Answer to Question #101864 in Chemistry for Julie ann

Question

Phenylacetic acid. (C6H5CH2COOH,HPAc) is one of the substance that builds in the blood of person with phenylketonuria, an inherited disorder, that if untreated, causes mental retardation and death. In study of its properties, a biochemist finds that the ph of 0.12 M HPAc is 2.60. What is the Ka of HPAc?

Answer 1

Phenylacetic acid dissociates as:

HPAc <--> H⁺ + PAc^-

From here:

Ka = ([H⁺][PAc^-])/[HPAc] = [H⁺]²/[HPAc]

where [H+], [PAc-], [HPAc] - molar concentrations of protons, the conjugate base, and the undissociated acid, respectively.

As pH = -log[H⁺]:

[H⁺] = 10^-pH

From here, the concentration of [H⁺] ions of phenylacetic acid in the solution equals:

[H⁺] = 10^-2.6 = 0.0025 M

As [H⁺] = 0.0025 M, [HPAc] = 0.12 M, Ka of phenylacetic acid equals:

Ka = [H⁺]²/[HPAc] = 0.0025² / 0.12 = 5.2 × 10^-5

Answer: 5.2 × 10^-5.