4.4 pH Titration Curves

In the previous sections, we learned how to calculate the pH of various solutions. However, in a chemical reaction between an acid and a base (a neutralization reaction), the pH changes continuously as the reaction proceeds. A pH titration curve is a graph that plots the pH of the solution in the conical flask against the volume of the titrant added from the burette. This curve visually represents the entire neutralization process and helps us understand the nature of the acid and base involved.

Definition

A pH titration curve is a graphical representation of the change in pH of a solution as a titrant (acid or base) is added. The curve plots pH on the y-axis against the volume of titrant added on the x-axis.

Simple Explanation: It is a graph that shows how the acidity or alkalinity of a solution changes as you slowly add an acid or a base to it.

Core Concept

• Strong acid + Strong base
• Strong acid + Weak base
• Weak acid + Strong base
• Weak acid + Weak base

• Initial pH: The pH before any titrant is added.
• Equivalence Point: The point at which the moles of acid equal the moles of base (neutralization is complete). This is often in the middle of the steep vertical region of the curve.
• Final pH: The pH after excess titrant has been added.
• The vertical region (pH jump): The steep part of the curve where a small addition of titrant causes a large change in pH.

Detailed Explanation

In order to determine the concentration of an unknown solution, the technique of titration is used in neutralisation reactions between acids and alkalis. It involves adding a titrant of known concentration from a burette into a conical flask containing the analyte of unknown concentration. An indicator is added which will change colour at the endpoint of the titration. The endpoint is the point at which equal number of moles of titrant and analyte reacts with each other. The equivalence point is halfway the vertical region of the curve.

Equivalence point → moles of alkali = moles of acid

This is also known as the equivalence point, and this is the point at which neutralisation takes place. There are different types of titration curves depending on the strength of acid or alkalis used.

a. Strong Acid and Strong Alkali pH Titration Curve

• Example: Hydrochloric acid (HCl) in the conical flask, titrated with sodium hydroxide (NaOH) from the burette.
• Initial pH: About 1-2 (since HCl is a strong acid and ionizes completely).
• As NaOH is added: The pH increases slightly as H^+ ions react with OH^- ions to form water. The change is not much until the volume gets close to the equivalence point.
• Equivalence Point: The pH surges upwards very steeply. At the equivalence point, all H^+ ions have been neutralised, so the pH is 7 (neutral).
• After Equivalence Point: Adding more NaOH increases the pH as now there is an excess of OH^- ions. The final pH is about 13-14.
• Curve Shape: The vertical region is very long, going from about pH 3 to pH 11.

The textbook figure (Fig 4.2) represents the titration curve of 1.0 mol dm^-3 HCl (25 cm³) with NaOH. Hence, 25 cm³ of titrant (NaOH) is used to neutralise 25 cm³ of HCl. The pH titration curve for HCl added to a NaOH has the same shape. The initial pH and final pH are the other way around. The equivalence point is still 7.

b. Strong Acid and Weak Alkali pH Titration Curve

• Example: Hydrochloric acid (HCl) in the conical flask, titrated with a weak alkali like ammonia (NH_3) from the burette.
• Initial pH: About 1-2 (strong acid).
• As NH_3 is added: The pH increases slightly as more H^+ ions react with NH_3.
• Equivalence Point: The equivalence point is not neutral. The solution is still acidic, with a pH of about 5.5. This is because all H^+ have reacted with NH_3 to form NH_4^+, which is a relatively strong acid, causing the solution to be acidic.
• After Equivalence Point: As more NH_3 is added, the pH increases to above 7 but below that of a strong alkali (since NH_3 is a weak alkali). The final pH is around 10-11.
• Curve Shape: The vertical region is shorter and is shifted to the acidic side (centered around pH 5.5).

