Calculate the pH of a 1.4 solution of allantoin at 25 C.

Question

The base protonation constant K_b of allantoin (C₄H₄N₃O₃NH₂) is 9.12 x 10^-6. 

Calculate the pH of a 1.4 solution of allantoin at 25 C. Round your answer to 

 1 decimal place.

pH =

Answer 1

Let’s write the protonation reaction as B + H2O < -- >  BH+ + OH- where B represent allantoin.

Kb = [OH-] [BH+] / [B – BH+]

Since Kb is very small, [B – BH+] can be approximated by [B].

Also, as [OH-] = [BH+],

Kb = [OH-]^2 / [B]

As we know Kb, we can calculate [OHJ-]

[OH-] = √ (Kb / [B]) = √ (9.12 x 10^-6 / 1.4 M) = 2.55 x 10^-3

But [H+] = 10^-14 / 2.55 x 10^-3 = 3.92 x 10^-12

And pH = - log 3.92 x 10^-12 = 11.4

Please check math.