E. Solutions and Solubility · Solutions and Solubility

Acid-Base Titration: How Much Acetic Acid Is in Vinegar?

E2.7 E2.6 E2.5 A1.2 A1.5 A1.6 A1.13About 75 minutes

Learning goals

I can describe the equipment and procedure for an acid-base titration and explain each step.
I can distinguish the equivalence point from the endpoint and choose a suitable indicator.
I can calculate the concentration of an acid (such as acetic acid in vinegar) from titration data.
I can evaluate titration data for precision and identify sources of error.

Words to know

titration
A procedure in which a solution of known concentration is added gradually to a measured volume of another solution until the reaction is just complete.

titrant
The solution of known concentration in the burette.

analyte (sample)
The solution of unknown concentration in the flask.

equivalence point
The point at which the amounts of acid and base are exactly in the mole ratio of the balanced equation.

endpoint
The point at which the indicator changes colour; a well-chosen indicator makes the endpoint very close to the equivalence point.

burette
A long graduated tube with a tap, used to deliver measured volumes; read to two decimal places by estimating between the 0.1 mL marks.

acid-base indicator
A weak acid or base whose colour changes over a particular pH range, such as phenolphthalein (colourless to pink, pH 8.2 to 10).

Checking the label

A bottle of white vinegar in a Canadian grocery store usually says 5% acetic acid. How would a food-inspection lab check that? It would perform a titration: carefully adding a base of known concentration to a measured volume of vinegar until all of the acid is neutralized, and then using stoichiometry to work backward to the acid's concentration. Titration is one of the most common analytical methods in chemistry, used for food, medicines, wine, swimming pools and water quality.

Remember from earlier lessons

Neutralization: CH₃COOH(aq) + NaOH(aq) → NaCH₃COO(aq) + H₂O(l), net ionic CH₃COOH(aq) + OH⁻(aq) → CH₃COO⁻(aq) + H₂O(l). A weak acid needs the same amount of base as a strong acid of equal moles. Solution stoichiometry: n = cV and the mole ratio.

The equipment

Burette: holds the titrant (here, NaOH of known concentration). You record the starting and final readings; the difference is the volume added.
Volumetric pipette (with bulb): delivers an exact volume of the analyte (vinegar), e.g. 10.00 mL, into the flask.
Erlenmeyer flask: its sloped sides let you swirl without splashing.
Indicator: a few drops, chosen to change colour at the right pH.
A white tile or paper under the flask makes the colour change easy to see.

A titration set-up. The burette delivers sodium hydroxide into a measured volume of vinegar until the indicator turns faint pink. Not to scale.

The procedure

Rinse the burette with a little of the NaOH solution (so water does not dilute it), then fill it. Run some out to remove the air bubble in the tip. Record the initial reading at the bottom of the meniscus, to two decimal places.
Pipette exactly 10.00 mL of vinegar into a clean Erlenmeyer flask. Add about 50 mL of distilled water (this does not change the moles of acid, and it makes the colour easier to see) and 2 drops of phenolphthalein.
Rough trial: add NaOH fairly quickly while swirling until the solution stays pink. This tells you roughly where the endpoint is.
Accurate trials: refill, and add NaOH quickly to about 1 mL before the rough endpoint, then drop by drop, swirling, until one drop turns the whole solution a faint pink that lasts 30 seconds. Record the final reading.
Repeat until you have three trials within 0.20 mL of each other. Average those.

Endpoint and equivalence point

The equivalence point is where the moles of OH⁻ added exactly equal the moles of acid originally present. You cannot see it directly. The endpoint is where the indicator changes colour. Choose an indicator that changes colour at the pH of the equivalence point:

weak acid + strong base (vinegar + NaOH): the solution at equivalence contains acetate ions, a weak base, so the pH is above 7 (about 9). Use phenolphthalein (colourless → pink, pH 8.2 to 10).
strong acid + strong base: equivalence at pH 7. Bromothymol blue (yellow → blue, pH 6.0 to 7.6) works well; phenolphthalein also works because the pH rises so steeply.
strong acid + weak base: equivalence below 7; methyl orange (red → yellow, pH 3.1 to 4.4).

