29. Concerning Lotta Topaigne, Given that the pKa for uric acid is 5.7 and that uric acid is 20 times less soluble than sodium urate, explain which is more likely to precipitate in the toe (pH = 7.4) and which is more likely to precipitate in the kidney tubule (pH = 6.3).

In the blood, the pH is 7.4, so from the Hendersen Hasselbach equation

pH = pKa + Log [Sodium Urate]/[Uric Acid]

7.4 = 5.7 + Log [Sodium Urate]/[Uric Acid]

1.7 =  Log [Sodium Urate]/[Uric Acid]

50 = [Sodium Urate]/[Uric Acid]

So, the concentration of sodium urate is 50 times greater than uric acid in blood.  Even though uric acid is 20 times less soluble, sodium urate will precipitate first.

In the Urine, where the pH tends to be acidic, let’s assume a pH of 6.3

pH = pKa + Log [Sodium Urate]/[Uric Acid]

6.3 = 5.7 + Log [Sodium Urate]/[Uric Acid]

0.6 =  Log [Sodium Urate]/[Uric Acid]

4 = [Sodium Urate]/[Uric Acid]

So, the concentration of Sodium Urate is 4 times greater than Uric Acid in urine at pH of 6.3.  But  uric acid is 20 times less soluble, uric acid will precipitate first.