Amantadine (weak base, pKa = 10.8) is a sparingly water-soluble drug used in treating some viral diseases. At which ONE of the following pH values is amantadine most soluble in water?

Question

BlackTom AI · Accepted Answer

For a weak base, protonation (formation of the charged BH+) increases aqueous solubility, so the lower the pH relative to the base’s pKa the greater the fraction present as the soluble protonated form.

Relevant concept and equation:
Use the Henderson–Hasselbalch relationship for a base: pH = pKa + log([B]/[BH+]). Rearranged gives [B]/[BH+] = 10^(pH − pKa). The fraction protonated (soluble form) is:
fraction BH+ = [BH+]/([B]+[BH+]) = 1 / (1 + 10^(pH − pKa)).

Step-by-step calculation (pKa = 10.8):
1) pH = 6.5: exponent = pH − pKa = 6.5 − 10.8 = −4.3
   10^(−4.3) ≈ 5.01 × 10^(−5)
   fraction BH+ = 1 / (1 + 5.01×10^(−5)) ≈ 0.99995 ≈ 99.995%

2) pH = 7.5: exponent = 7.5 − 10.8 = −3.3
   10^(−3.3) ≈ 5.01 × 10^(−4)
   fraction BH+ ≈ 1 / (1 + 5.01×10^(−4)) ≈ 0.9995 ≈ 99.95%

3) pH = 8.5: exponent = 8.5 − 10.8 = −2.3
   10^(−2.3) ≈ 5.01 × 10^(−3)
   fraction BH+ ≈ 1 / (1 + 5.01×10^(−3)) ≈ 0.995 ≈ 99.5%

4) pH = 9.5: exponent = 9.5 − 10.8 = −1.3
   10^(−1.3) ≈ 5.01 × 10^(−2)
   fraction BH+ ≈ 1 / (1 + 5.01×10^(−2)) ≈ 0.952 ≈ 95.2%

Why the correct answer is correct:
Because amantadine is a weak base (pKa 10.8), it is most water-soluble when it is predominantly in its protonated (charged) BH+ form. The calculations show that pH 6.5 gives the highest fraction protonated (~99.995%), so solubility is greatest at pH 6.5.

Why the other options are incorrect:
Options b (7.5), c (8.5) and d (9.5) give progressively lower fractions protonated (99.95%, 99.5%, 95.2% respectively), so each corresponds to lower solubility than pH 6.5.

Conclusion:
The most soluble pH among the choices is pH = 6.5, which matches the provided correct answer (a).

Amantadine (weak base, pKa = 10.8) is a sparingly water-soluble drug used in treating some viral diseases. At which ONE of the following pH values is amantadine most soluble in water?单项选择题

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