A calculated titration curve for 10.00 mL of vinegar (0.831 mol/L acetic acid) with 0.500 mol/L NaOH. The pH jumps steeply near the equivalence point, and the jump passes right through phenolphthalein's colour-change range.

Trial	Initial reading (mL)	Final reading (mL)	Volume NaOH (mL)
1 (rough)	0.00	17.10	17.10
2	0.35	16.95	16.60
3	16.95	33.60	16.65
4	1.20	17.82	16.62

Sample titration data: 10.00 mL of vinegar titrated with 0.500 mol/L NaOH(aq). Trials 2 to 4 agree within 0.05 mL.

Worked example

Example 1: Acetic acid in vinegar

Use the sample data above. Find (a) the average volume of NaOH, (b) the molar concentration of acetic acid, (c) its concentration in % m/v. (M(CH₃COOH) = 60.06 g/mol) Compare with the label (5%).

(a) Use only the accurate trials (2, 3, 4), which agree within 0.20 mL: (16.60 + 16.65 + 16.62) ÷ 3 = 16.62 mL. The rough trial is not included.
(b) n(NaOH) = cV = 0.500 mol/L × 0.01662 L = 0.008310 mol. Mole ratio 1 : 1, so n(CH₃COOH) = 0.008310 mol. c = n ÷ V = 0.008310 mol ÷ 0.01000 L = 0.831 mol/L.
(c) 0.831 mol/L × 60.06 g/mol = 49.9 g/L = 4.99 g/100 mL = 4.99% m/v.
Compare: 4.99% agrees with the label's 5% (a percentage difference of about 0.2%).

0.831 mol/L acetic acid, or 4.99% m/v, consistent with the 5% label.

Worked example

Example 2: A strong acid titration

A 25.00 mL sample of HCl(aq) needs 21.36 mL of 0.1050 mol/L NaOH(aq) to reach the endpoint with bromothymol blue. Find [HCl].

Equation: HCl + NaOH → NaCl + H₂O (1 : 1).
n(NaOH) = 0.1050 × 0.02136 = 0.002243 mol = n(HCl).
c = 0.002243 ÷ 0.02500 = 0.08971 mol/L (four significant digits, matching the data).

[HCl] = 0.08971 mol/L

Precision, accuracy and error (A1.8, A1.13)

Precision: do repeated trials agree? Within 0.20 mL (or better, 0.10 mL) is the usual goal. Accuracy: how close is the result to the true value (e.g. the label)?

Common errors and their effect on the calculated acid concentration:

Overshooting the endpoint (dark pink instead of faint pink): volume of base too large → concentration too high.
Burette rinsed with water, not NaOH: the NaOH is diluted, so more is needed → concentration too high.
Air bubble in the burette tip that comes out during the titration: reading is too large → concentration too high.
Pipette not rinsed with vinegar (water left inside dilutes the sample): fewer moles of acid → concentration too low.
Adding distilled water to the flask does not cause an error: the moles of acid stay the same.

Sodium hydroxide slowly absorbs CO₂ from the air, so labs standardize it (titrate it against a very pure acid) before use.

Just for fun

A titration is the only time in chemistry class when you are trying to make something slightly pink. One drop too many and it's flamingo pink: the chemistry version of adding too much hot sauce.

Hands-on activity

Kitchen titration of vinegar with baking soda and cabbage indicator

You need: red cabbage indicator (from the Arrhenius lesson; store it in the fridge), white vinegar, apple cider vinegar (optional, for comparison), baking soda, water, a 10 mL medicine syringe or a medicine dropper, a measuring spoon, 3 small clear glasses, and a white sheet of paper.

