IB Chemistry HL 3.1.11 Hl Conjugate Pair Relationship Questions

Use real HL exam questions to rearrange Ka×Kb=Kw, solve conjugate-pair constants and convert between pKa, pKb and pKw.

Exam points

Use Ka × Kb = Kw for a conjugate acid–base pair and rearrange the relationship to calculate a missing dissociation constant.
Solve a conjugate-pair problem involving Ka, Kb and Kw, including calculating the resulting weak-acid or weak-base pH when the mark scheme requires it.
Convert between pKa, pKb and pKw for a conjugate pair and use the relationship to compare the paired acid/base constants.

[Maximum number: 4]

When nitrogen gas and hydrogen gas are allowed to react in a closed container the following equilibrium is established.

\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) \quad \Delta H=-92.6 \mathrm{~kJ}

Determine the pH of a $0.100 \mathrm{~mol} \mathrm{dm}^{-3}$ solution of ammonia, $\mathrm{NH}_{3}(\mathrm{aq})$ , using tables 2 and 15 of the data booklet.

$\quad K_{\mathrm{b}}=\frac{\left[\mathrm{NH}_{4}^{+}\right]\left[\mathrm{OH}^{-}\right]}{\left[\mathrm{NH}_{3}\right]}=1.8 \times 10^{-5} / 10^{-4.75}$ ;
[ $\mathrm{NH}_{4}^{+}$ ] $=\left[\mathrm{OH}^{-}\right]$ and $\left[\mathrm{NH}_{3}\right] \approx 1.00 \times 10^{-1}\left(\mathrm{~mol} \mathrm{dm}^{-3}\right)$ ;
$\left[\mathrm{OH}^{-}\right]=\left(\sqrt{1.8 \times 10^{-6}}=\right) 1.3 \times 10^{-3}\left(\mathrm{~mol} \mathrm{dm}^{-3}\right) / \mathrm{pOH}=2.89$ ;
pH=(14.0-2.89=) 11.1;

Award [4] for correct final answer.

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IB Chemistry HL 3.1.11 Hl Conjugate Pair Relationship Questions question 1