Acid-base titrations

Chemistry 1110 · CCEA AS Level · 10 min read · Updated: Aug 31, 2026

Acid-Base Titrations

Welcome to one of the most practical and rewarding topics in AS Chemistry! Have you ever wondered how food scientists test the exact acidity of lemon juice, or how environmental scientists check water quality in rivers? They use a technique called volumetric analysis, specifically titrations.

Don't worry if quantitative chemistry seems intimidating at first. By breaking the procedure down into simple steps—preparing solutions, using apparatus correctly, and applying a straightforward 4-step calculation recipe—you will master this topic in no time!

Did you know? Titrations are widely used in medicine, from determining the concentration of vitamin C in tablets to measuring blood glucose levels!

1. Standard Solutions

What is a Standard Solution?

A standard solution is simply a solution whose concentration is accurately known. In any titration, you need at least one solution with a known concentration to figure out the unknown concentration of another.

To make a primary standard solution directly, we use a chemical known as a primary standard. Not all substances can be used as primary standards!

Characteristics of a Good Primary Standard:

• High purity: It must be completely pure (typically \(>99.9\%\)) so no impurities alter the calculated moles.
• Stability in air: It must not absorb moisture or carbon dioxide from the air (it must not be hygroscopic or deliquescent).
• Known chemical formula: It must have a completely fixed and known composition.
• Relatively high molar mass (\(M_{\text{r}}\)): A larger molar mass means you weigh out a greater mass, which minimises the percentage weighing error.

Why isn't solid sodium hydroxide (\(\text{NaOH}\)) a primary standard? Solid \(\text{NaOH}\) readily absorbs water vapour and carbon dioxide (\(\text{CO}_2\)) from the air, meaning its mass is never pure \(\text{NaOH}\). Therefore, a solution of \(\text{NaOH}\) must always be standardised against an acid primary standard (such as hydrated ethanedioic acid or potassium hydrogenphthalate).

Step-by-Step: Preparing a Standard Solution

1. Weigh accurately: Weigh the solid solute using a balance and a weighing boat, recording the mass to \(2\) or \(3\) decimal places. Use the method of weighing by difference (weigh the boat with solid, empty the solid into a beaker, reweigh the boat, and subtract).
2. Dissolve: Add a small volume of deionised water (approx. \(50\text{ cm}^3\) to \(100\text{ cm}^3\)) to the solid in a beaker and stir with a glass rod until completely dissolved.
3. Transfer quantitatively: Pour the solution into a volumetric flask using a filter funnel. Rinse the beaker, glass rod, and funnel with deionised water, pouring all washings into the volumetric flask.
4. Make up to the mark: Add deionised water until the bottom of the meniscus is level with the graduation line at eye level. Use a dropping pipette for the last few drops to avoid overshooting.
5. Invert to mix: Stopper the volumetric flask and invert it repeatedly (at least \(10\) to \(15\) times) to ensure thorough mixing and uniform concentration throughout.

Key Takeaway: A primary standard must be pure, stable, and have a high \(M_{\text{r}}\). Always include washings when transferring, and invert the volumetric flask to mix.

2. Titration Apparatus and Rinsing Rules

The Key Apparatus

• Volumetric Pipette: Delivers an exact, fixed volume of solution (e.g. \(25.0\text{ cm}^3\)) into the conical flask.
• Burette: Delivers a variable, accurately measured volume of solution into the conical flask.
• Conical Flask: Holds the reaction mixture. Its sloped sides prevent splashing when swirled.
• White Tile: Placed under the conical flask to make the colour change at the end point easy to see.

The Golden Rules of Rinsing

Getting the rinsing wrong is the most common reason for inaccurate practical results. Here is the simple logic:

• Burette: Rinse with deionised water, then rinse with the solution to be filled into it. (Rinsing only with water would dilute your reagent!)
• Pipette: Rinse with deionised water, then rinse with the solution to be measured. (Again, residual water would dilute your sample!)
• Conical Flask: Rinse ONLY with deionised water. Do not rinse with the solution being pipetted into it! Residual deionised water does not change the total number of moles of reagent placed inside.

