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Strength is how completely an acid ionises and concentration is how much is dissolved; $K_a$ and $pK_a$ put a number on strength.
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By the end of this lesson you will be able to describe any acid solution as strong or weak and, separately, as concentrated or dilute; calculate the hydronium concentration of a weak acid from the share that ionises; write and evaluate $K_a$; rank acids by $pK_a$; and say which properties differ between a strong and a weak acid of the same concentration and which do not.
Last lesson an acid became a proton donor, and you saw that ethanoic acid's reaction with water is written with a double arrow. From the equilibrium unit you can write an equilibrium constant and use an ICE table. This lesson puts those together: a weak acid is an equilibrium, and its constant measures how strong it is.
A strong acid gives every one of its molecules' acidic protons to water: it is fully ionised, and its reaction with water is written with a single arrow. A weak acid gives only a small share of them at equilibrium: it is partly ionised. Concentration is the amount of acid dissolved per litre, in mol/L; concentrated and dilute describe it. The acid dissociation constant, $K_a$, is the equilibrium constant for an acid giving its proton to water. $pK_a = -\log_{10} K_a$.
Put a bottle of vinegar next to a bottle of dilute hydrochloric acid and ask which is stronger. Everyday language would pick whichever has more acid in it. Chemistry asks two separate questions.
How completely does the acid ionise? That is strength. Hydrochloric acid gives every proton to water:
$$\mathrm{HCl + H_2O \rightarrow H_3O^+ + Cl^-}$$
In the solution there are essentially no $\mathrm{HCl}$ molecules left, only ions. Ethanoic acid does something different:
$$\mathrm{CH_3COOH + H_2O \rightleftharpoons H_3O^+ + CH_3COO^-}$$
At $0.1$ mol/L only about one molecule in a hundred has given up its proton at any moment; the other ninety-nine are whole. The reaction reaches equilibrium far to the left.
How much acid is in each litre? That is concentration, and it is set by whoever made up the solution. So the two properties combine freely:
| concentrated | dilute | |
|---|---|---|
| strong | $5$ mol/L hydrochloric acid | $0.001$ mol/L hydrochloric acid |
| weak | $5$ mol/L ethanoic acid | $0.001$ mol/L ethanoic acid |
Diluting hydrochloric acid does not make it weak — every molecule in the dilute solution is still ionised. Concentrating ethanoic acid does not make it strong — most of its molecules still hold their protons.
The common strong acids are few enough to learn: hydrochloric, hydrobromic, hydroiodic, nitric, sulfuric (its first proton) and perchloric. Almost every other acid you meet, including every carboxylic acid, is weak.
Another way: picture
Picture a hundred acid molecules in a litre. In a strong acid all hundred have split into a hydronium ion and an anion. In a weak acid perhaps one has, and ninety-nine are whole. Diluting either one takes molecules out of the litre; it does not change which kind of picture each one is.
Another way: steps
To describe any acid solution:
A weak acid, written generally as HA, is an equilibrium:
$$\mathrm{HA + H_2O \rightleftharpoons H_3O^+ + A^-} \qquad K_a = \frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]}$$
Water is the solvent, present in huge excess, and is left out of the expression just as a solid is. A larger $K_a$ means the equilibrium lies further right: more of the acid ionised, a stronger acid. Like every equilibrium constant, $K_a$ changes only with temperature; the values below are at $25$ °C.
Because $K_a$ values are tiny and span many powers of ten, chemists quote $pK_a = -\log_{10} K_a$. If $K_a = 10^{-5}$ then $pK_a = 5$. The minus sign reverses the direction: the smaller the $pK_a$, the stronger the acid, and each step of one in $pK_a$ is a factor of ten in $K_a$.
| Acid | $K_a$ at $25$ °C | $pK_a$ |
|---|---|---|
| hydrofluoric | $6.8 \times 10^{-4}$ | $3.17$ |
| methanoic | $1.8 \times 10^{-4}$ | $3.75$ |
| ethanoic | $1.8 \times 10^{-5}$ | $4.76$ |
| hypochlorous | $3.0 \times 10^{-8}$ | $7.53$ |
| hydrocyanic | $6.2 \times 10^{-10}$ | $9.21$ |
Working out $K_a$ from measurements is an ICE table: if $0.10$ mol/L of acid ionises by $x$, the equilibrium row is $0.10 - x$, $x$, $x$, and $K_a = x^2 \div (0.10 - x)$.
Compare $0.1$ mol/L hydrochloric acid with $0.1$ mol/L ethanoic acid. At any moment the hydrochloric acid has about a hundred times as many hydronium ions. So it has a lower pH, it conducts electricity much better (ions carry the current), and it fizzes with magnesium much faster (hydronium ions are what react).
Now add sodium hydroxide until each is neutralised. Both need exactly the same volume. As hydroxide removes hydronium ions from the ethanoic acid, its equilibrium shifts to the right — Le Chatelier again — and more molecules ionise, until every one has given up its proton. The same happens with excess magnesium: the weak acid is slower and gives the same total hydrogen.
