Hydrocortisone succinate (weak acid; pKa = 5.1) is a prodrug intended for formulating injections as the sodium salt. At which ONE of the following pH values would you expect this compound to be least soluble in water?

Question

BlackTom AI · Accepted Answer

For a weak acid, aqueous solubility is greatest when the acid is ionized (as A–) and least when it exists mainly as the neutral, protonated form (HA). The Henderson–Hasselbalch equation quantifies the ratio of ionized to unionized species: pH = pKa + log([A–]/[HA]).

Step-by-step reasoning and calculations:
1. Given: hydrocortisone succinate is a weak acid with pKa = 5.1. Compute the fraction ionized α = [A–]/([HA]+[A–]) = 1/(1 + 10^(pKa – pH)).
2. Evaluate α at each pH:

- pH 4:
  10^(pKa – pH) = 10^(5.1 – 4) = 10^1.1 ≈ 12.59
  α = 1/(1 + 12.59) = 1/13.59 ≈ 0.0736 → ~7.4% ionized

- pH 6:
  10^(5.1 – 6) = 10^(–0.9) ≈ 0.1259
  α = 1/(1 + 0.1259) = 1/1.1259 ≈ 0.8889 → ~88.9% ionized

- pH 7.2:
  10^(5.1 – 7.2) = 10^(–2.1) ≈ 0.00794
  α = 1/(1 + 0.00794) ≈ 0.9921 → ~99.2% ionized

- pH 8:
  10^(5.1 – 8) = 10^(–2.9) ≈ 0.00126
  α = 1/(1 + 0.00126) ≈ 0.9987 → ~99.9% ionized

3. Interpretation: At pH 4 only ~7% of the drug is in the ionized (water-soluble) form; at pH 6–8 the drug is predominantly ionized (>88–99.9%) and therefore much more soluble. Because the sodium salt formulation relies on the deprotonated (ionic) form to dissolve, lowering pH below the pKa shifts equilibrium to the neutral, poorly soluble HA and can cause precipitation.

Why the correct answer is correct:
- pH 4 is furthest below the pKa (5.1), yielding the lowest fraction ionized and thus the lowest water solubility for this weak acid (sodium salt will reprotonate and be least soluble).

Why the other choices are incorrect:
- pH 6, 7.2, and 8 are at or above the pKa, producing much higher ionization and greater solubility; therefore they cannot be the point of least solubility.

Conclusion: The compound will be least soluble at pH 4, which matches the provided correct answer (d. pH 4).

Hydrocortisone succinate (weak acid; pKa = 5.1) is a prodrug intended for formulating injections as the sodium salt. At which ONE of the following pH values would you expect this compound to be least soluble in water?单项选择题

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