When the acid is hydrolyzed, the reaction is
HA --> H⁺ + A⁻
So,
Ka = [H⁺][A⁻]/[HA]
Apply the ICE approach:
HA --> H⁺ + A⁻
I 0.3 0 0
C -X +X +X
E 0.3-X X X
Ka = [X][X]/[0.3-X]
X = H⁺ = A⁻
The formula for pH is:
pH = -log[X]
5.2 = -log[X]
Solving for X,
X = 6.31*10⁻⁶
Therefore,
Ka = [6.31*10⁻⁶][6.31*10⁻⁶]/[0.3-6.31*10⁻⁶]
Ka = 1.33×10⁻¹⁰