Difficulty: Intermediate Prerequisites: Basic acid-base chemistry (pH, strong vs weak acids), molarity and dilution calculations, familiarity with lab glassware (burets, volumetric pipettes).
This topic sits at the intersection of acid-base equilibrium and quantitative analysis. It builds on what you already know about pH and Ka, and extends it into a practical lab technique: using a titration curve to identify an unknown weak acid by its pKa. If you are comfortable with equilibrium expressions and the pH scale, you are ready for this. If not, review those first.
When you slowly add a strong base (like NaOH) to a weak acid and plot pH against volume added, you get a titration curve with a characteristic S-shape. The pH at the half-equivalence point, where exactly half the acid has been neutralised, equals the pKa of the acid. Match that pKa to a table of known acids and you have identified your unknown.
Titration
A quantitative analytical method in which a solution of known concentration (the titrant) is added incrementally to a solution of unknown concentration (the analyte) until the reaction between them is complete. In simple terms, you drip one solution into another, measuring as you go, until the reaction finishes.
Titrant
The solution of known concentration added from the buret during a titration. Think of it as the "known" that you are adding to figure out the "unknown."
Analyte
The substance whose concentration or identity is being determined in a titration. This is the mystery solution sitting in the flask.
Weak acid
An acid that only partially dissociates in water, establishing an equilibrium between its undissociated form (HA) and its ions (H+ and A-). Think of it as an acid that does not go "all in" when dissolved. Only a fraction of its molecules release H+ ions at any given moment.
Strong base
A base that dissociates completely in water (e.g. NaOH breaks fully into Na+ and OH-). In simple terms, every molecule that dissolves contributes an OH- ion, no holdouts.
Equivalence point
The point in a titration where the moles of titrant added exactly equal the moles of analyte originally present. For a weak acid titrated with a strong base, the pH at the equivalence point is above 7 because the conjugate base of the weak acid makes the solution basic. Think of it as the moment every acid molecule has been neutralised, with nothing left over on either side.
Half-equivalence point
The point where exactly half the moles of the weak acid have been neutralised. At this point, [HA] = [A-], and the pH of the solution equals the pKa of the acid. This is the single most useful point on the curve for identification purposes: read the pH here and you have the pKa.
pKa
The negative base-10 logarithm of the acid dissociation constant Ka. A smaller pKa means a stronger acid (within the weak acid category). pKa = -log(Ka). In simple terms, it is a convenient number that tells you how readily a weak acid gives up its proton. Lower number, more willing.
Ka (acid dissociation constant)
The equilibrium constant for the dissociation of a weak acid in water: Ka = [H+][A-] / [HA]. A larger Ka means the acid dissociates more. It is the quantitative measure of acid strength.
Buffer region
The relatively flat portion of a titration curve, centred on the half-equivalence point, where the solution resists changes in pH because both HA and A- are present in significant amounts. This is the zone where adding base barely moves the pH, because the solution is buffering.
Henderson-Hasselbalch equation
An equation relating pH, pKa, and the ratio of conjugate base to weak acid: pH = pKa + log([A-]/[HA]). At the half-equivalence point, [A-] = [HA], so the log term is zero and pH = pKa. That is why this equation underpins the whole identification method.
Titration curve
A plot of solution pH (y-axis) against the volume of titrant added (x-axis). The shape of this curve reveals whether the analyte is a strong or weak acid and where the equivalence point falls. Think of it as the story of the reaction told in a graph.
A measured volume of weak acid (the analyte) is placed in a flask.
A strong base (the titrant, e.g. NaOH) is added slowly from a buret.
The neutralisation reaction is: HA + OH- --> A- + H2O.
pH is recorded after each addition and plotted against the total volume of base added.
A weak acid/strong base titration curve has four distinct regions:
Initial region (before any base is added)
pH is determined by the weak acid equilibrium alone.
The starting pH is above 0 but typically well below 7 (in this experiment, pH = 1.75 for 0.10 M unknown acid).
A strong acid of the same concentration would start at a lower pH because it dissociates fully.
Buffer region (from first addition up to the equivalence point)
Both HA and A- are present in solution. The solution resists pH changes.
The curve rises gradually through this region.
The midpoint of this region is the half-equivalence point, where [HA] = [A-] and pH = pKa.
In the lab data, this region runs roughly from 0 mL to about 18 mL of NaOH added, with the curve climbing slowly from pH 1.75 to around pH 4.6.
Equivalence point region (the steep rise)
A very small addition of base causes a large pH jump.
At the equivalence point itself, all the weak acid has been converted to its conjugate base A-.
The pH at the equivalence point for a weak acid/strong base titration is above 7 (in this experiment, the steep jump occurs around 18-19 mL of NaOH added, with pH leaping from roughly 4.6 to 9.2).
Post-equivalence region (excess base)
Beyond the equivalence point, added OH- has nothing to react with and simply accumulates.
pH levels off in the strongly basic range (pH 10-12 in this experiment).
Calculate the volume of base needed to reach the equivalence point. In this experiment: moles of acid = 0.10 M x 10.00 mL = 1.00 mmol. Volume of NaOH at equivalence = 1.00 mmol / 0.055 M = 18.18 mL.
The half-equivalence point is at half that volume: approximately 9.09 mL of NaOH added.
Read the pH at that volume from the titration curve. That pH equals the pKa.
