A standard hydrogen electrode is immersed in an acetic acid solution. This electrode is connected by an external circuit to an iron nail dipping into 0.10 M FeCl₂. If E_cell is found to be 0.24 V, what is the pH of the acetic acid solution

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The Nernst equation for the iron electrode is:E = E° - (RT/nF)ln[Fe2+]/[Fe]where E° is the standard electrode potential, R is the gas constant, T is the temperature, n is the number of electrons transferred, and F is the Faraday constant.Substituting the given values into the equation, we get:0.24 V = -0.44 V - (0.0257 V/K * 298 K / 2 * 96485 C/mol)ln[Fe2+]/[Fe]Solving for [Fe2+]/[Fe], we get:[Fe2+]/[Fe] = 1.0 x 10^-6The equilibrium constant for the dissociation of acetic acid is:Ka = [H+][CH3COO-]/[CH3COOH]Substituting the given values into the equation, we get:1.8 x 10^-5 = [H+][CH3COO-]/[CH3COOH]Since the concentration of CH3COO- is equal to the concentration of Fe2+, we can substitute [Fe2+] into the equation:1.8 x 10^-5 = [H+][1.0 x 10^-6]/[CH3COOH]Solving for [H+], we get:[H+] = 3.88 x 10^-3 MThe pH of the solution is:pH = -log[H+] = 3.88

A Standard Hydrogen Electrode Is Immersed in an Acetic Acid