent
One mole of H⁺ ions.
Base equivalent
One mole of OH⁻ ions.
Normality (N)
Concentration expressed as the number of equivalents per litre. Normality = molarity × number of equivalents per mole.
Gram equivalent weight (GEW)
The mass of a compound that produces one equivalent. GEW = molar mass / number of equivalents per mole.
Add small volumes of titrant (known concentration) to the titrand (unknown concentration) until the equivalence point is reached
At the equivalence point: number of acid equivalents = number of base equivalents
Two ways to detect the equivalence point: plotting pH against titrant volume (pH meter) or watching for a colour change (indicator)
Strong acid + strong base
Equivalence point at pH 7 (for monovalent species)
Curve starts at low pH, has a nearly vertical jump through pH 7, then levels off at high pH
Adding titrant near the equivalence point causes the most dramatic pH change
At the start and end of the titration, pH changes slowly
On a pH meter, the equivalence point is the midpoint of the steep vertical region
Weak acid + strong base
Initial pH is higher than the strong acid case (weak acid is less dissociated)
Curve rises more gradually, with a less steep jump at the equivalence point
Equivalence point is above pH 7 because the conjugate base (A⁻) is left in solution and is weakly basic
A buffer region exists before the equivalence point, centred at the half-equivalence point where pH = pKa
Strong acid + weak base
Mirror image of the weak acid + strong base curve
Initial pH is in the basic range, drops gradually
Equivalence point is below pH 7 because the conjugate acid (BH⁺) is left in solution and is weakly acidic
Example: HCl + NH₃ → NH₄⁺ + Cl⁻
Weak acid + weak base
Curve is an intermediate between the two above
Initial pH between 3 and 11, very shallow slope approaching the equivalence point
Equivalence point is near pH 7 but can shift depending on the relative strengths of the acid and base
Hardest to detect with an indicator because the pH change at equivalence is gradual
Must be a weaker acid or base than the substance being titrated; otherwise the indicator is consumed before the analyte
Endpoint: the pH at which the indicator changes to its final colour
Choosing the right indicator: find the equivalence point pH, then pick the indicator whose pKa is closest to that pH
Polyprotic acids have multiple equivalence points, one for each proton
Half-equivalence point: half of a given proton has been removed; this is the centre of each buffer region
For a diprotic acid like H₂CO₃ titrated with NaOH, equivalence point 1 is where all first protons are lost (rapid pH change), followed by a second buffer region and equivalence point 2
A buffer contains a weak acid and its conjugate base (acid buffer, e.g. CH₃COOH + CH₃COO⁻ Na⁺) or a weak base and its conjugate acid (base buffer, e.g. NH₃ + NH₄⁺ Cl⁻)
How they work: adding a strong base (e.g. NaOH) to an acid buffer consumes H⁺, and the equilibrium shifts to produce more H⁺ from HA, so pH barely changes. Adding a strong acid (e.g. HCl) converts A⁻ back to HA (a weak acid), so pH barely changes.
Buffers work best within ±1 pH unit of their pKa
Buffering region on a titration curve: the flattest portion, where [HA] ≈ [A⁻]
Half-equivalence point: [HA] = [A⁻], pH = pKa, buffering capacity is optimal
CO₂ + H₂O ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺
In respiratory acidosis (too much H⁺ in blood), the body increases breathing rate to blow off CO₂, shifting the equilibrium left and reducing [H⁺]
This is the primary buffer system in human blood
For a weak acid buffer: pH = pKa + log([A⁻] / [HA])
For a weak base buffer: pOH = pKb + log([BH⁺] / [B])
When [A⁻] = [HA], the log term is zero and pH = pKa (the half-equivalence point)
Doubling both [HA] and [A⁻] does not change pH (the ratio stays the same) but doubles the buffering capacity
Acid equivalent = one mole of H⁺; base equivalent = one mole of OH⁻
Polyvalent: each mole of acid or base releases more than one equivalent
H₂SO₄ produces 2 acid equivalents per mole (first dissociation goes to completion; second is in equilibrium)
H₃PO₄ produces 3 acid equivalents per mole
Normality = [acid or base] × number of equivalents per mole
Example: a 2 M H₃PO₄ solution has a normality of 6
Gram equivalent weight (GEW) = molar mass / number of equivalents
Example: H₂SO₄ has molar mass 98 g/mol and 2 equivalents, so GEW = 49 g
At the equivalence point: N_A × V_A = N_B × V_B
Common polyvalent acids: H₃PO₄, H₂SO₄, H₂CO₃
Common polyvalent bases: Al(OH)₃, Ca(OH)₂, Mg(OH)₂
Titration is a routine analytical method in quality control: labs titrate solutions to verify concentrations of acids in industrial products, the acidity of wine, and the alkalinity of water samples. The bicarbonate buffer system keeps blood pH between 7.35 and 7.45, and disruptions (respiratory acidosis, metabolic alkalosis) are diagnosed by measuring blood gas values.
