Final answer:
The pH of the 0.53M formic acid solution is approximately 2.38, which is closest to option (b) 2.20, calculated using the given Ka value of formic acid (1.8×10^-4) and the formula for pH. The closely resemblance option that matches with the answer is (b) 2.20.
Step-by-step explanation:
The pH of a 0.53M solution of formic acid (HCOOH) can be calculated using the acid dissociation constant (Ka) and the formula for pH. Formic acid is a weak acid, and its dissociation can be represented by the equation HCOOH → H+ + HCOO-. The Ka value of formic acid is 1.8×10-4.
First, we use the expression for the acid dissociation constant Ka = [H+][HCOO-] / [HCOOH]. Assuming that the degree of dissociation is small, the concentration of HCOOH will remain approximately 0.53M, while concentrations of H+ and HCOO- will be equal and can be represented as x.
So, Ka = x^2 / (0.53 - x) ≈ x^2 / 0.53 because x is small compared to 0.53. Solving for x gives us the concentration of hydronium ions in the solution, from which we can calculate pH.
pH = -log[H+]
After solving for x, we find that the pH of the solution is approximately 2.38, which is closest to option (b) 2.20 from the multiple choices given. This could vary slightly depending on how the quadratic equation is solved and the rounding during calculation.