At which ONE of the following pH values would lignocaine hydrochloride (weak base; pKa = 7.9; a local anaesthetic and antiarrhythmic drug) have the slowest dissolution rate?

Question

BlackTom AI · Accepted Answer

Using the Henderson–Hasselbalch relationship for a weak base gives the key insight: the ionized (protonated) form BH+ is far more water‑soluble than the neutral base B, so lower pH (more protonation) increases solubility and speeds dissolution; higher pH (deprotonation) reduces solubility and slows dissolution.

1) Relevant concepts:
- Lignocaine hydrochloride is the protonated salt of a weak base (pKa = 7.9 refers to BH+ ⇌ B + H+).
- Henderson–Hasselbalch for a base: pH = pKa + log([B]/[BH+]) or equivalently [BH+]/[B] = 10^(pKa−pH).
- Fraction protonated (soluble form) = [BH+]/([B]+[BH+]) = 1/(1+10^(pH−pKa)).

2) Step‑by‑step reasoning and calculations:
Compute fraction protonated at each pH using 10^(pKa−pH):

- pH 6: pKa − pH = 7.9 − 6 = 1.9 → 10^1.9 = 79.43.
  Fraction protonated = 79.43/(1 + 79.43) = 79.43/80.43 = 0.9876 → 98.8% protonated (highly soluble).

- pH 7: pKa − pH = 0.9 → 10^0.9 = 7.94.
  Fraction = 7.94/(1 + 7.94) = 7.94/8.94 = 0.888 → 88.8% protonated (very soluble).

- pH 8: pKa − pH = −0.1 → 10^(−0.1) = 0.794.
  Fraction = 0.794/(1 + 0.794) = 0.794/1.794 = 0.443 → 44.3% protonated (moderate solubility).

- pH 9: pKa − pH = −1.1 → 10^(−1.1) = 0.0794.
  Fraction = 0.0794/(1 + 0.0794) = 0.0794/1.0794 = 0.0736 → 7.36% protonated (mostly neutral, poorly soluble).

3) Why the correct answer is correct:
At pH 9 the drug is overwhelmingly in the unprotonated, neutral form (only ~7% protonated), which has much lower aqueous solubility; lower solubility leads to the slowest dissolution rate.

4) Why other options are incorrect:
pH 6, 7 and 8 produce much higher proportions of the soluble protonated form (98.8%, 88.8%, 44.3% respectively), so dissolution would be faster at those pH values than at pH 9.

Conclusion: The slowest dissolution rate occurs at pH 9, confirming the provided answer (b. pH 9).

At which ONE of the following pH values would lignocaine hydrochloride (weak base; pKa = 7.9; a local anaesthetic and antiarrhythmic drug) have the slowest dissolution rate?Single choice

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