Quick Review Box:
• Pipette \(\rightarrow\) rinse with solution it delivers.
• Burette \(\rightarrow\) rinse with solution it contains.
• Conical flask \(\rightarrow\) rinse with deionised water only.

Key Takeaway: Never rinse a conical flask with the solution you put into it—only rinse it with deionised water!

3. Acid-Base Indicators

How Indicators Work

An indicator is a weak acid (or base) that changes colour depending on the \(\text{pH}\) of the solution. The moment when the indicator permanently changes colour is called the end point of the titration.

The two main indicators used in AS Chemistry are phenolphthalein and methyl orange:

• Phenolphthalein:
    • In acid: Colourless
    • In alkali: Pink
    • End point (titrating acid with alkali): First permanent pale pink colour.
    • End point (titrating alkali with acid): Colour change from pink to colourless.

• Methyl Orange:
    • In acid: Red
    • In alkali: Yellow
    • End point (titrating alkali with acid): Orange (colour change from yellow to orange).

Choosing the Correct Indicator

The choice of indicator depends on the combination of acid and base:

• Strong Acid + Strong Base (e.g. \(\text{HCl}\) and \(\text{NaOH}\)): Either phenolphthalein or methyl orange can be used because the \(\text{pH}\) change at the equivalence point is very large.
• Strong Acid + Weak Base (e.g. \(\text{HCl}\) and \(\text{NH}_3\)): Use methyl orange.
• Weak Acid + Strong Base (e.g. \(\text{CH}_3\text{COOH}\) and \(\text{NaOH}\)): Use phenolphthalein.
• Weak Acid + Weak Base: Neither indicator is suitable because there is no sharp \(\text{pH}\) change.

Memory Trick:
• Strong Acid \(\rightarrow\) Methyl orange (think: SAM).
• Weak Acid \(\rightarrow\) Phenolphthalein (think: WAP).

Key Takeaway: Match the indicator to the strength of the acid and base so that the indicator changes colour sharply at the equivalence point.

4. Carrying Out the Titration & Handling Data

Burette Readings and Concordancy

1. Remove the funnel: Always remove the funnel from the top of the burette after filling to prevent stray drops falling in.
2. Fill the jet: Ensure the space below the tap (the jet) is filled with liquid and contains no air bubbles.
3. Reading the burette: Always read the bottom of the meniscus at eye level. Burettes are read to \(2\) decimal places, where the final digit is either \(0\) or \(5\) (e.g. \(21.40\text{ cm}^3\) or \(21.45\text{ cm}^3\)).
4. Rough Titre: The first run is a rough estimate to find the approximate volume needed. Add liquid quickly while swirling.
5. Accurate Titres: Perform further runs, adding liquid dropwise near the end point until you obtain concordant results.

What are Concordant Results?

Concordant titres are titres that are within \(0.10\text{ cm}^3\) of each other (e.g. \(22.30\text{ cm}^3\) and \(22.40\text{ cm}^3\)).

Rule for calculating the mean titre:
• Use only the concordant titres.
• Never include the rough titre in your average!
• Express your mean titre to \(2\) decimal places.

Example: If your titres are \(23.80\text{ cm}^3\) (rough), \(22.40\text{ cm}^3\) (titre 1), \(22.60\text{ cm}^3\) (titre 2), and \(22.45\text{ cm}^3\) (titre 3):
Concordant titres = \(22.40\text{ cm}^3\) and \(22.45\text{ cm}^3\) (within \(0.10\text{ cm}^3\)).
\(\text{Mean titre} = \frac{22.40 + 22.45}{2} = 22.43\text{ cm}^3\).

Key Takeaway: Concordant titres must be within \(0.10\text{ cm}^3\) of each other. Only average concordant accurate titres.