The pH titration curve for strong acid added to a weak alkali has the same shape. The initial and final pH are the other way around. The equivalence point is still about 5.5.

c. Weak Acid and Strong Alkali pH Titration Curve

• Example: Ethanoic acid (CH_3COOH) in the conical flask, titrated with a strong alkali like NaOH from the burette.
• Initial pH: About 2-3 (weak acid, so the pH is higher than that of a strong acid of the same concentration).
• As NaOH is added: The pH increases slightly as more H^+ ions react with OH^-.
• Equivalence Point: The equivalence point is not neutral. The solution is slightly basic, with a pH of about 9. This is because all H^+ in CH_3COOH have reacted with OH^-, but the resulting CH_3COO^- is a relatively strong base, causing the solution to be basic.
• After Equivalence Point: As more NaOH is added, the pH increases to about 13-14.
• Curve Shape: The vertical region is shorter and is shifted to the basic side (centered around pH 9).

The pH titration curve for weak acid added to a strong alkali has the same shape. The initial and final pH are the other way around. The equivalence point is still about 9.

d. Weak Acid and Weak Alkali pH Titration Curve

• Example: Ethanoic acid (CH_3COOH) in the conical flask, titrated with a weak alkali like ammonia (NH_3).
• Initial pH: About 2-3 (weak acid).
• As NH_3 is added: The pH increases gradually.
• Curve Shape: There is no vertical region. There is a "point of inflexion" at the equivalence point. The curve does not provide much other information, and the change in pH is very gradual.
• Equivalence Point: The equivalence point is difficult to detect with an indicator, and the pH is roughly neutral or slightly acidic/basic depending on the relative strengths of the acid and base.

The textbook notes that in these pH titration curves, there is no vertical region. There is a 'point of inflexion' at the equivalence point. The curve does not provide much other information.

Intermediate Level

The titration curve is a plot of pH versus volume of titrant. The key features are the initial pH, the equivalence point, and the vertical region. The shape depends on the strengths of the acid and base. For a strong acid-strong base titration, the equivalence point is at pH 7, and the vertical region is very steep and long. For a strong acid-weak base, the equivalence point is acidic (pH ~5.5), and the vertical region is shorter. For a weak acid-strong base, the equivalence point is basic (pH ~9), and the vertical region is also shorter. For a weak acid-weak base, there is no steep vertical region, and the equivalence point is difficult to detect. The choice of an indicator is crucial; it must change colour within the vertical region of the curve.

Important Points

• - Titration Curve: A graph of pH vs. volume of titrant.
• - Equivalence Point: The point where moles of acid = moles of base.
• - Strong Acid + Strong Base: Equivalence point pH = 7. Long vertical region.
• - Strong Acid + Weak Base: Equivalence point pH < 7 (acidic). Vertical region shifted left.
• - Weak Acid + Strong Base: Equivalence point pH > 7 (basic). Vertical region shifted right.
• - Weak Acid + Weak Base: No vertical region. Gradual change.
• - Indicator: Should change colour within the vertical region of the curve.

Remember

• - Strong acid + strong base = pH 7 at equivalence.
• - Strong acid + weak base = acidic equivalence (pH < 7).
• - Weak acid + strong base = basic equivalence (pH > 7).
• - Weak acid + weak base = no sharp equivalence.
• - The steeper the vertical region, the easier it is to find the equivalence point.
• - The curve starts at the pH of the solution in the flask.

Common Mistakes

• - Assuming the equivalence point is always at pH 7. This is only true for strong acid-strong base titrations. For weak acid-strong base, it is >7; for strong acid-weak base, it is <7.
• - Confusing the endpoint with the equivalence point. The endpoint is where the indicator changes colour (an experimental observation). The equivalence point is the theoretical point where the reaction is complete. A good indicator makes these two points as close as possible.
• - Thinking that all titration curves have a steep vertical region. Weak acid-weak base titrations do not have a steep vertical region; the pH changes very gradually.
• - Not considering the initial pH. The starting point of the curve tells you the strength of the acid in the flask. A strong acid starts at a lower pH than a weak acid of the same concentration.
• - Forgetting that the curve is not symmetric. The shape is different on either side of the equivalence point due to the different species present.