So anything that depends on the ions present now tells strong from weak. Anything that depends on the total amount of acid does not.
A dilute acid is a weak acid. Dilute describes how much is dissolved; weak describes how much of it ionises. Hydrochloric acid at $0.001$ mol/L is strong and dilute.
A strong acid is a dangerous one. Hydrofluoric acid is weak and very dangerous; the danger comes from the fluoride, not from the hydronium ions.
A weak acid neutralises less alkali. Equal amounts of any two monoprotic acids neutralise equal amounts of alkali. Strength decides how fast and at what pH, not how much.
A larger $pK_a$ is a stronger acid. The minus sign in the definition makes it the other way round.
Every acid ionises fully in water. Only the strong acids do. In a weak acid most molecules are whole at equilibrium.
Methanoic acid at $0.20$ mol/L is $3$% ionised at equilibrium.
A weak acid: only the ionised share makes hydronium ions.
$[\mathrm{H_3O^+}] = 0.20 \times 3 \div 100 = 0.006$ mol/L.
One hydronium ion for each molecule that ionised.
Hydrochloric acid at the same $0.20$ mol/L would give $0.20$ mol/L of hydronium ions — over thirty times as many.
Same concentration, different strength.
An ethanoic acid solution at equilibrium has $[\mathrm{CH_3COOH}] = 0.050$ mol/L and $[\mathrm{H_3O^+}] = [\mathrm{CH_3COO^-}] = 0.00095$ mol/L.
The two ions are equal because each ionised molecule makes one of each.
$K_a = 0.00095^2 \div 0.050 = 9.025 \times 10^{-7} \div 0.050$.
The hydronium concentration squared, over the acid left.
$K_a = 1.8 \times 10^{-5}$, so $pK_a = 4.74$ — ethanoic acid's value to the precision of the data.
A constant at this temperature, whatever the concentration.
Nitric acid is on the list of strong acids, so it is fully ionised; $0.003$ mol/L is dilute.
Two questions, answered separately.
Every molecule gives one hydronium ion, so $[\mathrm{H_3O^+}] = \ldots$
…$0.003$ mol/L, the same as the acid's concentration.
A solution of propanoic acid has a concentration of $0.2$ mol/L. At equilibrium $1$% of the acid molecules have given their proton to water. What is the hydronium ion concentration, in mol/L?
Answer: mol/L
Match each solution to the description that fits it. Hydrochloric and nitric acids ionise completely in water; ethanoic and methanoic acids do not.
| strong and concentrated | strong and dilute | weak and concentrated | weak and dilute | |
|---|---|---|---|---|
| hydrochloric acid at 5 mol/L | ||||
| nitric acid at 0.001 mol/L | ||||
| ethanoic acid at 5 mol/L | ||||
| methanoic acid at 0.001 mol/L |
hydrofluoric acid, written HA, is dissolved at $0.4$ mol/L: $\mathrm{HA + H_2O \rightleftharpoons H_3O^+ + A^-}$. Let $x$ be the concentration that ionises. Write $K_a$ as an expression in $x$.
Answer:
Solution P is hydrochloric acid at $0.001$ mol/L. Solution Q is ethanoic acid at $2$ mol/L. Which description is correct?
Put these weak acids in order from strongest to weakest.
Number the steps in order (write the number in the box):
Two solutions each contain $0.5$ mol/L of acid: hydrochloric acid and ethanoic acid, equal volumes. For each quantity, is the hydrochloric acid's value higher, lower or the same as the ethanoic acid's?
| hydrochloric acid compared with ethanoic acid | |
|---|---|
| concentration of hydronium ions | |
| pH | |
| electrical conductivity | |
| initial rate of reaction with magnesium | |
| volume of sodium hydroxide solution needed to neutralise it | |
| total volume of hydrogen with excess magnesium |
Rainwater absorbs carbon dioxide from the air, which forms carbonic acid, a weak acid. A sample of water from a carbonated drink contains $0.02$ mol/L of carbonic acid, and its hydronium ion concentration is measured as $0.0003$ mol/L. What percentage of the carbonic acid molecules have given up a proton?
Answer: %
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A solution of a weak acid HA is at equilibrium: $\mathrm{HA + H_2O \rightleftharpoons H_3O^+ + A^-}$. The concentrations are $[\mathrm{HA}] = 0.02$ mol/L and $[\mathrm{H_3O^+}] = [\mathrm{A^-}] = 0.004$ mol/L. Write $K_a$ as $N \times 10^{-5}$ mol/L and give $N$.
Answer:
You can keep strength and concentration apart and read $K_a$ and $pK_a$. Say out loud why equal amounts of hydrochloric and ethanoic acid need the same alkali to neutralise them. Next: a scale that turns hydronium concentrations spread over fourteen powers of ten into numbers from 0 to 14 — the pH scale.
10. Your turn: nitric acid at $0.003$ mol/L. Is it strong or weak, concentrated or dilute, and what is its hydronium concentration?, step 3