Titrations and Buffers

A titration is a laboratory technique for determining the concentration of an unknown solution by reacting it, in a controlled way, with a solution of known concentration. This subtopic covers how a titration works, how to monitor and read one, how the resulting titration curve differs depending on acid/base strength, how polyprotic species titrate, and buffers — solutions built from a weak acid/base pair that resist changes in pH, including the Henderson-Hasselbalch equation, buffer capacity, and the bicarbonate buffer system that keeps blood pH stable.

Key Takeaways

• A titration determines an unknown concentration by reacting a titrand with a titrant of known concentration until the equivalence point (moles titrant = moles titrand) is reached; for acid-base titrations, NₐVₐ = N_bV_b.

• A pH meter or an indicator (e.g., phenolphthalein, colorless below ~pH 8.2, pink above ~pH 10) monitors the titration. The endpoint (where the indicator visibly changes) ideally coincides with the equivalence point (the theoretical stoichiometric point), but the two aren't always identical.

• Equivalence point pH depends on acid/base strength: strong-strong = pH 7; strong acid/weak base < pH 7; weak acid/strong base > pH 7; weak-weak is variable and such titrations are rarely performed.

• A polyprotic/polyvalent species produces multiple equivalence points and buffer regions during titration, one per ionizable proton or hydroxide, each with its own pKa.

• A buffer (weak acid/conjugate base or weak base/conjugate acid) resists pH change via the common ion effect: H⁺ + A⁻ → HA, and HA + OH⁻ → A⁻ + H₂O.

• The Henderson-Hasselbalch equation, pH = pKa + log([A⁻]/[HA]), calculates a buffer's pH from its pKa and component ratio.

• Buffer capacity is maximized when the buffer's component ratio is close to 1:1 (pH near pKa) and scales with the total concentration of buffer components; it's strongest within about one pH unit of pKa.

• The bicarbonate buffer system (HCO₃⁻/H₂CO₃, pKa ≈ 6.1) maintains blood pH ≈ 7.4 via a ~20:1 HCO₃⁻:H₂CO₃ ratio, actively regulated by the respiratory system (CO₂ exhalation) and renal system (H⁺ excretion, HCO₃⁻ reabsorption) — an open system that buffers effectively even though blood pH sits more than one unit from the pair's own pKa.

What Is a Titration?

In a titration, the solution of unknown concentration — the titrand — sits in a flask. A solution of known concentration — the titrant — is added gradually from a burette while the reaction between the two is monitored. The equivalence point is reached when the titrant added is exactly enough to completely react with the titrand: the moles of titrant equal the moles of titrand, based on the reaction's stoichiometry.

At the equivalence point in an acid-base titration, the number of equivalents of acid and base are equal. As established when polyvalence and normality were first introduced, normality (N) measures concentration in equivalents of solute per liter of solution, which makes it directly useful here:

NₐVₐ = N_bV_b

Worked example: 20.0 mL of an HCl solution of unknown normality is titrated to the equivalence point by 15.0 mL of 0.200 N NaOH. What is the normality of the HCl?

NₐVₐ = N_bV_b → Nₐ(20.0 mL) = (0.200 N)(15.0 mL) → Nₐ = (0.200 × 15.0) / 20.0 = 0.150 N

Monitoring a Titration: pH Meters, Indicators, and the Endpoint

Two tools are commonly used to track a titration as it proceeds:

• A pH meter is an electronic device that measures the solution's pH directly, allowing precise, continuous monitoring as titrant is added.

• An indicator is a substance that changes color at or near the equivalence point. The choice of indicator depends on the pH expected at the equivalence point. Phenolphthalein, for example, is colorless below about pH 8.2 and fully pink by about pH 10, transitioning across that range — which makes it well suited to titrations involving strong acids and strong bases, where the equivalence point sits at pH 7 but the curve rises so steeply nearby that the indicator still changes right around the true equivalence point.

It's important to distinguish the equivalence point from the endpoint. The equivalence point is the theoretical point at which moles of titrant added exactly equal moles of titrand present. The endpoint is the point at which the indicator visibly changes color, signaling that the titration should stop. Ideally the two coincide, but there can be a slight difference, minimized by choosing an indicator whose color-change pH is close to the expected equivalence point.

Titration Curves for Strong and Weak Acids and Bases

Acid-base titrations can involve any combination of strong and weak species, and the shape of the resulting titration curve — pH plotted against volume of titrant added — depends on which combination is used.

