At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0 . Assume, the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm, x m = k C^ 1/n If the plot of ₁₀(x/m) against ₁₀C gives a straight line with slope 1 , the value of k in L mol ⁻¹ is ____. Given: The molar mass of acetic acid is 60 g mol

Step-by-step solution

Given the pH of the resulting solution is 3.0 , the concentration of H^+ ions is: [H^+] = 10⁻³ M For the dissociation of acetic acid ( CH₃COOH CH₃COO^- + H^+ ), the acid dissociation constant is given by: K_a = [CH₃COO^-][H^+] [CH₃COOH] Assuming [CH₃COO^-] [H^+] and the equilibrium concentration of acetic acid is C , we can use the approximation: K_a = [H^+]^2 C 1.0 10⁻⁵ = (10⁻³)^2 C C = 10⁻⁶ 1.0 10⁻⁵ = 0.1 M The number of moles of acetic acid remaining in the 50 mL ( 0.05 L ) solution at equilibrium is: n_ eq = C