Spectrophotometric Determination of pH

Question

Formic acid (HCOOH) is a weak acid that partially dissociates as follows, with a K_a = 0.0001778:

HCOOH + H₂O ↔ H₃O⁺ + HCOO^-

Calculate the [H⁺] and pH of a 0.559 M solution of formic acid

Now calculate the [H⁺] and pH of a 0.00729 M solution of formic acid.

This one is stumping me I'm getting the answer wrong and I don't think it is significant figures.

Answer 1

So, let’s take a look at this problem.

HCOOH + H₂O ↔ H₃O⁺ + HCOO^- Ka = 1.778x10^-4

Ka = [H⁺][CH3COO^-] / [CH3COOH]

1.778x10^-4 = (x)(x) / 0.559-x. And assuming x is small …

1.778x10^-4 = (x)(x) / 0.559

x² = 9.94x10^-5

x = [H⁺] = 9.97x10^-3 M

pH = - log 9.97x10^-3 (same as you except for rounding)

ph = 2.00. Which agrees with your answer

Since we get the same answer, I’m not going to do the second part as I’m sure we’ll get the same answer again. If it’s not rounding (sig figs), then I suggest the answer sheet is wrong.