Acid Base Titration – Definition, Curve, Calculations, and Examples

An acid base titration is a quantitative analytical technique in which a solution of known concentration reacts with an acid or base of unknown concentration to determine its molarity through stoichiometric neutralization.

Key Takeaways: Acid-Base Titration

• Acid-base titration determines the concentration of an unknown acid or base using a standard solution.
• The reaction involves neutralization, where acids and bases form water and a salt.
• The equivalence point occurs when the reaction is complete based on mole ratios, not necessarily when pH = 7.
• The half-equivalence point provides direct access to $pK_a$ or $pK_b$​.
• The endpoint is indicated by a color change using an indicator and approximates the equivalence point.
• Titration curves graph pH vs. volume of titrant and reveal key features of the reaction.
• Different types of titrations (strong/weak acid/base combinations) produce different curve shapes.
• Accurate titrations require proper indicator selection and careful technique.

What Is an Acid Base Titration?

Acid-base titration is a laboratory technique used to find the concentration of an unknown acid or base by adding a measured volume of a standard solution (the titrant) to a solution of unknown concentration, the analyte, until the reaction reaches a stoichiometric completion point.

The method relies on the predictable reaction between acids and bases:

• Acids donate protons (H⁺)
• Bases accept protons or produce OH⁻

At the point of neutralization, the amount of acid equals the amount of base in terms of moles, allowing calculation of the unknown concentration. In practice, this is carried out using a burette to deliver precise volumes of titrant into a flask containing the analyte and an indicator or a pH probe.

The defining feature is that the reaction between acid and base is quantitative and predictable, allowing concentration to be calculated from measured volumes.

Purpose and Applications

Acid base titration is one of the most widely used analytical techniques because it is:

• Precise, often within <1% error
• Based on well-understood reaction chemistry
• Adaptable to many chemical systems

Common applications include:

• Determining the concentration of unknown solutions in chemistry labs
• Quality control in pharmaceuticals and food production
• Measuring acidity in environmental samples (water, soil)
• Determining the acid content of vinegar or citric acid in beverages
• Monitoring industrial processes involving acids and bases

These titrations are valued for their precision, simplicity, and relatively low cost.

Theory of Acid Base Titration

Acid-base titrations are based on neutralization reactions, where an acid reacts with a base to form water and a salt.

General Reaction

$$\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$$

H⁺ + OH⁻ → H₂​O

This net ionic equation applies to strong acid–strong base systems. For weak acids or bases, equilibrium must also be considered.

Example:$$\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}$$

Strong vs Weak Systems

Strong acids and bases fully dissociate, so calculations depend only on stoichiometry.

Weak acids and bases require equilibrium expressions:$$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$$

This becomes critical:

• Before equivalence (buffer region)
• At half-equivalence
• After equivalence

Stoichiometry and Mole Relationships

The fundamental calculation comes from mole balance at equivalence:

$$n_{\text{acid}} = n_{\text{base}}$$$$M_a V_a \cdot n_a = M_b V_b \cdot n_b$$

Where:

• $n_a$​, $n_b$​ = number of acidic or basic protons per molecule

Important clarification:
This is not always a 1:1 ratio. For example:

• H₂​SO₄​ reacts with 2 mol NaOH per mole acid
• Polyprotic systems require careful accounting of equivalents

Types of Acid Base Titration

Different combinations of acids and bases produce different titration behaviors.

Strong Acid–Strong Base

• Example: HCl + NaOH (hydrochloric acid + sodium hydroxide)
• Equivalence point at pH = 7
• Sharp vertical pH change
• No buffer region
• Most straightforward calculations

At equivalence: solution contains neutral salt and water

Weak Acid–Strong Base

• Example: CH₃COOH + NaOH (acetic acid + sodium hydroxide)
• Equivalence point pH > 7 because the conjugate base hydrolyzes water, producing OH⁻
• Buffer region present
• Half-equivalence point where pH = pKa

Weak Base–Strong Acid

• Example: NH₃ + HCl (Ammonia with hydrochloric acid)
• Equivalence point pH < 7 because conjugate acid produces H₃O⁺
• Buffer region present

Weak Acid–Weak Base

• Example: Acetic acid with ammonia
• No sharp equivalence point
• Indicator selection is difficult
• Often analyzed using equilibrium constants instead

Table Comparing Strong vs Weak Titration Calculations

Useful shortcut summary

• Strong/strong titrations: mostly stoichiometry, except pH after equivalence depends on excess strong reagent.
• Weak acid/strong base titrations: stoichiometry plus buffer chemistry before equivalence, conjugate base hydrolysis at equivalence.
• Weak base/strong acid titrations: stoichiometry plus buffer chemistry before equivalence, conjugate acid hydrolysis at equivalence.

