Final answer:
The acid dissociation constant (Ka) for caproic acid is calculated using the provided pH and the concentration of the saturated solution. After converting the given concentration to molarity, and using the pH to determine [H+], the Ka can be found by plugging these values into the expression for Ka.
Step-by-step explanation:
To calculate the acid dissociation constant (Ka) for caproic acid, we can use the provided pH and the concentration of the saturated solution. Since the solution is saturated, we can assume that the concentration of the acid (C₅H₁₁COOH) at equilibrium equals the initial concentration, 11g/L, which we need to convert into moles per liter (molarity).
Firstly, we calculate the molar mass of caproic acid to be 116.16 g/mol (by adding the atomic masses of C, H, and O accordingly). This gives us the molarity of caproic acid: 11 g/L ÷ 116.16 g/mol = 0.0947 M.
With a pH of 2.94, we have a concentration of hydrogen ions [H+] of 10-2.94 M. Since the acid is weak, we assume the concentration of caproic acid remains close to initial concentration. Therefore, the concentration of the conjugate base [C₅H₁₁COO-] is also approximately 10-2.94 M.
The expression for the acid dissociation constant is Ka = [H+][C₅H₁₁COO-]/[C₅H₁₁COOH]. Since [C₅H₁₁COOH] changes little and is approximately equal to the initial molarity, we plug in 0.0947 M for [C₅H₁₁COOH] and 10-2.94 M for both [H+] and [C₅H₁₁COO-]. The calculation gives us the Ka value for caproic acid.