Quick Revision

A pH titration curve is a graph showing how the pH changes as a titrant is added to a solution. The shape of the curve depends on the strength of the acid and base. For a strong acid-strong base titration, the equivalence point is at pH 7, with a long vertical region. For a strong acid-weak base, the equivalence point is acidic (pH < 7) with a shorter vertical region. For a weak acid-strong base, the equivalence point is basic (pH > 7) with a shorter vertical region. For a weak acid-weak base, there is no sharp vertical region. The choice of indicator is based on matching its colour change to the equivalence point of the titration.

60-Second Revision

A titration curve plots pH vs. volume of titrant. The equivalence point is where moles of acid = moles of base. For strong acid + strong base, equivalence is at pH 7. For strong acid + weak base, it is acidic (pH < 7). For weak acid + strong base, it is basic (pH > 7). For weak acid + weak base, there is no steep vertical region. The indicator must change colour within the vertical region of the curve.

Frequently Asked Questions (FAQs)

Q1. What is a pH titration curve? Answer: A pH titration curve is a graph that plots the pH of the solution in the conical flask against the volume of titrant added from the burette. It visually represents the entire neutralization process and helps to understand the nature of the acid and base involved.

• Strong Acid + Strong Base: The curve starts at a low pH, has a long, steep vertical region, and the equivalence point is at pH 7. The final pH is high.
• Weak Acid + Strong Base: The curve starts at a higher pH (than strong acid), has a shorter vertical region, and the equivalence point is basic (pH > 7, around 9).
• Strong Acid + Weak Base: The curve starts at a low pH, has a shorter vertical region, and the equivalence point is acidic (pH < 7, around 5.5).
• Weak Acid + Weak Base: The curve has no steep vertical region; there is only a gradual change in pH. The equivalence point is difficult to detect with an indicator.

Q3. What is the equivalence point, and how does it relate to the shape of the titration curve? Answer: The equivalence point is the point in a titration at which the moles of acid equal the moles of base. It is the point where neutralization is complete. On the titration curve, it is located in the middle of the steep vertical region (if one exists). For a strong acid-strong base titration, it is at pH 7. For other combinations, the pH at the equivalence point is different (acidic for strong acid-weak base, basic for weak acid-strong base).

Q4. Why is the equivalence point of a strong acid-weak base titration acidic? Answer: In a strong acid-weak base titration, the acid is fully ionized, and the base is partially ionized. At the equivalence point, all the base has been neutralized, and the resulting solution contains the conjugate acid of the weak base (e.g., NH_4^+ when NH_3 is used). This conjugate acid can donate protons to water, making the solution acidic. Therefore, the pH is less than 7.

Q5. Why is the equivalence point of a weak acid-strong base titration basic? Answer: In a weak acid-strong base titration, the acid is only partially ionized. At the equivalence point, all the acid has been neutralized, and the resulting solution contains the conjugate base of the weak acid (e.g., CH_3COO^- when CH_3COOH is used). This conjugate base can accept protons from water, generating hydroxide ions and making the solution basic. Therefore, the pH is greater than 7.

Q6. Why is there no sharp vertical region in a weak acid-weak base titration? Answer: In a weak acid-weak base titration, both the acid and the base are only partially ionized. The pH changes gradually throughout the titration because the reaction is not as complete as in strong acid/strong base titrations. There is no sudden change in pH when the equivalence point is reached, making it difficult to detect with an indicator.

Q7. How is the equivalence point detected in a titration? Answer: The equivalence point can be detected using an indicator, which changes colour within the vertical region of the curve, or by using a pH meter to continuously monitor the pH and plotting the curve. The endpoint (the observed colour change) should ideally coincide with the equivalence point.

