What is [H3O+] and the pH of a solution of H2CO3 with [H2CO3]Total = 4.5 x 10-4 M?

Question

What is [H3O+] and the pH of a solution of H2CO3 with [H2CO3]Total = 4.5 x 10-4 M? (Use the pKa value for H2CO3 given in Problem 3.)  Hint: This is not a buffer. 

Answer 1

From a pKa of 6.3, the Ka will be 1x10^-6.3 or 5.01x10^-7

For H₂CO₃ dissociation, we have

H₂CO₃ + H₂O <==> H₃O⁺ + HCO₃^-

Ka = [H₃O⁺][HCO₃^-] / [ [H₂CO₃]

5.01x10^-7 = (x)(x) / 4.5x10^-4 - x (assume x is small relative to 4.5x10-4 and ignore it in the denominator)

5.01x10^-7 = x² / 4.5x10^-4

x² = 2.26x10^-10

x = 1.5x10^-5 (which is less than 5% of 4.5x10^-4 so above assumption was valid and no need for quadratic)

[H₃O⁺] = 1.5x10^-5 M

pH = -log 1.5x10^-5

pH = 4.82

(be sure to check the math)