Strong acid + strong base (e.g., 10 mL of 0.1 N HCl titrated with 0.1 N NaOH): early in the titration, the solution is dominated by the fully-dissociated strong acid, so pH starts low and changes only slightly as small amounts of base are added. Near the equivalence point, [H⁺] drops sharply and the curve becomes steep. The equivalence point falls at pH 7, since the only products are water and a neutral salt (NaCl) that doesn't affect pH. Beyond the equivalence point, excess strong base drives the pH up, though the rate of change slows as the solution becomes uniformly basic.

Strong acid + weak base (e.g., HCl titrated into NH₃): the solution starts basic, dominated by the weak base ammonia. As HCl is added, NH₃ is gradually converted to its conjugate acid, ammonium (NH₄⁺). The equivalence point falls below pH 7, because the reaction's product, NH₄⁺, is itself a weak acid.

Weak acid + strong base (e.g., hypochlorous acid, HClO, titrated with NaOH): the solution starts acidic, but only mildly so, since HClO is a weak acid that only partially dissociates. As NaOH is added, HClO converts to its conjugate base, hypochlorite (ClO⁻). The equivalence point falls above pH 7, because ClO⁻ is a weak base.

Weak acid + weak base: the equivalence point isn't fixed at any particular pH — it depends on the relative strengths of the specific weak acid and weak base involved, and can fall above or below 7. The titration curve lacks the sharp inflection seen with a strong species, which makes the equivalence point hard to pinpoint and indicators far less useful. For this reason, weak acid/weak base titrations are rarely performed in practice; the most informative titrations involve at least one strong species.

Titrating Polyvalent Acids and Bases

As established when polyvalence and normality were first introduced, a polyprotic acid or polyvalent base can donate or accept more than one H⁺ or OH⁻ per molecule. Titrating one of these species is more complex than titrating a monoprotic species, because each ionizable proton (or hydroxide) produces its own equivalence point.

The titration curve for a polyvalent species shows multiple distinct stages, one for each proton or hydroxide donated or accepted. Before each equivalence point lies a buffer region, where pH changes only gradually with added titrant, because a weak acid and its conjugate base (or weak base and conjugate acid) are both present and resisting the pH change. Each proton in a polyprotic acid has its own pKa, and the differences between those pKa values are what produce distinctly separate buffer regions and equivalence points along the curve.

Buffers: Composition and Mechanism

A buffer is a solution that resists changes in pH when small amounts of acid or base are added to it. Buffers are essential for keeping the pH of biological systems, industrial processes, and chemical reactions within a controlled range.

A buffer solution is built from one of two pairings:

• A weak acid (HA) and its conjugate base (A⁻).

• A weak base (B) and its conjugate acid (BH⁺).

A buffer works through the common ion effect and Le Chatelier's principle: whichever species is added (acid or base), the buffer's other component reacts with it, minimizing the resulting change in pH.

• Adding a small amount of acid (H⁺): the conjugate base neutralizes it, forming the weak acid: H⁺ + A⁻ → HA

• Adding a small amount of base (OH⁻): the weak acid neutralizes it, forming water and the conjugate base: HA + OH⁻ → A⁻ + H₂O

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates a buffer's pH to the pKa of its weak acid and the ratio of its two components:

pH = pKa + log([A⁻]/[HA])

where pKa is the negative logarithm of the weak acid's dissociation constant (Ka), [A⁻] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. An analogous relationship holds for a weak-base buffer, expressed in terms of pKb and the ratio of conjugate acid to weak base.

Worked example: A buffer is made from 0.30 M acetic acid (CH₃COOH, Ka = 1.8×10⁻⁵) and 0.30 M sodium acetate (CH₃COONa). What is the buffer's pH?

pKa = −log(1.8×10⁻⁵) ≈ 4.74. Since [A⁻] = [HA] = 0.30 M, the ratio [A⁻]/[HA] = 1, and log(1) = 0:

pH = 4.74 + log(1) = 4.74

Buffer Capacity

Buffer capacity is the amount of acid or base that can be added to a buffer before it undergoes a significant change in pH. A high-capacity buffer can neutralize a large amount of added acid or base with little pH change; a low-capacity buffer is overwhelmed by a small amount.

Two factors determine buffer capacity:

• Concentration of the buffer components: capacity is directly proportional to the concentration of the weak acid and conjugate base (or weak base and conjugate acid) present — higher concentrations mean a greater ability to neutralize added acid or base.

• Ratio of the buffer components: capacity is greatest when the ratio of weak acid to conjugate base (or weak base to conjugate acid) is close to 1:1 — equivalently, when the buffer's pH is close to its pKa (or pKb). Buffer capacity is highest when pH is within about one pH unit of pKa, since that's the range where meaningful amounts of both the weak acid and its conjugate base are present to respond to an added acid or base.