Q8. Why is the shape of the titration curve important? Answer: The shape of the titration curve tells us about the strength of the acid and base involved. It also helps in selecting the correct indicator for the titration. The indicator must change colour in the pH range of the vertical region. If the indicator's colour change is outside this range, it will not accurately indicate the equivalence point.

Q9. What happens to the pH during a titration of a strong acid with a strong base as the equivalence point is approached? Answer: As the equivalence point is approached, the pH changes very rapidly with the addition of just a small amount of titrant. This is because the concentrations of H^+ and OH^- are both very low, and the addition of a small amount of titrant can significantly change their ratio. This rapid change creates the steep vertical region of the curve.

Multiple Choice Questions (MCQs)

Q1. In a titration of a strong acid with a strong base, what is the pH at the equivalence point? A. 7 B. Less than 7 C. Greater than 7 D. Always 14 Correct Answer: A Explanation: The equivalence point of a strong acid-strong base titration is at pH 7 because the resulting solution is neutral (water and a salt of a strong acid and strong base).

• Q2. In a titration of a weak acid with a strong base, what is the pH at the equivalence point?
• A. 7
• B. Less than 7
• C. Greater than 7
• D. 0
• Correct Answer: C
• Explanation: The equivalence point is basic (pH > 7) because the conjugate base of the weak acid hydrolyzes to produce OH^- ions.

• Q3. In a titration of a strong acid with a weak base, what is the pH at the equivalence point?
• A. 7
• B. Less than 7
• C. Greater than 7
• D. 14
• Correct Answer: B
• Explanation: The equivalence point is acidic (pH < 7) because the conjugate acid of the weak base hydrolyzes to produce H^+ ions.

• Q4. Which titration curve has no steep vertical region?
• A. Strong acid + strong base
• B. Strong acid + weak base
• C. Weak acid + strong base
• D. Weak acid + weak base
• Correct Answer: D
• Explanation: In a weak acid-weak base titration, the pH changes gradually, and there is no sharp vertical region. The equivalence point is difficult to detect.

• Q5. What is the shape of the titration curve for a strong acid-strong base titration?
• A. It has a long, steep vertical region.
• B. It has no vertical region.
• C. It has a short, shallow vertical region.
• D. It is a straight line.
• Correct Answer: A
• Explanation: The strong acid-strong base titration curve has a long, steep vertical region because the pH changes very rapidly near the equivalence point.

• Q6. What is the equivalence point of a titration?
• A. The point where the indicator changes colour.
• B. The point where moles of acid equal moles of base.
• C. The point where the pH is always 7.
• D. The point where the titration begins.
• Correct Answer: B
• Explanation: The equivalence point is the theoretical point where the moles of acid equal the moles of base, meaning neutralization is complete.

Q7. Which of the following indicators is suitable for a strong acid-strong base titration? A. An indicator with a pH range of 3-5 B. An indicator with a pH range of 6-8 C. An indicator with a pH range of 9-11 D. An indicator with a pH range of 12-14 Correct Answer: B Explanation: The equivalence point of a strong acid-strong base titration is at pH 7. The indicator must change colour near pH 7. An indicator with a pH range of 6-8 (like phenolphthalein or bromothymol blue) is suitable.

Q8. Why does the equivalence point of a weak acid-strong base titration have a pH > 7? A. Because the strong base is in excess. B. Because the conjugate base of the weak acid hydrolyzes to produce OH^-. C. Because the acid is fully ionized. D. Because water is neutral. Correct Answer: B Explanation: At the equivalence point, the solution contains the conjugate base of the weak acid. This conjugate base reacts with water to produce OH^- ions, making the solution basic.

• Q9. In the titration of HCl with NaOH, what is the pH range of the vertical region?
• A. 1-2
• B. 3-11
• C. 5-6
• D. 13-14
• Correct Answer: B
• Explanation: The strong acid-strong base titration curve has a long vertical region, typically from about pH 3 to pH 11.

