What is the [H₃O⁺] in a buffer that consists of 0.30 M HCOOH and 0.20 M HCOONa? For HCOOH, K_a = 1.7 × 10^-4 A) 1.1 × 10^-4 M B) 2.6 × 10^-4 M C) 4.3 × 10^-4 M D) 6.7 × 10^-5 M E) None of these choices are correct.

Question

Quizplus · Accepted Answer

The first step is to write the balanced equation for the dissociation of HCOOH: HCOOH + H2O ⇌ H3O+ + HCOO- Ka = [H3O+][HCOO-]/[HCOOH] Since HCOONa is a salt of a weak acid, it will hydrolyze in water and produce OH-: HCOO- + H2O ⇌ OH- + HCOOH Kb = [OH-][HCOOH]/[HCOO-] We know from the problem that the concentration of HCOOH is 0.30 M, and the concentration of HCOONa is 0.20 M. We can use the equilibrium constants to solve for the concentrations of H3O+, OH-, HCOO-, and HCOOH. The concentration of HCOO- is equal to the concentration of Na+ from the salt, which is 0.20 M. Using the equation for Ka and assuming x is the concentration of H3O+: 1.7 × 10^-4 = x^2 / (0.30 - x) x = 1.06 × 10^-3 M Using the equation for Kb and assuming y is the concentration of OH-: 1.7 × 10^-4 = y(x + 0.20) / (0.30 - x) y = 5.62 × 10^-6 M Now we can use the equation for pH to solve for the pH of the buffer: pH = pKa + log([salt]/[acid]) pH = 3.76 + log(0.20/0.30) pH = 3.56 Finally, we can use the equation for pOH to solve for the pOH of the buffer: pOH = pKb + log([acid]/[salt]) pOH = 10.77 + log(0.30/0.20) pOH = 10.96 Using the equation pH + pOH = 14, we can solve for [H3O+] and [OH-]: [H3O+] = 10^-pH = 2.24 × 10^-4 M [OH-] = 10^-pOH = 9.61 × 10^-5 M Now we can use the concentrations of H3O+ and OH- to calculate H₃O⁺: H₃O⁺ = [H3O+] + [OH-] - [HCOO-] H₃O⁺ = 2.24 × 10^-4 + 9.61 × 10^-5 - 0.20 H₃O⁺ = 2.57 × 10^-4 M Therefore, the answer is B) 2.6 × 10^-4 M.

What Is the [H3O+] in a Buffer That Consists of 0.30

What Is the [H₃O⁺] in a Buffer That Consists of 0.30