\text{pH} = \text{p}K_a + \log \frac{[\text{A}^-]}{[\text{HA}]}\text{pOH} = \text{p}K_b + \log \frac{[\text{BH}^+]}{[\text{B}]}\text{Normality} = [\text{acid or base}] \times \text{number of equivalents per mole}\text{GEW} = \frac{\text{molar mass}}{\text{number of equivalents}}N_A \times V_A = N_B \times V_B \quad (\text{at the equivalence point})Students often assume every titration has an equivalence point at pH 7. This is true only for strong acid + strong base. Weak acid + strong base gives an equivalence point above 7; strong acid + weak base gives one below 7.
A common error is confusing the equivalence point with the endpoint. The equivalence point is a calculated stoichiometric reality. The endpoint is the observable colour change of the indicator. They are close but not always identical.
Students frequently think that adding more buffer components changes the pH. Doubling both [HA] and [A⁻] does not change pH (the Henderson-Hasselbalch ratio stays the same); it doubles the buffering capacity.
Many students confuse normality with molarity. They are the same only for monoprotic acids and monobasic bases. For H₂SO₄, a 1 M solution is 2 N.
⚠️ Be able to sketch all four titration curve shapes from memory and label the equivalence point, buffer region, and half-equivalence point on each.
⚠️ Henderson-Hasselbalch calculations appear frequently. Know both the acid and base versions.
⚠️ Indicator selection questions: find the equivalence point pH first, then match pKa of the indicator to that pH.
⚠️ Normality and GEW calculations are standard. Remember: Normality = Molarity × equivalents, and GEW = molar mass / equivalents.
⚠️ The relationship N_A × V_A = N_B × V_B at the equivalence point is a must-know for titration calculations.
⚠️ The bicarbonate buffer system is tested in both chemistry and biology contexts. Know the equilibrium and how respiratory rate shifts it.
True or false: The equivalence point of a weak acid titrated with a strong base is at pH 7. (Answer: False. It is above 7.)
Fill in the blank: At the half-equivalence point of a weak acid titration, pH = ______. (Answer: pKa)
True or false: A 1 M H₃PO₄ solution has a normality of 3. (Answer: True. Three equivalents per mole.)
Fill in the blank: The gram equivalent weight of H₂SO₄ (molar mass 98) is ______ grams. (Answer: 49)
True or false: Doubling the concentration of both HA and A⁻ in a buffer changes its pH. (Answer: False. It doubles the capacity but pH stays the same.)
Q: A buffer is made from 0.10 M acetic acid (pKa = 4.76) and 0.10 M sodium acetate. What is the pH?
A: pH = pKa + log([A⁻]/[HA]) = 4.76 + log(0.10/0.10) = 4.76 + 0 = 4.76.
Q: You are titrating a weak base with a strong acid. Where is the equivalence point relative to pH 7, and why?
A: Below pH 7. At the equivalence point, the weak base has been fully converted to its conjugate acid (BH⁺), which is weakly acidic. The conjugate acid donates protons to water, pushing pH below 7.
Q: What is the normality of a 0.50 M Ca(OH)₂ solution?
A: Ca(OH)₂ provides 2 OH⁻ equivalents per mole. Normality = 0.50 × 2 = 1.0 N.
Q: 25.0 mL of a 0.20 N acid is titrated to the equivalence point with a base of unknown normality. If 50.0 mL of base is required, what is the base's normality?
A: N_A × V_A = N_B × V_B. 0.20 × 25.0 = N_B × 50.0. N_B = 5.0 / 50.0 = 0.10 N.
Q: Why does the bicarbonate buffer system respond to respiratory acidosis by increasing breathing rate?
A: The equilibrium CO₂ + H₂O ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺ lies to the right when CO₂ accumulates, raising [H⁺]. Faster breathing expels CO₂, shifting the equilibrium left and lowering [H⁺] back towards normal.
Q: An indicator has a pKa of 8.0. Would it be a good choice for a strong acid / strong base titration? What about a weak acid / strong base titration?
A: For strong acid + strong base the equivalence point is at pH 7, so an indicator with pKa 8.0 is acceptable (the steep pH jump spans a wide range around 7, so 8.0 falls within it). For weak acid + strong base the equivalence point is above 7, so pKa 8.0 may be a better match depending on the exact equivalence pH.
Titration and buffer chemistry depend on everything from Parts 1 and 2: you need to classify the acid and base (Arrhenius, Brønsted-Lowry, or Lewis), know whether each is strong or weak, and use Ka/Kb to predict equilibrium concentrations before you can interpret a titration curve or calculate a buffer's pH. The bicarbonate buffer system bridges general chemistry and physiology, showing up again in courses on biochemistry and respiratory medicine. Normality and equivalents also appear in redox chemistry, where one equivalent is one mole of electrons rather than one mole of H⁺.
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