5. Titration Calculations Step-by-Step

The 4-Step Calculation Recipe

Whenever you face a titration calculation, follow this universal recipe:

1. Find moles of known substance: Use \(n = c \times V\) (where volume \(V\) is converted to \(\text{dm}^3\) by dividing by \(1000\)).
2. Use the balanced equation: Look at the stoichiometry (molar ratio) to find the moles of the unknown substance.
3. Scale up if necessary: If only a portion (aliquot) of a larger volume was titrated, multiply by the scaling factor (e.g. \(\times 10\) if \(25.0\text{ cm}^3\) was taken from \(250.0\text{ cm}^3\)).
4. Answer the question: Find the concentration (\(c = \frac{n}{V}\)), mass (\(m = n \times M_{\text{r}}\)), or molar mass (\(M_{\text{r}} = \frac{m}{n}\)).

Core Formulas to Remember

• \(\text{Moles } (n) = \text{concentration } (c) \times \text{volume in dm}^3 = \frac{c \times V\text{ (in cm}^3\text{)}}{1000}\)
• \(\text{Concentration } (c) = \frac{n}{V\text{ (in dm}^3\text{)}}\)
• \(\text{Mass } (m) = n \times M_{\text{r}}\)
• \(\text{Concentration in g dm}^{-3} = \text{concentration in mol dm}^{-3} \times M_{\text{r}}\)

Worked Example 1: Finding an Unknown Concentration

Problem: A \(25.0\text{ cm}^3\) sample of sodium hydroxide (\(\text{NaOH}\)) solution required \(21.50\text{ cm}^3\) of \(0.100\text{ mol dm}^{-3}\) hydrochloric acid (\(\text{HCl}\)) for neutralisation. Calculate the concentration of the \(\text{NaOH}\) solution in \(\text{mol dm}^{-3}\).

Chemical Equation:
\(\text{HCl(aq)} + \text{NaOH(aq)} \rightarrow \text{NaCl(aq)} + \text{H}_2\text{O(l)}\)

Step 1: Moles of known (\(\text{HCl}\)):
\(n(\text{HCl}) = c \times V = 0.100\text{ mol dm}^{-3} \times \left(\frac{21.50}{1000}\text{ dm}^3\right) = 0.00215\text{ mol}\)

Step 2: Mole ratio:
From the equation, \(1\text{ mol HCl} : 1\text{ mol NaOH}\).
Therefore, \(n(\text{NaOH}) = 0.00215\text{ mol}\).

Step 3: Calculate concentration of \(\text{NaOH}\):
\(c(\text{NaOH}) = \frac{n}{V} = \frac{0.00215\text{ mol}}{\left(\frac{25.0}{1000}\text{ dm}^3\right)} = \frac{0.00215}{0.0250} = 0.0860\text{ mol dm}^{-3}\)

Worked Example 2: Determining the Molar Mass of an Unknown Acid

Problem: \(1.50\text{ g}\) of an unknown solid monoprotic acid (\(\text{HA}\)) was dissolved in deionised water and made up to \(250.0\text{ cm}^3\) in a volumetric flask. A \(25.0\text{ cm}^3\) sample of this solution required \(24.00\text{ cm}^3\) of \(0.100\text{ mol dm}^{-3}\text{ NaOH}\) solution for neutralisation. Calculate the relative formula mass (\(M_{\text{r}}\)) of the acid \(\text{HA}\).

Chemical Equation:
\(\text{HA(aq)} + \text{NaOH(aq)} \rightarrow \text{NaA(aq)} + \text{H}_2\text{O(l)}\)

Step 1: Moles of \(\text{NaOH}\) used:
\(n(\text{NaOH}) = 0.100 \times \frac{24.00}{1000} = 0.00240\text{ mol}\)

Step 2: Moles of \(\text{HA}\) in the \(25.0\text{ cm}^3\) sample:
Ratio is \(1:1\), so \(n(\text{HA}\text{ in }25.0\text{ cm}^3) = 0.00240\text{ mol}\)

Step 3: Scale up to the total \(250.0\text{ cm}^3\) volumetric flask:
\(\text{Scaling factor} = \frac{250.0\text{ cm}^3}{25.0\text{ cm}^3} = 10\)
\(n(\text{HA}\text{ in }250.0\text{ cm}^3) = 0.00240\text{ mol} \times 10 = 0.0240\text{ mol}\)

