Distinguish between the strength and the concentration of acids and bases, including investigation of the degree of ionisation and the relationship between ionisation, conductivity, and pH

What this dot point is asking

NESA wants you to clearly distinguish two ideas that students often blur: the strength of an acid (its degree of ionisation, an intrinsic property) and the concentration of an acid (how much is dissolved, an extrinsic property). You should be able to compare pH, conductivity and reactivity of strong and weak acids at equal concentration, and explain everything in terms of the position of the ionisation equilibrium. This builds on properties of acids and bases and is the prerequisite for pH calculations and titration curve shapes.

The answer

Strength vs concentration

• Strength describes the degree of ionisation in water. A strong acid ionises essentially 100 percent. A weak acid ionises only a few percent (often less than 1 percent at typical concentrations).
• Concentration describes how much acid is dissolved per litre, regardless of how much has ionised.

These properties are independent: you can have a dilute strong acid or a concentrated weak acid.

Strong acids and bases

Strong acids are essentially fully ionised in water. The common examples for HSC:

• $HCl$, $HBr$, $HI$ (hydrohalic acids except $HF$, which is weak).
• $HNO_3$ (nitric acid).
• $H_2SO_4$ (sulfuric acid, fully ionised for the first proton, partially for the second).
• $HClO_4$ (perchloric acid).

Strong bases are also fully ionised:

• Group 1 hydroxides: $NaOH$, $KOH$.
• Heavier Group 2 hydroxides: $Ca(OH)_2$, $Ba(OH)_2$.

Weak acids and bases

A weak acid only partially ionises, setting up an equilibrium:

The acid dissociation constant ($K_a$) measures the position of this equilibrium:

A small $K_a$ means a weak acid (very little ionised); a large $K_a$ means a stronger acid.

For weak bases the equivalent constant is $K_b$. For ammonia, $K_b = 1.8 \times 10^{-5}$.

Conductivity

Electrical conductivity of a solution depends on the total concentration of ions. At equal acid concentration, a strong acid produces many more ions than a weak acid, so it conducts much better.

This is a definitive HSC experiment: dip a conductivity probe (or a small bulb circuit) into 0.1 mol/L $HCl$ and 0.1 mol/L $CH_3COOH$. The $HCl$ lights the bulb brightly; the ethanoic acid lights it dimly. Both have the same nominal concentration; only the degree of ionisation differs.

pH at equal concentration

For two solutions of equal concentration:

• Strong acid has the lower pH (more ions, lower $[H^+]$ value... wait, higher $[H^+]$, so lower pH).
• Weak acid has a higher pH (less ionised, lower $[H^+]$).

For a 0.10 mol/L solution:

• $HCl$: $[H^+] = 0.10$ mol/L, pH = 1.00.
• $CH_3COOH$ ($K_a = 1.8 \times 10^{-5}$): $[H^+] \approx 1.34 \times 10^{-3}$ mol/L, pH = 2.87.

Reactivity at equal concentration

A strong acid reacts faster initially because more $H^+$ is present at any instant. However, a weak acid reacts to the same final extent with a stoichiometric excess of, for example, magnesium, because as $H^+$ is consumed the equilibrium shifts right (Le Chatelier) and more weak acid ionises.

Mark schemes reward students who explicitly separate kinetics (initial rate, set by $[H^+]$) from stoichiometry (total Mg consumed, set by moles of acid).

Dilution effect on degree of ionisation

When a weak acid is diluted, the percent ionisation increases. Mathematically, if $K_a$ is fixed and $c$ decreases, then $x/c = \sqrt{K_a/c}$ grows. In the limit of infinite dilution every weak acid becomes 100 percent ionised. This is a Le Chatelier consequence: dilution favours the side with more particles.

Examples in context

Example 1. Cleaning toilets: HCl-based versus citric-acid-based products. Domestic toilet cleaners sold across NSW supermarkets split into two camps: hydrochloric acid (Harpic Power Plus, around 10 percent w/v) and citric acid (Earth Choice, around 5 percent w/v). At equimolar concentration HCl ionises fully and gives pH near 0.8, while citric acid ($K_a = 7.4 \times 10^{-4}$) ionises only 4 percent and gives pH near 2.1. Conductivity meters reflect the same difference, with HCl solutions conducting more than 20 times better. The HCl product attacks limescale 30 times faster but also corrodes chrome, while the citric product is gentler and biodegradable. Strength versus concentration explains every consumer trade-off.

Example 2. NSW HSC depth study comparing acetic and hydrochloric acid. A typical Stage 6 lab task gives students 0.10 mol L$^{-1}$ acetic acid and 0.10 mol L$^{-1}$ HCl. Measurements at 25 degrees C consistently give pH 1.0 for HCl and pH 2.87 for acetic acid, conductivity 39 vs 1.3 mS cm$^{-1}$, and reaction with magnesium ribbon producing visible hydrogen in 12 seconds for HCl but 90 seconds for acetic acid. Students compute the percent ionisation of acetic acid as $10^{-2.87} / 0.10 = 1.3$ percent, neatly demonstrating that strength and concentration are independent variables. The depth study is the canonical practical NESA examines.

Try this

Q1. Distinguish between the strength and concentration of an acid using the terms ionisation and moles per litre. [3 marks]

• Cue. Strength: degree of ionisation (intrinsic property, measured by $K_a$); concentration: moles per litre (how much is present).

Q2. A 0.20 mol L$^{-1}$ solution of a weak acid HA has pH 3.40. Calculate the percent ionisation and the $K_a$ of HA. [3 marks]

• Cue. $[H^+] = 10^{-3.40} = 4.0 \times 10^{-4}$ mol L$^{-1}$; percent ionisation = 0.20 percent; $K_a = (4.0 \times 10^{-4})^2 / 0.20 = 8.0 \times 10^{-7}$.

Q3. Two solutions are tested with a conductivity probe: 0.10 mol L$^{-1}$ HCl reads 39 mS cm$^{-1}$ and 0.10 mol L$^{-1}$ $CH_3COOH$ reads 1.3 mS cm$^{-1}$. (a) Account for the difference. (b) Predict the conductivity of 0.010 mol L$^{-1}$ HCl. (c) State whether reacting either acid with excess magnesium gives the same volume of $H_2$ at completion. [2+1+2 marks]

• Cue. (a) HCl fully ionised, more ions; acetic acid only 1.3 percent ionised. (b) Roughly 4 mS cm$^{-1}$ (ten-fold dilution drops conductivity roughly proportionally). (c) Same volume eventually because both deliver the same total moles of $H^+$.