Answer: pH = 1.19
Step-by-step explanation:
The formula for Ka is: Ka = [H+][A-]/[HA]
where: [H+] = concentration of H+ ions
[A-] = concentration of conjugate base ions
[HA] = concentration of undissociated acid molecules
Equation of reaction: Cl₂CHCOOH ---> H+ + Cl₂CHCOO-
From the equation above, dichloroacetic acid dissociates one H+ ion for every Cl₂CHCOO- ion,
so [H+] = [Cl₂CHCOO-].
Let x represent the concentration of H+ that dissociates from HA, then [HA] = C - x where C is the initial concentration.
Substituting these values into the Ka equation:
Ka = x · x / (C -x)
Ka = x²/(C - x)
(C - x)Ka = x²
x² = CKa - Kax
x² + Kax - CKa = 0
Solve for x using the quadratic formula:
x = [-b ± √(b² - 4ac)]/2a
Note: There are two solutions for x. However only the positive value of x is used since x represents a concentration of ions in solution, and so cannot be negative.
x = [-Ka + √(Ka² + 4CKa)]/2
Substitute the values for Ka and C in the equation above:
Ka = 5.0 x 10^-2
C = 0.15 M
x = {-5.0 x 10^-2 + √[(5.0. x 10^-2)² + 4(0.15)(5.0 x 10^-2)]}/2
x = (-5.0 x 10^-2 + 1.80 x 10^-1)/2
x = 0.13/2
x = 6.50 x 10^-2
To find pH, we use the formula;
pH = -log[H+]
pH = -log(x)
pH = -log(6.50 x 10^-2)
pH = -(-1.19)
pH = 1.19