E2.7 Determine acid or base concentration by titration

Ontario Grade 11 Chemistry

Solutions and Solubility

A Grade 11 guide to using a measured reaction to determine an unknown acid or base concentration

Imagine adding a clear solution from a burette to a flask that contains another clear solution and a few drops of indicator. At first, the indicator may show one colour. Near the end of the reaction, one added drop can cause a lasting colour change. That visible change helps show when enough acid or base has been added to react with the sample. In a titration, measured volumes and a balanced chemical equation let you calculate the sample’s concentration.

What you will learn

Explain how a titration can determine an unknown acid or base concentration.
Use a balanced neutralization equation to find the mole relationship between acid and base.
Calculate concentration from measured volume and known concentration, using consistent units and appropriate significant digits.

1. Review the quantities and the reaction

Concentration tells how much dissolved substance is present in a given volume of solution. In this lesson, concentration is expressed in moles per litre, written as mol/L. A mole is a chemistry counting unit. Volume is often measured in millilitres during a titration, but it must be changed to litres when it is used with concentration in mol/L to calculate moles.

The relationship between concentration, amount in moles, and volume is useful here. Rearranging it lets you find moles from a known concentration and volume, or concentration from a known amount and volume.

An acid-base neutralization reaction is a reaction in which an acid and a base react. For example, nitric acid reacts with potassium hydroxide to form water and the salt potassium nitrate. A balanced equation shows the number of each type of particle that reacts. In this example, one mole of acid reacts with one mole of base.

A titration is a method for finding the concentration of an acid or base by reacting it with a solution whose concentration is known. The known solution is added in measured amounts to a measured sample of the unknown solution. The balanced equation—not just the colour change—sets the amount relationship used in the calculation.

n=cV

Use concentration in mol/L and volume in L when calculating moles.
Balance the reaction before using its mole ratio.
A mole ratio comes from the coefficients in the balanced equation.

2. What the colour change tells you

An indicator is a substance that changes colour over a particular range of conditions. A few drops are added to the sample in the flask. As the known solution is added, the reaction uses up acid or base particles from the sample. Near the point where the reacting amounts match the balanced equation, a small extra addition can produce a lasting indicator colour change.

The equivalence point is the point at which the acid and base have reacted in the exact mole ratio shown by the balanced equation. The endpoint is the observed indicator colour change used to signal that point. They describe different things: one is the reaction condition, and the other is the visible observation. A suitable indicator helps the endpoint occur close to the equivalence point.

In a typical setup, a measured sample goes into a flask, and the solution of known concentration goes into a burette. A burette is a graduated tube with a tap that allows liquid to be added in controlled amounts. Record the starting and ending burette readings. The volume delivered is the ending reading minus the starting reading.

Swirl the flask as solution is added so the liquids mix. Near the colour change, add the known solution drop by drop. A lasting colour change signals the endpoint. Record the delivered volume and use it in the calculation. Do not treat a colour change by itself as a concentration measurement; the known concentration and reaction equation are also needed.

Endpoint is an observation; equivalence point is the reaction condition.
Delivered burette volume equals final reading minus initial reading.
The indicator helps identify the endpoint, while stoichiometry connects measured volumes to reacting amounts.

3. A reliable calculation method

Start with the balanced chemical equation. Identify which solution has the known concentration and which concentration is unknown. Keep track of which measured volume belongs to each solution.

Convert each volume from millilitres to litres before using the concentration relationship. Find the moles of the known solution from its concentration and delivered volume. Then use the coefficients in the balanced equation to determine the moles of the unknown solution.

Finally, divide the unknown moles by the volume of the unknown sample in litres. This gives its concentration in mol/L. Check that the result answers the question and that the units are correct. Round the final result to match the precision of the measured data; do not round intermediate values more than necessary.

c=\frac{n}{V}

Use the balanced equation’s coefficients to connect the two amounts in moles.
Use the sample volume—not the burette volume—to calculate the unknown sample concentration.
For a one-to-one reaction, the reacting moles are equal. Other balanced reactions may have a different mole ratio.

4. Check units and meaning

A concentration calculation should end in mol/L. If you use millilitres directly in a calculation with mol/L, the units will not match the concentration relationship. Convert millilitres to litres first, or convert both volumes in a consistent way and track the units carefully.

A result should also make sense for the measured quantities. For a one-to-one reaction, a greater number of moles of known solution means a greater number of moles of unknown solution reacted. If the unknown sample volume is fixed, that means a greater calculated concentration. If your answer is far from this relationship, review the volume conversion, burette subtraction, equation, and mole ratio.

Significant digits communicate the precision of measurements. Record readings as instructed for the measuring equipment, keep extra digits during calculations, and round the final concentration to a precision justified by the supplied measurements.