Step 4: Calculate the molar mass (\(M_{\text{r}}\)):
\(M_{\text{r}} = \frac{\text{mass}}{\text{moles}} = \frac{1.50\text{ g}}{0.0240\text{ mol}} = 62.5\text{ g mol}^{-1}\)
Relative formula mass \(M_{\text{r}} = 62.5\)

Key Takeaway: Always remember to scale up when an aliquot (a portion) from a standard solution flask is used in the titration!

6. Common Mistakes to Avoid in Exams

• Forgetting to divide by 1000: Volumes are usually measured in \(\text{cm}^3\). Always convert to \(\text{dm}^3\) when calculating moles!
• Including the rough titre in the average: The rough titre is only an estimate and must be excluded when calculating the mean titre.
• Averaging non-concordant values: Only use values within \(0.10\text{ cm}^3\) of each other.
• Forgetting the scaling factor: If you prepared a \(250.0\text{ cm}^3\) solution but only titrated \(25.0\text{ cm}^3\), remember that the flask contains \(10\times\) the number of moles.
• Incorrect stoichiometry: Always check the balanced equation. If the reaction is \(2\text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}\), the ratio is \(2:1\), meaning \(n(\text{NaOH}) = 2 \times n(\text{H}_2\text{SO}_4)\).

Chapter Summary Review

• A primary standard must be pure, stable, have a known formula, and have a high \(M_{\text{r}}\).
• Rinse the burette and pipette with their respective solutions; rinse the conical flask with deionised water only.
• Phenolphthalein is colourless in acid and pink in alkali (ideal for weak acid - strong base).
• Methyl orange is red in acid and yellow in alkali (ideal for strong acid - weak base).
• Concordant titres are within \(0.10\text{ cm}^3\) of each other.
• Use the 4-step method: Moles of known \(\rightarrow\) Mole ratio \(\rightarrow\) Scale up \(\rightarrow\) Calculate unknown.

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is a standard solution and what properties define a good primary standard?

A standard solution has an accurately known concentration. A good primary standard must be highly pure, stable in air, have a known formula, and have a relatively high molar mass ( \(M_{\text{r}}\)) to minimise percentage weighing errors.

What are the key experimental steps required to prepare a standard solution accurately?

Weigh by difference, dissolve the solid in a beaker using deionised water, transfer quantitatively into a volumetric flask with washings, make up to the mark with a dropper at eye level, and invert 10 to 15 times to mix thoroughly.

What are the key pieces of apparatus used in a titration and what are their functions?

A volumetric pipette delivers an exact fixed volume, a burette delivers a variable measured volume, a conical flask holds the reaction mixture and prevents splashing, and a white tile improves visibility of the end-point colour change.

What are the correct rinsing rules for a pipette, a burette, and a conical flask?

Rinse the pipette and burette with deionised water followed by the solution they will contain. Rinse the conical flask only with deionised water.

What are the colour changes for phenolphthalein and methyl orange in acid and alkali?

Phenolphthalein is colourless in acid and pink in alkali. Methyl orange is red in acid, yellow in alkali, and orange at its end point.

How do you choose between phenolphthalein and methyl orange for different acid-base combinations?

Use phenolphthalein for weak acid - strong base, methyl orange for strong acid - weak base, and either indicator for strong acid - strong base.

How should burette readings be recorded and what defines concordant titres?

Read the bottom of the meniscus at eye level to 2 decimal places (ending in .00 or .05). Concordant titres are values within \(0.10\text{ cm}^3\) of each other.

What is the general 4-step recipe for solving titration calculation problems?

1. Calculate moles of known substance (\(n = c \times V\)). 2. Use the stoichiometric ratio to find moles of unknown. 3. Apply a scaling factor if an aliquot was taken. 4. Calculate required quantity (\(c\), \(m\), or \(M_{\text{r}}\)).

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