Q10. What is the effect of a weak acid on the starting pH of a titration curve compared to a strong acid of the same concentration? A. The starting pH is lower for the weak acid. B. The starting pH is higher for the weak acid. C. The starting pH is the same for both. D. The starting pH is not measurable for a weak acid. Correct Answer: B Explanation: A weak acid only partially ionizes, so its H^+ concentration is lower than that of a strong acid of the same concentration. Therefore, the starting pH of a weak acid is higher (less acidic) than that of a strong acid.

Multiple Choice Questions (MCQs)

• Q1. What is a pH titration curve?
• A. A graph of pH vs. volume of titrant added.
• B. A graph of temperature vs. time.
• C. A graph of concentration vs. volume.
• D. A graph of pressure vs. volume.
• Correct Answer: A
• Explanation: A pH titration curve is a graph that plots the pH of the solution against the volume of titrant added during a titration.

• Q2. At the equivalence point of a strong acid-strong base titration, the pH is:
• A. 7
• B. Less than 7
• C. Greater than 7
• D. 14
• Correct Answer: A
• Explanation: The equivalence point of a strong acid-strong base titration is neutral, with a pH of 7.

• Q3. In a titration of a weak acid with a strong base, the pH at the equivalence point is:
• A. 7
• B. Less than 7
• C. Greater than 7
• D. 0
• Correct Answer: C
• Explanation: The equivalence point is basic (pH > 7) because the conjugate base of the weak acid hydrolyzes to produce OH^-.

• Q4. In a titration of a strong acid with a weak base, the pH at the equivalence point is:
• A. 7
• B. Less than 7
• C. Greater than 7
• D. 14
• Correct Answer: B
• Explanation: The equivalence point is acidic (pH < 7) because the conjugate acid of the weak base hydrolyzes to produce H^+.

• Q5. Which titration curve has no steep vertical region?
• A. Strong acid + strong base
• B. Strong acid + weak base
• C. Weak acid + strong base
• D. Weak acid + weak base
• Correct Answer: D
• Explanation: In a weak acid-weak base titration, the pH changes gradually, and there is no sharp vertical region.

• Q6. What is the equivalence point?
• A. The point where the indicator changes colour.
• B. The point where moles of acid equal moles of base.
• C. The point where the pH is always 7.
• D. The point where the titration begins.
• Correct Answer: B
• Explanation: The equivalence point is the theoretical point where the moles of acid equal the moles of base, meaning neutralization is complete.

• Q7. Why is an indicator used in titrations?
• A. To change the pH of the solution.
• B. To indicate the endpoint of the titration by changing colour.
• C. To speed up the reaction.
• D. To act as a catalyst.
• Correct Answer: B
• Explanation: An indicator is used to detect the endpoint of the titration by changing colour at a specific pH, which should be close to the equivalence point.

• Q8. The vertical region of a strong acid-strong base titration curve typically spans from about:
• A. pH 1 to 3
• B. pH 3 to 11
• C. pH 5 to 6
• D. pH 13 to 14
• Correct Answer: B
• Explanation: The vertical region of a strong acid-strong base titration is very steep, typically spanning from about pH 3 to pH 11.

Q9. What does the starting pH of a titration curve tell you? A. The strength of the base. B. The strength of the acid. C. The concentration of the salt. D. The temperature of the solution. Correct Answer: B Explanation: The starting pH of the curve reflects the acid in the conical flask. A strong acid will have a lower starting pH than a weak acid of the same concentration.

Q10. Why is a weak acid-weak base titration not suitable for indicator-based titrations? A. Because the pH change is too sudden. B. Because there is no sharp vertical region, making the endpoint difficult to detect. C. Because the reaction is too fast. D. Because the reaction is too exothermic. Correct Answer: B Explanation: In a weak acid-weak base titration, the pH changes gradually, so there is no sharp vertical region. This makes it difficult to detect the endpoint with an indicator.