In this experiment, the pKa was found to be 3.15.
Once you have the pKa, compare it against a reference table of known weak acids.
The lab report identified the unknown as hydrofluoric acid (HF), which has a literature pKa of 3.17, a close match to the experimental value of 3.15.
Small discrepancies between experimental and literature values are expected due to measurement error, temperature variation, and impurities.
K_a = \frac{[H^+][A^-]}{[HA]}This is the acid dissociation constant expression for a generic weak acid HA.
pK_a = -\log(K_a)Converts Ka to a more convenient scale. A smaller pKa means a stronger weak acid.
pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)The Henderson-Hasselbalch equation. At the half-equivalence point, [A-] = [HA], so log(1) = 0, and pH = pKa.
Equivalence point volume calculation:
Moles of acid = concentration of acid x volume of acid. Volume of base at equivalence = moles of acid / concentration of base.
For this experiment: (0.10 M)(10.00 mL) / 0.055 M = 18.18 mL of NaOH.
Titration is a routine method in pharmaceutical quality control: manufacturers titrate drug formulations to verify that the active ingredient concentration falls within its labelled range. The same principles are used in environmental testing, where water samples are titrated to determine acidity levels in lakes and rivers affected by acid rain. Hydrofluoric acid itself, the acid identified in this experiment, is used industrially for glass etching, semiconductor manufacturing, and petroleum refining.
Students often assume the equivalence point pH is always 7.0. It is not. For a weak acid/strong base titration, the equivalence point is above 7 because the conjugate base (A-) hydrolyses in solution to produce OH-.
Students confuse the equivalence point with the half-equivalence point. The equivalence point is where all the acid is neutralised. The half-equivalence point is where half is neutralised, and that is where pH = pKa.
Students sometimes believe that a lower pKa means a weaker acid. The opposite is true within the weak acid category: a lower pKa corresponds to a stronger weak acid (it dissociates more readily).
Students sometimes read the buret volume directly as the volume of NaOH added, forgetting to subtract the initial buret reading. Volume added = final buret reading minus initial buret reading.
Expect to be asked to sketch or interpret a weak acid/strong base titration curve and label key points (initial pH, buffer region, half-equivalence point, equivalence point, post-equivalence region).
A common exam question gives you a titration curve and asks you to determine the pKa. The answer is simply the pH at the half-equivalence point.
You may be asked to calculate the equivalence point volume using M_acid x V_acid = M_base x V_base.
Know why the equivalence point pH is above 7 for this type of titration. The conjugate base of the weak acid hydrolyses, producing OH-.
Exams frequently ask you to identify an unknown acid given its experimental pKa and a reference table.
True or False: At the half-equivalence point of a weak acid/strong base titration, pH = pKa. (True)
True or False: The equivalence point pH of a weak acid/strong base titration is exactly 7.0. (False, it is above 7)
Fill in the blank: The Henderson-Hasselbalch equation is pH = pKa + log( ______ / ______ ). ([A-] / [HA])
True or False: A weak acid with pKa = 2.5 is a stronger acid than one with pKa = 4.8. (True)
Fill in the blank: In the buffer region of a titration curve, both ______ and ______ are present in significant concentrations. (HA and A-)
Q: A 25.00 mL sample of 0.10 M weak acid is titrated with 0.10 M NaOH. What volume of NaOH is needed to reach the equivalence point?
A: 25.00 mL. Since the concentrations are equal, equal volumes are needed: (0.10)(25.00) = (0.10)(V), so V = 25.00 mL.
Q: You are given a titration curve for a weak acid/strong base titration. The equivalence point occurs at 20.0 mL of NaOH. At what volume of NaOH is pH = pKa?
A: 10.0 mL, which is half the equivalence point volume.
Q: Why is the equivalence point pH above 7 in a weak acid/strong base titration?
A: At the equivalence point, all the weak acid HA has been converted to its conjugate base A-. The conjugate base undergoes hydrolysis (A- + H2O --> HA + OH-), producing hydroxide ions, which makes the solution basic.
Q: A student reads a pKa of 3.15 from a titration curve. A reference table lists the following pKa values: acetic acid 4.76, hydrofluoric acid 3.17, formic acid 3.75, nitrous acid 3.40. Which acid is the most likely identity of the unknown?
A: Hydrofluoric acid (HF), because its literature pKa of 3.17 is closest to the experimental value of 3.15.
Q: Explain what happens to the pH when you add NaOH in the buffer region of a weak acid titration curve, and why the change is small.
A: The added OH- reacts with HA to form more A-. Because both HA and A- are present in large amounts, the ratio [A-]/[HA] changes only slightly, so the Henderson-Hasselbalch equation (pH = pKa + log([A-]/[HA])) produces only a small pH shift.
This material connects directly to chemical equilibrium: the Ka expression is just a specific case of the general equilibrium constant Keq applied to acid dissociation. If you understand Le Chatelier's principle, you can reason about what happens when base is added (equilibrium shifts right, more dissociation).
Buffer solutions are a natural extension. The buffer region of the titration curve is a working buffer in action, and understanding why pH changes slowly there prepares you for buffer design problems in later chapters.
The concept of conjugate acid-base pairs runs through this entire topic. At the equivalence point, the solution is essentially a solution of the conjugate base, and its pH depends on Kb, which links back to the Kw = Ka x Kb relationship.
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