Lactic acid,HC₃H₅O₃,is found in sour milk.What is the pH of 0.30 M lactic acid? (K_a = 1.4 × 10−⁴)

Question

Quizplus · Accepted Answer

To calculate the pH of a solution of lactic acid, we need to use the dissociation constant (Ka) of lactic acid, which is given by K_a = 1.4 × 10−⁴. The equation for the dissociation of lactic acid in water is: CH3CH(OH)COOH ⇌ CH3CH(OH)COO-S1U1P + H+ The Ka expression for this reaction is: Ka = [CH3CH(OH)COO-S1U1P][H+] / [CH3CH(OH)COOH] We can assume that the concentration of lactic acid will not change significantly upon dissociation, so we can start by writing the Ka expression in terms of the initial concentration of lactic acid: Ka = [CH3CH(OH)COO-S1U1P][H+] / [CH3CH(OH)COOH] ≈ [CH3CH(OH)COO-S1U1P][H+] / (0.30 M) At equilibrium, the concentration of lactic acid will be equal to the concentration of lactate ions (CH3CH(OH)COO-S1U1P), so we can simplify the Ka expression further: Ka = [CH3CH(OH)COO-S1U1P][H+] / (0.30 M) ≈ [H+]^2 / (0.30 M) Solving for [H+], we get: [H+] = sqrt(Ka x 0.30 M) = sqrt(1.4 x 10^-4 x 0.30) = 1.19 x 10^-3 M Taking the negative log of this value gives us the pH: pH = -log[H+] = -log(1.19 x 10^-3) = 2.19 Therefore, the pH of 0.30 M lactic acid is 2.19, which is choice C.

Lactic Acid,HC3H5O3,is Found in Sour Milk

Lactic Acid,HC₃H₅O₃,is Found in Sour Milk