Calculate solubility of phenobarbital at solution pH equal to 6.8 at 25 °C.

General information:
Phenobarbital is a weakly acidic compound. Its solubility is influenced by solution pH according to the following equation:

Where S is solubility, and So is intrinsic solubility. Assuming that phenobarbital has an intrinsic solubility equal to 0.005 molar (M) and pKa equal to 7.4 at 25 °C then solubility at pH equal to 6.8 can be calculated as the following.

Calculations:

Ka  = 10^-pKa

Ka = 10^-7.4 = 3.98 × 10^-8

[H₃O⁺] = 10^-pH

[H₃O⁺] = 10^-pH = 10^-6.8 = 1.59 × 10^-7

S = 0.005 ( 1 + 0.25)

S = 0.005 × 1.25

S = 0.00625 M

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