Question

Trichloroacetic acid is sometimes used in the treatment of warts. Calculate the pH of a 3.0 M solution of trichloroacetic acid. (ka = 2.0 x 10^-1)

Answer 1

for simplicity lets write weak acid as HA

HA -----> H+ + A-

3.00 0 0

3.00-x x x

Ka = [H+][A-]/[HA]

Ka = x*x/(c-x)

0.2 = x^2 / (3-x)

0.6 - 0.2*x = x^2

x^2 + 0.2*x -0.6 = 0

This is quadratic equation (ax^2+bx+c=0)

a = 1.0

b = 0.2

c = -0.6

Roots can be found by

x = {-b + sqrt(b^2-4*a*c)}/2a

x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 2.440

roots are :

x = 0.681 and x = -0.881

since x can't be negative, the possible value of x is

x = 0.681

pH = -log [H+] = -log (0.681) = 0.17

Answer: 0.17