Make the titrant: dissolve 1 level teaspoon of baking soda in 100 mL of water. Stir well and let any undissolved powder settle.
In a glass, put 1 teaspoon (5 mL) of vinegar and about 30 mL of cabbage indicator. It turns pink-red.
Fill the syringe with the baking soda solution. Add it to the vinegar 1 mL at a time, swirling and waiting for fizzing to stop each time. Near the end, add it a few drops at a time.
The endpoint is when the colour changes from pink/purple to blue and stays. Record the total volume of baking soda solution.
Repeat twice more. Are your trials within 1 mL of each other?
Repeat with apple cider vinegar. Which vinegar contains more acid per teaspoon?

What to look for: the colour shifts from pink to purple to blue as the acid is used up. If one vinegar needs more baking soda solution, it contains more acetic acid per 5 mL. Your answer is a comparison, not an exact concentration, because the baking soda concentration and the endpoint are not precise. List two ways the school-lab titration is more precise (burette, standard NaOH, phenolphthalein's sharp change). Everything can go down the drain.

Your turn

What is the difference between the endpoint and the equivalence point?

Why is phenolphthalein a good indicator for vinegar + NaOH?

Titration readings: initial 2.15 mL, final 20.43 mL. What volume was added?

10.00 mL of vinegar needs 14.80 mL of 0.600 mol/L NaOH. Find [CH₃COOH].

Convert 0.888 mol/L acetic acid into % m/v.

Trials: 15.42, 15.95, 15.48, 15.45 mL. Which should be averaged? Find the average.

Why is the burette rinsed with NaOH solution instead of water before filling?

More practice: warm-up

What piece of glassware delivers the titrant?

What colour is phenolphthalein in acid? In base?

Why use an Erlenmeyer flask instead of a beaker?

To how many decimal places is a burette read in this lesson?

Does adding distilled water to the acid in the flask change the volume of base needed?

More practice: on your own

20.00 mL of H₂SO₄ is titrated with 0.150 mol/L NaOH; the average volume is 24.60 mL. Find [H₂SO₄].

A student overshoots the endpoint, so the solution turns dark pink. Will the calculated vinegar concentration be too high or too low? Explain.

Which indicator would you choose for titrating ammonia (a weak base) with HCl? Why?

A 25.00 mL sample of NaOH is titrated with 0.1000 mol/L HCl; 18.75 mL is needed. Find [NaOH].

Explain why the rough trial is not included in the average.

Challenge

A 10.00 mL sample of vinegar is diluted to 100.0 mL in a volumetric flask. A 25.00 mL portion of the diluted vinegar needs 20.85 mL of 0.1000 mol/L NaOH. Find the acetic acid concentration in the original vinegar, in mol/L and % m/v.

The NaOH used in a titration had absorbed CO₂ from the air, so its true concentration was lower than the label. Would the calculated acid concentration be too high or too low? Explain.

Using the titration curve in this lesson, explain why the pH at the equivalence point is above 7 for acetic acid + NaOH, but 7 for HCl + NaOH.

Check your understanding

Quiz

In a titration, the solution of known concentration in the burette is the

The endpoint of a titration is when

10.00 mL of vinegar needs 16.00 mL of 0.500 mol/L NaOH. [CH₃COOH] is

Which indicator is best for acetic acid titrated with NaOH?

A student forgets to rinse the burette with NaOH (it had water in it). The calculated acid concentration will be

Which set of trials is precise enough to average?

For parents and teachers

Big idea (E2.7): titration uses a measured volume of a standard solution to find an unknown concentration through stoichiometry.

How to help: During the kitchen titration, ask your teen to name what plays the role of each piece of lab equipment (syringe = burette; cabbage = indicator; teaspoon = pipette) and what makes the lab version more precise. Check their calculation with the road map: volume × concentration → moles → mole ratio → concentration.

Common difficulties:

Including the rough trial or an outlier in the average.
Forgetting to convert mL to L.
Using a 1 : 1 ratio for diprotic acids like H₂SO₄.
Confusing endpoint and equivalence point.
Deciding whether an error makes the answer too high or too low: follow the error through the formula c = n/V.

Safety: sodium hydroxide is corrosive; titrations with it are done in a supervised school lab with goggles. The kitchen titration uses only vinegar, baking soda and cabbage water.