Check that the final unit is mol/L.
Subtract the initial burette reading from the final reading.
Retain extra digits until the final answer, then round appropriately.

Worked example

Finding nitric acid concentration

A 25.00 mL sample of nitric acid is titrated with 0.1200 mol/L potassium hydroxide. The burette reading changes from 1.25 mL to 19.90 mL at the endpoint. Determine the nitric acid concentration.

Write the balanced reaction
Nitric acid reacts with potassium hydroxide in a one-to-one mole ratio. The balanced equation shows that one mole of each reactant is used for each other.
$\mathrm{HNO_3(aq)+KOH(aq)\rightarrow KNO_3(aq)+H_2O(l)}$
Find the delivered base volume
Subtract the initial burette reading from the final reading. This is the volume of potassium hydroxide that reached the flask.
$19.90\ \mathrm{mL}-1.25\ \mathrm{mL}=18.65\ \mathrm{mL}=0.01865\ \mathrm{L}$
Calculate moles of base
Multiply the known base concentration by its volume in litres. The units reduce to moles.
$n(\mathrm{KOH})=(0.1200\ \mathrm{mol/L})(0.01865\ \mathrm{L})=0.002238\ \mathrm{mol}$
Use the mole ratio
The coefficients for nitric acid and potassium hydroxide are both one. Therefore, the nitric acid in the sample has the same number of moles as the potassium hydroxide delivered.
$n(\mathrm{HNO_3})=0.002238\ \mathrm{mol}$
Calculate the acid concentration
Convert the acid sample volume to litres, then divide the acid moles by that volume. The measured values support four significant digits.
$V(\mathrm{HNO_3})=0.02500\ \mathrm{L};\quad c(\mathrm{HNO_3})=\frac{0.002238\ \mathrm{mol}}{0.02500\ \mathrm{L}}=0.08952\ \mathrm{mol/L}$

Answer: The nitric acid concentration is 0.08952 mol/L.

Check: The equation has a one-to-one ratio, so equal moles of acid and base react. Dividing the acid moles by the acid sample volume gives mol/L, as required.

Common mistakes and how to avoid them

Using the final burette reading as the delivered volume.

Correction: Subtract the initial reading from the final reading to find the amount delivered.

Assuming acid and base always react in equal mole amounts.

Correction: Use the coefficients in the balanced equation. Equal moles apply only when the equation gives a one-to-one ratio.

Using the burette volume as the volume of the unknown sample when calculating its concentration.

Correction: Use the measured volume of the unknown sample for the final concentration calculation. Use the burette volume to calculate the moles of known solution delivered.

Reporting a concentration without units or using millilitres as though they were litres.

Correction: Convert volumes to litres for calculations with mol/L, and report the final concentration in mol/L.

Lesson summary

A titration determines an unknown acid or base concentration by reacting a measured sample with a solution of known concentration.
Use the indicator’s lasting colour change to identify the endpoint, and use the balanced equation to find the mole ratio.
Calculate moles from concentration and volume, use the equation’s coefficients, and divide unknown moles by the unknown sample volume in litres.
Check the delivered volume, units, and significant digits before reporting the result.

Check your understanding

Question 1

A 20.00 mL acid sample reacts with 15.00 mL of 0.1000 mol/L base. The balanced equation has a one-to-one mole ratio. What is the acid concentration?

0.07500 mol/L
0.1000 mol/L
0.1333 mol/L
0.7500 mol/L

Show answer and explanation

0.07500 mol/L

The base amount is (0.1000 mol/L)(0.01500 L) = 0.001500 mol. The one-to-one ratio gives the same acid amount. Dividing by 0.02000 L gives 0.07500 mol/L.

Question 2

A burette reading is 2.10 mL before adding solution and 17.45 mL at the endpoint. What volume was delivered?

15.35 mL
17.45 mL
19.55 mL
0.01535 mL

Show answer and explanation

15.35 mL

Delivered volume is the final reading minus the initial reading: 17.45 mL − 2.10 mL = 15.35 mL.

Key terms

Concentration: The amount of dissolved substance in a stated volume of solution; here it is measured in mol/L.
Titration: A method that uses a measured reaction with a solution of known concentration to determine an unknown acid or base concentration.
Indicator: A substance that changes colour over a particular range of conditions and helps show the titration endpoint.
Endpoint: The observed change, often a lasting indicator colour change, used to signal that the titration is complete.
Equivalence point: The point at which the reacting acid and base amounts match the mole ratio in the balanced equation.
Burette: A graduated tube with a tap that delivers and measures controlled volumes of solution.

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E2.7 · Determine acid or base concentration by titration