The Bicarbonate Buffer System

One of the most important buffer systems in the human body is the bicarbonate buffer system, built from carbonic acid (H₂CO₃) and bicarbonate (HCO₃⁻). It helps hold blood pH around 7.4, essential for normal physiological function.

• Adding acid (excess H⁺): H⁺ reacts with HCO₃⁻ to form H₂CO₃, minimizing the drop in pH.

• Adding base (excess OH⁻): OH⁻ reacts with H₂CO₃ to form HCO₃⁻ and water, minimizing the rise in pH.

A supplied detail, independently verified — the transcript doesn't state either number: carbonic acid's physiological pKa is about 6.1, and normal blood maintains an HCO₃⁻:H₂CO₃ ratio of roughly 20:1 to hold pH at 7.4 (via the Henderson-Hasselbalch equation above). Notice that blood pH (7.4) sits more than one full pH unit away from the pair's own pKa (6.1) — by the buffer capacity rule just covered, that should make for a weak buffer. The bicarbonate system still works because, unlike a sealed benchtop buffer, it's an open system: the body actively regulates the concentration of both components rather than letting the ratio passively drift.

That active regulation comes from two organ systems:

• Respiratory system: adjusts the amount of CO₂ (which exists in equilibrium with H₂CO₃) in the blood by changing the breathing rate. Faster breathing (hyperventilation) exhales more CO₂, reducing H₂CO₃ and H⁺ and raising pH. Slower breathing (hypoventilation) retains CO₂, increasing H₂CO₃ and H⁺ and lowering pH.

• Renal system: the kidneys excrete H⁺ and reabsorb HCO₃⁻ from the urine, adjusting the buffer's bicarbonate side over a slower timescale.

Common MCAT Mistakes

• Confusing the equivalence point with the endpoint. The equivalence point is the theoretical stoichiometric point; the endpoint is when the indicator visibly changes. They're usually close but not automatically identical.

• Assuming every titration's equivalence point sits at pH 7. Only strong acid/strong base titrations land at pH 7. Strong-weak combinations land off-neutral, because the leftover conjugate ion hydrolyzes.

• Forgetting that buffer capacity depends on both concentration and ratio. A buffer with the "right" 1:1 ratio but very dilute components still has low capacity — both factors matter together.

• Assuming the bicarbonate buffer is a weak buffer just because blood pH is far from its pKa. On a closed benchtop system that reasoning would hold, but the bicarbonate system is actively regulated by the lungs and kidneys, which is what makes it effective despite the pH-pKa gap.

MCAT-Style Concept Check

Question: A weak acid HA (pKa = 5.20) is mixed with its conjugate base A⁻ such that [A⁻] = 3[HA]. What is the pH of this buffer?

• A) 4.72

• B) 5.20

• C) 5.68

• D) 6.20

Answer: C

Explanation: Using the Henderson-Hasselbalch equation, pH = pKa + log([A⁻]/[HA]) = 5.20 + log(3) ≈ 5.20 + 0.48 = 5.68. Choosing (B) mistakenly ignores the [A⁻]/[HA] ratio and assumes pH always equals pKa, which is only true when the ratio is exactly 1:1.

FAQ

What's the difference between the equivalence point and the endpoint of a titration?

The equivalence point is the theoretical point where moles of titrant exactly equal moles of titrand, based on stoichiometry. The endpoint is the practical point where the chosen indicator visibly changes color. A well-chosen indicator makes the two nearly coincide, but they aren't defined the same way.

Why does a weak acid/strong base titration have an equivalence point above pH 7?

At the equivalence point, all of the weak acid has been converted into its conjugate base. That conjugate base is itself a weak base, and it hydrolyzes in water to produce a small excess of OH⁻, pushing the solution's pH above 7.

What determines how effective a buffer is at resisting pH change?

Two factors: the total concentration of the buffer's weak acid/conjugate base (or weak base/conjugate acid) pair, and how close their ratio is to 1:1. Buffer capacity is highest when concentration is high and the ratio is near 1:1 — equivalent to the buffer's pH sitting close to its pKa.

Why is the bicarbonate buffer system able to maintain blood pH even though 7.4 is far from its pKa of 6.1?

Because it's an open system, not a sealed one. The respiratory system adjusts CO₂ (and therefore H₂CO₃) through breathing rate, and the renal system adjusts HCO₃⁻ through excretion and reabsorption — this active, ongoing regulation compensates for the pH-pKa gap that would otherwise make it a weak buffer.