Acids, Bases and pH: Quick Revision

A brief note on Acids, Bases and pH. Read it before a test. Try each question at the end before you open its answer.

Three ideas

• Arrhenius: acids give $\text{H}^+$, bases give $\text{OH}^-$, in water.
• Bronsted-Lowry: acids donate protons, bases accept them. A conjugate pair differs by one proton.
• Lewis: acids accept an electron pair, bases donate one. $\text{BF}_3$ is a Lewis acid.
• Strong acids and bases ionise fully. A strong acid has a very weak conjugate base.

Water and pH

• $K_w = [\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}$ at $298\ \text{K}$. It grows with temperature.
• $\text{pH} = -\log_{10}[\text{H}_3\text{O}^+]$, and $\text{pH} + \text{pOH} = 14$ at $298\ \text{K}$.
• One pH unit is a tenfold change. Neutral means equal ions.

Weak acids and bases

• $K_a = \dfrac{[\text{H}_3\text{O}^+][\text{A}^-]}{[\text{HA}]}$ and $\text{p}K_a = -\log_{10} K_a$. Smaller pKa, stronger acid.
• $\alpha \approx \sqrt{K_a/C}$ and $[\text{H}_3\text{O}^+] \approx \sqrt{K_a C}$ when $\alpha$ is small.
• Weak base: $[\text{OH}^-] \approx \sqrt{K_b C}$.
• Conjugate pair: $K_a K_b = K_w$, and $\text{p}K_a + \text{p}K_b = 14$.

A worked example

Compare $0.050\ \text{mol/L}$ of a strong acid with $0.050\ \text{mol/L}$ of acetic acid.

1. Strong acid. $[\text{H}_3\text{O}^+] = 0.050\ \text{mol/L}$, so the pH is $1.30$.
2. Acetic acid. $[\text{H}_3\text{O}^+] \approx \sqrt{1.8 \times 10^{-5} \times 0.050} = 9.5 \times 10^{-4}\ \text{mol/L}$, so the pH is about $3.0$.
3. Meaning. Same concentration, but the weak acid has about fifty times fewer hydronium ions.

Practice with new numbers

A program to try

The program finds the pH of the strong acid and of acetic acid, solving the weak one exactly.

Mistakes to avoid

• The minus sign in pH. pH is minus the logarithm.
• The square root. $\sqrt{K_a C}$, not $K_a C$.
• The pOH of a base. Take it away from 14 for the pH.
• Two hydroxides. $\text{Ba(OH)}_2$ gives two $\text{OH}^-$ per unit.
• Weak and dilute. They mean different things.

Check yourself

1. What is the conjugate acid of $\text{NH}_3$?

2. What is the pH of a solution with $[\text{H}_3\text{O}^+] = 1.0 \times 10^{-6}\ \text{mol/L}$?

3. Which is the stronger acid: pKa 2 or pKa 5?

4. Why is $\text{BF}_3$ an acid though it has no hydrogen?

5. A weak acid is diluted. Does its pH rise or fall?