Titration Curves and Chemical Regions

A titration curve is a quantitative map of the chemistry occurring at every stage of the titration.

Regions of a Titration Curve (Weak Acid–Strong Base Example)

1. Initial region
   • Dominated by weak acid equilibrium
   • Use $K_a$
2. Buffer region
   • Mixture of HA and A⁻
   • Use Henderson–Hasselbalch equation:

$$\text{pH} = pK_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$

3. Half-equivalence point
   • $[\text{A}^-] = [\text{HA}]$
   • $\text{pH} = pK_a$
4. Equivalence point
   • All acid converted to conjugate base
   • Solve using base hydrolysis
5. Post-equivalence
   • Excess strong base determines pH

Equivalence Point vs Endpoint

Good titrations minimize the difference between the two.

• Equivalence point: exact stoichiometric point
• Endpoint: experimental signal

Choice of Indicators

Indicators are weak acids or bases that change color over a specific pH range.

Common indicators:

Practical Guidance

• Strong acid–strong base: many indicators work
• Weak acid–strong base: use indicators with pH > 7 (e.g., phenolphthalein)
• Weak base–strong acid: use lower pH indicators (e.g., methyl orange)

Important lab insight:

• Look at the curve
• Choose an indicator that changes color within the vertical region

Step-by-Step Laboratory Procedure for an Acid Base Titration

A standard acid base titration follows a fairly consistent sequence. The exact acid, base, and indicator may change, but the workflow remains the same.

1. Gather and inspect the equipment

You typically need a burette, burette clamp, ring stand, funnel, Erlenmeyer flask, volumetric pipette or graduated pipette, wash bottle, white tile or white paper, indicator, and the titrant and analyte solutions.

Make sure the burette is clean and that the stopcock works properly. Check the glassware for cracks. Dirty glassware or contaminated solutions can ruin a titration before it even begins.

2. Rinse the burette with deionized water, then with titrant

First rinse the burette with deionized water. Then rinse it with a small portion of the titrant solution.

This second rinse matters because any water left inside the burette would dilute the titrant and change its concentration at the start of the titration.

3. Fill the burette with titrant

Place a funnel in the top of the burette and add the titrant. Remove the funnel afterward. Fill the burette slightly above the zero mark if possible.

Then open the stopcock briefly to fill the burette tip and remove any air bubbles. Read the initial burette volume at eye level.

4. Measure the analyte accurately

Use a pipette to transfer a known volume of the analyte into a clean Erlenmeyer flask. A common volume is 25.00 mL, but the exact amount depends on the experiment.

If needed, add a small amount of distilled water to the flask. This does not change the number of moles of analyte, so it does not affect the result. It only changes the total volume in the flask.

5. Add the indicator

Add 2 to 3 drops of a suitable acid base indicator. Do not add a large amount because excess indicator can slightly alter the chemistry and make the endpoint harder to judge.

For some titrations, instead of an indicator, you use a pH meter and monitor pH continuously.

6. Perform a rough titration

Begin adding titrant while swirling the flask constantly. At first you can add titrant fairly quickly. As you approach the endpoint, the temporary indicator color change will begin to linger longer.

Near the endpoint, slow down to dropwise addition. A rough titration helps estimate the approximate endpoint volume so later trials can be done more carefully.

7. Perform careful titrations

Repeat the titration with fresh analyte samples. This time, as you approach the rough endpoint volume, add the titrant one drop at a time while swirling continuously.

Rinse down the walls of the flask with distilled water if splashes occur. Again, this does not change the number of moles present, but it ensures all analyte remains in the reacting solution.

The endpoint is reached when the indicator changes color and that color persists for about 30 seconds.

8. Record the final burette reading

Read the final volume at eye level. The volume of titrant delivered is:

$$V_{\text{titrant}} = V_{\text{final}} – V_{\text{initial}}$$

9. Repeat until concordant trials are obtained

Most labs require at least three consistent trials. Concordant trials are titrations whose delivered volumes agree closely, often within 0.10 mL or your instructor’s specified tolerance.

10. Perform the calculation

Use the balanced chemical equation to determine the mole ratio. Then calculate the unknown concentration.

For a 1:1 reaction:

$$M_a V_a = M_b V_b$$

For other stoichiometries:

$$M_a V_a \times n_a = M_b V_b \times n_b$$

where $n_a$​ and $n_b$​ are the stoichiometric coefficients or the number of transferable acidic/basic equivalents.

Common Mistakes in Acid Base Titration

These are the most common errors in lab and in written work.

