Apply the Bronsted-Lowry theory, distinguish strong and weak acids and bases using Ka, Kb and pKa, calculate pH of strong and weak acids and of buffers, explain buffer action, and interpret titration curves and indicator choice

What this dot point is asking

SEAB wants you to use the Bronsted-Lowry definition, distinguish strong from weak acids and bases through $K_a$, $K_b$ and $pK_a$, calculate the pH of strong acids, weak acids and buffers, explain buffer action with equations, and interpret titration curves and choose indicators. The weak-acid pH and buffer calculations are reliable Paper 2 questions, and titration-curve interpretation appears in both written and practical papers.

The answer

Bronsted-Lowry theory

A Bronsted-Lowry acid is a proton ($\text{H}^+$) donor; a base is a proton acceptor. Each acid has a conjugate base (what remains after losing $\text{H}^+$), and each base has a conjugate acid:

Strong versus weak

A strong acid fully dissociates ($\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-$); a weak acid only partially dissociates, described by an acid dissociation constant:

A larger $K_a$ (smaller $pK_a$) means a stronger acid. Strength (degree of dissociation) is distinct from concentration.

pH calculations

• Strong acid: $[\text{H}^+]$ equals the acid concentration (full dissociation). For $0.10$ mol dm$^{-3}$ HCl, pH $= 1.0$.
• Weak acid: $[\text{H}^+] = \sqrt{K_a \times [\text{HA}]}$ using the weak-acid approximation.
• Strong base: find $[\text{OH}^-]$, then $[\text{H}^+] = K_w/[\text{OH}^-]$, then pH.

Buffers

A buffer resists pH change on adding small amounts of acid or base. It is made from a weak acid and its conjugate base (an acidic buffer) or a weak base and its conjugate acid (a basic buffer). Its pH is given by:

How it works. The buffer holds large reservoirs of both HA and $\text{A}^-$:

• Added $\text{H}^+$ is removed by the conjugate base: $\text{A}^- + \text{H}^+ \rightarrow \text{HA}$.
• Added $\text{OH}^-$ is removed by the weak acid: $\text{HA} + \text{OH}^- \rightarrow \text{A}^- + \text{H}_2\text{O}$.

So the ratio $[\text{salt}]/[\text{acid}]$ changes only slightly and pH is nearly constant.

Titration curves and indicators

A titration curve plots pH against volume of titrant. The equivalence point is the steep vertical section. Choose an indicator whose colour-change range falls within that vertical section:

The half-equivalence point of a weak acid is where $[\text{HA}] = [\text{A}^-]$, so pH $= pK_a$, a quick way to read $pK_a$ off a curve.

Examples in context

Example 1. Blood as a buffer. The hydrogencarbonate buffer keeps blood pH near $7.4$. Added acid from metabolism reacts with $\text{HCO}_3^-$ to form carbonic acid, while added base reacts with the carbonic acid, so the pH stays within the narrow range cells tolerate. SEAB uses this physiological example to test the equations of buffer action in an applied context.

Example 2. Reading $pK_a$ from a titration curve. When a weak acid is titrated with strong base, the pH at the half-equivalence point equals the $pK_a$ of the acid, because $[\text{HA}] = [\text{A}^-]$ there. Candidates are routinely asked to read this off a printed curve and identify the acid from a data-booklet-style list of $pK_a$ values, linking the graph to the buffer equation.

Try this

Q1. Calculate the pH of $0.0500$ mol dm$^{-3}$ nitric acid (a strong acid). [1 mark]

• Cue. $[\text{H}^+] = 0.0500$, pH $= -\log(0.0500) = 1.30$.

Q2. Calculate the pH of $0.0100$ mol dm$^{-3}$ sodium hydroxide. [2 marks]

• Cue. $[\text{OH}^-] = 0.0100$; $[\text{H}^+] = 10^{-14}/0.0100 = 10^{-12}$; pH $= 12.0$.

Q3. Explain why a mixture of ammonia and ammonium chloride acts as a buffer, with equations. [3 marks]

• Cue. $\text{NH}_3$ (weak base) and $\text{NH}_4^+$ (conjugate acid). Added $\text{H}^+$: $\text{NH}_3 + \text{H}^+ \rightarrow \text{NH}_4^+$. Added $\text{OH}^-$: $\text{NH}_4^+ + \text{OH}^- \rightarrow \text{NH}_3 + \text{H}_2\text{O}$.