Welcome to Topic 12: Titration Curves, Indicators, and Buffers

In our previous look at Acid-base Equilibria, we learned how to calculate the \(pH\) of strong and weak acids. Now, we are going to look at what happens when we actually mix acids and bases together. This chapter is all about the "story" of a neutralisation reaction—how the \(pH\) changes step-by-step, how we choose the right "colour-changer" (indicator) to tell us when we're finished, and how we can create special solutions called buffers that stubbornly refuse to let their \(pH\) change!

Note: Before starting this, make sure you are comfortable with the basics of \(pH = -\log_{10}[H^+]\) and the concept of \(K_a\), which we covered in the first half of Topic 12.

1. Titration Curves

A titration curve is simply a graph showing how the \(pH\) of a solution changes as you add a reagent from a burette. Even if you find graphs a bit intimidating, these curves always follow a similar "S" shape. There are four main combinations you need to know.

Key Features of a Curve

  • Starting pH: Determined by the acid or base in the flask.
  • Equivalence Point: The exact point where the amount of acid and base are stochiometrically equal (they have neutralised each other).
  • Vertical Section: A very sharp rise (or fall) in \(pH\) around the equivalence point. This is where a single drop of reagent can change the \(pH\) by several units!
  • Finishing pH: Determined by the excess reagent being added from the burette.

The Four Combinations

1. Strong Acid (SA) vs Strong Base (SB):
Example: \(HCl\) and \(NaOH\).
Starts very low (around \(pH = 1\)), has a long vertical section from \(pH \approx 3\) to \(pH \approx 11\), and ends very high (around \(pH = 13\)). The equivalence point is exactly at \(pH = 7\).

2. Weak Acid (WA) vs Strong Base (SB):
Example: \(CH_3COOH\) and \(NaOH\).
Starts higher (around \(pH = 3\)). The vertical section is shorter, typically from \(pH \approx 7\) to \(pH \approx 11\). Important: The equivalence point is above 7 (basic) because the salt formed undergoes slight hydrolysis.

3. Strong Acid (SA) vs Weak Base (WB):
Example: \(HCl\) and \(NH_3\).
Starts low (\(pH = 1\)). The vertical section is from \(pH \approx 3\) to \(pH \approx 7\). The equivalence point is below 7 (acidic).

4. Weak Acid (WA) vs Weak Base (WB):
Example: \(CH_3COOH\) and \(NH_3\).
These curves are tricky! There is no vertical section. Because there is no sharp \(pH\) change, we cannot use a visual indicator for this type of titration.

Quick Review: The "stronger" reagent always "pulls" the equivalence point towards its side of the \(pH\) scale. SA/SB meets in the middle (\(pH = 7\)), WA/SB meets in the basic region (\(pH > 7\)), and SA/WB meets in the acidic region (\(pH < 7\)).

2. Choosing the Right Indicator

An indicator is actually a weak acid itself! We can represent it as \(HIn\). It has one colour when it is an acid (\(HIn\)) and a different colour when it loses its proton (\(In^-\)).

\(HIn(aq) \rightleftharpoons H^+(aq) + In^-(aq)\)

The Golden Rule for Indicators

For an indicator to work, its colour change range must fall entirely within the vertical section of the titration curve. If it changes colour too early or too late, your results will be inaccurate.

  • Methyl Orange: Changes colour between \(pH \approx 3.1 - 4.4\). Great for Strong Acid / Weak Base titrations.
  • Phenolphthalein: Changes colour between \(pH \approx 8.3 - 10.0\). Great for Weak Acid / Strong Base titrations.
  • Either: Both work for Strong Acid / Strong Base because the vertical section is so large (\(pH \ 3 - 11\)).

Did you know? We define \(pK_{in}\) as the \(pH\) at which the indicator is exactly halfway through its colour change. At this point, \([HIn] = [In^-]\).

3. Buffer Solutions

A buffer is a solution that resists changes in \(pH\) when small amounts of acid or base are added to it. Think of it like a "pH sponge."