Not rinsing the burette with titrant
Residual water dilutes the titrant and changes its effective concentration.

Leaving an air bubble in the burette tip
The first portion of titrant dispensed fills the tip instead of entering the flask, so the measured volume is too large.

Reading the burette incorrectly
Always read the meniscus at eye level. Parallax causes volume errors.

Adding titrant too quickly near the endpoint
This is one of the most common reasons students overshoot the endpoint.

Failing to swirl continuously
Poor mixing causes local excesses of titrant and inaccurate endpoint detection.

Using too much indicator
The indicator is a chemical reagent. Using too much can affect the pH or make the color change harder to interpret.

Choosing the wrong indicator
The transition range must match the steep region of the titration curve.

Recording too few decimal places
Burette readings are normally estimated to the nearest 0.01 mL.

Forgetting to remove the funnel from the burette
Residual drops from the funnel may enter the burette later and alter the measured volume.

Not rinsing analyte splashes from the flask walls
If some analyte sticks to the flask wall and does not react, the result is inaccurate.

Using the wrong stoichiometric ratio
Not all titrations are 1:1. For example:

$$\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}$$

Here, one mole of sulfuric acid reacts with two moles of sodium hydroxide.

Using total volume instead of delivered volume
Use burette final minus initial reading, not the final reading alone.

Forgetting to convert mL to L when needed
This matters when calculating moles directly from molarity.

Assuming equivalence point means pH 7
That is true only for strong acid-strong base titrations.

Confusing endpoint with equivalence point
The endpoint is the observed signal. The equivalence point is the stoichiometric point.

Ignoring weak acid or weak base equilibria
Weak acid and weak base titrations often require equilibrium calculations before, at, or after equivalence.

Worked Example Problems

Example 1: Strong Acid–Strong Base

Problem:
A 25.0 mL sample of HCl is titrated with 0.100 M NaOH. It takes 30.0 mL of NaOH to reach the equivalence point. What is the concentration of HCl?

Solution:$$M_a V_a = M_b V_b$$$$M_a (25.0) = 0.100 \times 30.0$$$$M_a = \frac{3.00}{25.0} = 0.120 \text{ M}$$

Answer: 0.120 M HCl

Example 2: Weak Acid–Strong Base

Problem:
A weak acid (HA) is titrated with NaOH. The pH at the half-equivalence point is 4.75. What is $K_a$​?

Solution:

At half-equivalence:$$\text{pH} = pK_a$$$$pK_a = 4.75$$$$K_a = 10^{-4.75} = 1.78 \times 10^{-5}$$

Answer: $K_a = 1.78 \times 10^{-5}$

ICE Table Examples

ICE tables are especially useful in weak acid and weak base titration problems because the solution composition depends on equilibrium, not just stoichiometric neutralization.

Example 1: Initial pH of a Weak Acid Before Titration

Problem: Find the pH of 0.100 M acetic acid, $K_a = 1.8 \times 10^{-5}$.

Step 1: Write the equilibrium

$$\text{CH}_3\text{COOH} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{CH}_3\text{COO}^-$$

Step 2: Set up the ICE table

Step 3: Write the equilibrium expression

$$K_a = \frac{[\text{H}_3\text{O}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}$$ $$1.8 \times 10^{-5} = \frac{x^2}{0.100 – x}$$

Because $K_a$ is small, let $0.100 – x \approx 0.100$:$$1.8 \times 10^{-5} = \frac{x^2}{0.100}$$$$x^2 = 1.8 \times 10^{-6}$$ $$x = 1.34 \times 10^{-3}$$

So:$$[\text{H}_3\text{O}^+] = 1.34 \times 10^{-3} \text{ M}$$ $$\text{pH} = -\log(1.34 \times 10^{-3}) = 2.87$$

Answer: $\text{pH} = 2.87$

Example 2: pH at the Equivalence Point for a Weak Acid-Strong Base Titration

Problem: 50.0 mL of 0.100 M acetic acid is titrated to equivalence with 0.100 M NaOH. Find the pH at the equivalence point. For acetic acid, $K_a = 1.8 \times 10^{-5}$5.

At equivalence, all acetic acid has been converted into acetate ion.

Step 1: Find moles of acetic acid

$$n = MV = (0.100)(0.0500) = 0.00500 \text{ mol}$$

So there are 0.00500 mol of acetate at equivalence.

