Chemistry · General chemistry II · Concept
Acid–base titration calculations
A titration adds a solution of known concentration, the titrant, to a measured volume of the analyte until the two have reacted in exactly the ratio of the balanced equation: the equivalence point. The moles of titrant used, n = cV, give the moles of analyte through the mole ratio, and dividing by the analyte’s volume gives its concentration. When a strong acid is titrated with a strong base, the pH rises slowly, jumps steeply near equivalence and is 7.00 at equivalence at 25 °C.
What a titration measures
A buret delivers the titrant into a flask holding a measured volume of the analyte. The equivalence point is reached when the titrant has supplied exactly the amount the balanced equation requires, and the buret volume there is the measurement.
From volume to concentration
Multiply the titrant’s volume, in liters, by its molarity to get moles. Convert to moles of analyte with the mole ratio from the balanced equation, then divide by the analyte’s volume in liters.
Mind the mole ratio
HCl and NaOH react 1 : 1, but sulfuric acid gives up two protons, so H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O needs twice as many moles of base as acid. The shortcut M₁V₁ = M₂V₂ works only for a 1 : 1 reaction; balance the equation first.
Endpoint and indicator
An indicator is a dye that changes color near the equivalence point. The volume at which it changes is the endpoint; a well-chosen indicator makes the endpoint and the equivalence point agree within a drop.
The pH along the curve
Before equivalence the leftover strong acid sets the pH, and after it the excess strong base does. At equivalence only water and a neutral salt remain, so the pH is 7.00 at 25 °C. Near equivalence a single drop moves the pH by several units, which is why the endpoint is sharp.
Weak acids
A weak acid titrated with a strong base has a buffer region, a pH equal to pKa halfway to equivalence and a pH above 7 at equivalence, because its conjugate base remains. The buffers page works such a curve point by point.
Common mistakes
- Using milliliters in n = cV without converting to liters.
- Applying M₁V₁ = M₂V₂ to a reaction that is not 1 : 1, such as H₂SO₄ with NaOH.
- Dividing by the combined volume at equivalence when the question asks for the analyte’s original concentration.
- Expecting pH 7 at every equivalence point: a weak acid titrated with a strong base gives a basic solution there.
Key terms
- Titration
- Adding a solution of known concentration, the titrant, to a sample until the reaction is complete, to find how much the sample contains. For acids and bases, a titration curve plots pH against volume added.
- Titrant and analyte
- The titrant is the solution added from the buret; the analyte is the substance being measured. Their reaction’s coefficients set how much titrant it takes to reach equivalence.
- Equivalence point
- The point in a titration where just enough titrant has been added to react completely with the sample. Its pH is 7 only for a strong acid with a strong base; halfway there, pH = pKa for a weak acid.
- Endpoint
- The point where the indicator changes color and the titration is stopped. It should be close to the equivalence point, but it isn’t exactly the same thing.
- Indicator
- A dye whose acid and base forms have different colors, so its color change signals the pH, such as phenolphthalein turning pink above about pH 8.2.
- Acid-base neutralization
- An acid reacting with a base to form water and a salt. The resulting solution isn’t always pH 7, especially when a weak acid or base is involved.
- Diprotic acid
- An acid with two ionizable protons, such as H₂SO₄ or H₂CO₃, which it loses in two steps with Ka1 > Ka2.
Work through an example
A 25.00 mL sample of hydrochloric acid is titrated with 0.1000 M NaOH, and the equivalence point is reached after 18.50 mL. Find the concentration of the acid.
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