How to Make One

There are two types of buffers you need to know:

  1. Acidic Buffer: A mixture of a weak acid and its conjugate base (usually as a salt). Example: Ethanoic acid (\(CH_3COOH\)) and Sodium ethanoate (\(CH_3COONa\)).
  2. Basic Buffer: A mixture of a weak base and its conjugate acid (salt). Example: Ammonia (\(NH_3\)) and Ammonium chloride (\(NH_4Cl\)).

How do they work? (The Chemistry Secret)

Let's use an acidic buffer (\(CH_3COOH / CH_3COO^-\)) as an example:

  • If you add \(H^+\) ions: The large "reservoir" of ethanoate ions (\(CH_3COO^-\)) reacts with the added \(H^+\) to form ethanoic acid:
    \(CH_3COO^-(aq) + H^+(aq) \rightarrow CH_3COOH(aq)\). The \(H^+\) is removed, so the \(pH\) stays steady!
  • If you add \(OH^-\) ions: The large "reservoir" of ethanoic acid molecules reacts with the \(OH^-\) to form water:
    \(CH_3COOH(aq) + OH^-(aq) \rightarrow CH_3COO^-(aq) + H_2O(l)\). The \(OH^-\) is removed, so the \(pH\) stays steady!

Buffer Calculations

To find the \(pH\) of an acidic buffer, we use the \(K_a\) expression of the weak acid:

\(K_a = \frac{[H^+][A^-]}{[HA]}\)

Rearranging to find \([H^+]\):

\([H^+] = K_a \times \frac{[HA]}{[A^-]}\)

Pro-tip: In a buffer, we assume the concentration of \([HA]\) is the initial acid concentration and \([A^-]\) is the initial salt concentration.

4. The Half-Neutralisation Point

This is a very clever shortcut often tested in exams. If you take a weak acid and add exactly half the volume of base needed to neutralise it, you have reached the half-neutralisation point.

At this specific point:
\([HA] = [A^-]\)

If we look at our formula: \([H^+] = K_a \times \frac{[HA]}{[A^-]}\), the ratio \(\frac{[HA]}{[A^-]}\) becomes 1.

Therefore: \([H^+] = K_a\) or \(pH = pK_a\).

Application: You can find the \(K_a\) of an unknown weak acid just by looking at its titration curve! Find the volume at the equivalence point, go to half that volume, and read the \(pH\) off the y-axis.

5. Enthalpy of Neutralisation

Neutralisation is exothermic (it releases heat). However, the amount of heat released depends on the strength of the acid and base.

  • Strong Acid + Strong Base: The enthalpy change (\(\Delta H_{neut}\)) is always approximately \(-57.6 \text{ kJ mol}^{-1}\). This is because the only real reaction happening is \(H^+(aq) + OH^-(aq) \rightarrow H_2O(l)\).
  • Weak Acid / Base: The value is usually less exothermic (less negative, e.g., \(-55 \text{ kJ mol}^{-1}\)). This is because some of the energy released is "used up" to force the weak acid to dissociate (break apart) completely into ions.

6. Buffers in the Body: Blood pH

Your blood must be kept at a very strict \(pH\) of around 7.4. If it varies by more than 0.5, it can be fatal! Your body uses the carbonic acid-hydrogencarbonate buffer system:

\(CO_2(aq) + H_2O(l) \rightleftharpoons H_2CO_3(aq) \rightleftharpoons H^+(aq) + HCO_3^-(aq)\)

  • If blood becomes too acidic (\(H^+\) increases), the equilibrium shifts to the left to remove \(H^+\). You might breathe faster to exhale the extra \(CO_2\).
  • If blood becomes too alkaline (\(H^+\) decreases), the equilibrium shifts to the right to produce more \(H^+\).

Key Takeaway: Buffers aren't just for the lab; they are essential for keeping you alive!

Summary Checklist:
1. Can you sketch the 4 types of titration curves?
2. Do you know why Phenolphthalein isn't used for SA/WB titrations?
3. Can you explain how a buffer "mops up" added \(H^+\) ions?
4. Remember: at half-neutralisation, \(pH = pK_a\).