Proton Transfer, Buffers, and Titrations

Driving question

How can one equilibrium model explain pH, buffer action, and the shape of a titration curve?

Proton transfer and conjugate pairs

A Brønsted–Lowry acid donates a proton and a base accepts one. In $\mathrm{HA(aq)+H_2O(l)\rightleftharpoons H_3O^+(aq)+A^-(aq)},$ $\mathrm{HA/A^-}$ and $\mathrm{H_2O/H_3O^+}$ are conjugate pairs. Charge and atoms are conserved. Water is omitted from $K_a=\frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]}.$ At $25\ ^\circ\mathrm{C}$, $K_w=[\mathrm{H_3O^+}][\mathrm{OH^-}]=1.0\times10^{-14}$ and $\mathrm{pH}+\mathrm{pOH}=14.00$. Neutral means $[\mathrm{H_3O^+}]=[\mathrm{OH^-}]$; pH 7 is neutral only when $K_w=1.0\times10^{-14}$.

Weak-acid calculation

For $0.100\ \mathrm{M}$ acetic acid with $K_a=1.8\times10^{-5}$, let $x=[\mathrm{H_3O^+}]$: $K_a=\frac{x^2}{0.100-x}.$ The approximation $0.100-x\approx0.100$ gives $x=1.34\times10^{-3}\ \mathrm{M}$ and $\mathrm{pH}=2.87$. Because $x/0.100=1.34\%$, the approximation is reasonable. A strong acid is defined by extensive ionization, not by high concentration.

Buffers

A buffer contains meaningful amounts of a weak acid and its conjugate base. Added $\mathrm{H_3O^+}$ is consumed by $\mathrm{A^-}$; added $\mathrm{OH^-}$ is consumed by $\mathrm{HA}$. For an ideal dilute buffer, $\mathrm{pH}=\mathrm{p}K_a+\log\!\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right).$ This relationship describes equilibrium after stoichiometric neutralization is handled. It does not mean a buffer prevents all pH change, and it fails after a component is nearly exhausted.

Titration reasoning

In a weak-acid/strong-base titration: before equivalence, neutralization stoichiometry determines remaining $\mathrm{HA}$ and produced $\mathrm{A^-}$; at half-equivalence, $[\mathrm{HA}]=[\mathrm{A^-}]$ so $\mathrm{pH}=\mathrm{p}K_a$; at equivalence, conjugate-base hydrolysis makes the solution basic; after equivalence, excess strong base controls pH. Choose an indicator whose transition interval lies within the steep equivalence-region change.

Media prompts

• Before: Predict the pH at half-equivalence for an acid with $\mathrm{p}K_a=4.76$.
• During: Identify which species consume a small addition of strong acid or strong base.
• After: Explain why the equivalence point is above pH 7 for a weak-acid/strong-base titration.
• Non-video fallback: Use the buffer and titration-region explanations above, then solve Question 4 in the quiz.

Practice

1. Identify both conjugate pairs in $\mathrm{NH_3+H_2O\rightleftharpoons NH_4^++OH^-}$.
2. Explain why diluting a buffer changes capacity more than its initial pH ratio.
3. Sketch how the equivalence-point pH changes when a weaker acid is titrated with the same strong base.

Laboratory connection

Complete the supervised microscale buffer-capacity investigation in lab.md. Online work does not replace supervised hands-on AP laboratory time.

Sources

• College Board, AP Chemistry Course and Exam Description, effective Fall 2024, Unit 8.
• OSHA, 29 CFR 1910.1450 Appendix A, laboratory chemical hygiene guidance.