Step 2: Find total volume

Because 50.0 mL of NaOH is needed to reach equivalence, total volume is:

$$50.0 \text{ mL} + 50.0 \text{ mL} = 100.0 \text{ mL} = 0.1000 \text{ L}$$

Step 3: Find acetate concentration

$$[\text{CH}_3\text{COO}^-] = \frac{0.00500}{0.1000} = 0.0500 \text{ M}$$

Step 4: Write hydrolysis equilibrium

$$\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^-$$

Step 5: Find $K_b$

$$K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}$$

Step 6: Set up the ICE table

Step 7: Solve

$$K_b = \frac{[\text{CH}_3\text{COOH}][\text{OH}^-]}{[\text{CH}_3\text{COO}^-]}$$$$5.56 \times 10^{-10} = \frac{x^2}{0.0500 – x}$$

Assume $0.0500 – x \approx 0.0500$:$$5.56 \times 10^{-10} = \frac{x^2}{0.0500}$$$$x^2 = 2.78 \times 10^{-11}$$$$x = 5.27 \times 10^{-6}$$

So:$$[\text{OH}^-] = 5.27 \times 10^{-6}$$$$\text{pOH} = -\log(5.27 \times 10^{-6}) = 5.28$$$$\text{pH} = 14.00 – 5.28 = 8.72$$

Answer: $\text{pH} = 8.72$

FAQs

What is the difference between equivalence point and endpoint?
The equivalence point is the exact stoichiometric point, while the endpoint is the observed color change of the indicator.

Why is the equivalence point not always at pH 7?
Only strong acid–strong base titrations have pH 7 at equivalence. Weak acids or bases form conjugates that shift pH.

What is a titrant?
The solution of known concentration added during titration.

What is a standard solution?
A solution with a precisely known concentration.

Why is a burette used?
It allows precise measurement of liquid volume added.

What is the half-equivalence point?
The point where half of the acid is neutralized. For weak acids, pH = pKa.

Can you perform titrations without indicators?
Yes, using a pH meter for more precise equivalence detection.

What causes titration error?
Overshooting the endpoint, incorrect indicator, reading errors, or improper mixing.

Glossary of Key Terms

Acid: A substance that donates hydrogen ions (H⁺) in solution.

Analyte: The solution of unknown concentration being analyzed in a titration.

Base: A substance that accepts hydrogen ions (H⁺) or produces hydroxide ions (OH⁻) in solution.

Burette: A graduated glass tube used to deliver precise volumes of titrant.

Buffer: A solution that resists changes in pH when small amounts of acid or base are added.

Buffer region: The portion of a titration curve where both a weak acid (or base) and its conjugate are present, allowing the solution to resist pH change.

Conjugate acid: The species formed when a base gains a proton.

Conjugate base: The species formed when an acid loses a proton.

Endpoint: The point in a titration at which an indicator changes color, signaling completion of the reaction.

Equivalence point: The point at which the amount of titrant added is stoichiometrically equal to the amount of analyte present.

Half-equivalence point: The point in a titration where half of the analyte has been neutralized, at which pH equals pKa for weak acids.

Hydrolysis: The reaction of a conjugate acid or base with water that affects the pH of a solution.

Indicator: A chemical that changes color over a specific pH range to signal the endpoint of a titration.

Initial pH: The pH of the analyte solution before any titrant is added.

Molarity (M): The concentration of a solution expressed as moles of solute per liter of solution.

Neutralization: A chemical reaction between an acid and a base that produces water and a salt.

pH: A logarithmic measure of hydrogen ion concentration in a solution.

pKa: The negative logarithm of the acid dissociation constant (Ka), indicating acid strength.

pOH: A logarithmic measure of hydroxide ion concentration in a solution.

Standard solution: A solution with a precisely known concentration used in titrations.

Stoichiometry: The quantitative relationship between reactants and products in a chemical reaction.

Titrant: The solution of known concentration that is added from a burette during a titration.

Titration: A laboratory technique used to determine the concentration of a solution by reacting it with a standard solution.

Titration curve: A graph of pH versus volume of titrant added during a titration.

References and Further Reading

• Harris, D.C. (2003). Quantitative Chemical Analysis (6th ed.). Macmillan. ISBN 0-7167-4464-3.
• Patnaik, P. (2004). Dean’s Analytical Chemistry Handbook (2nd ed.). McGraw-Hill Prof Med/Tech. ISBN 0-07-141060-0.
• Skoog, D.A.; West, D.M.; Holler, F.J. (2000). Analytical Chemistry: An Introduction (7th ed.). Emily Barrosse. ISBN 0-03-020293-0.
• Szabadváry, Ferenc (1993). History of Analytical Chemistry. Taylor & Francis. ISBN 2-88124-569-2.
• Vogel, A.I.; J. Mendham (2000). Vogel’s Textbook of Quantitative Chemical Analysis (6th ed.). Prentice Hall. ISBN 0-582-22628-7.