Challenge Problem: As we saw in Problem, as a preliminary experiment in their effort to me...

Challenge Problem: As we saw in Problem, as a preliminary experiment in their effort to measure the dissociation constant of acetic acid, Harned and Ehlers5 measured E0 for the cell without liquid junction shown. To complete the study and determine the dissociation constant, these workers also measured the potential of the following cell: Pt, H2(1 atm) | HOAc(m1), NaOAc(m2),NaCl(m3), AgCl(sat’d) | Ag

(a) Show that the potential of this cell is given by E = E0 – RT/F ln (βH3O+)(βCl-)mH+O+mCl- where βH3O+ and βCl2 are the activity coefficients of hydronium ion and chloride ion, respectively,and mH3O+ and mCl2 are their respective molal(mole solute/kg solvent) concentrations.

(b) The dissociation constant for acetic acid is given by

where βOAc- and βHOAc are the activity coefficients of acetate ion and acetic acid, respectively, and mOAc- and mHOAc are their respective equilibrium molal (mole solute/kg solvent) concentrations. Show that the potential of the cell in part (a) is given by

(c) As the ionic strength of the solution approaches zero, what happens to the right-hand side of the equation in (b)?

(d) As a result of answer to part (c), we can write the right-hand-side of the equation as 2(RT/F)ln K' .

Show that

(e) The ionic strength of the solution in the cell without liquid junction calculated by Harned and Ehlers is μ = m2 + m31 mH+ Show that this expression is correct.

(f) These workers prepared solutions of various molal analytical concentrations of acetic acid, sodium acetate, and sodium chloride and measured the potential of the cell presented at the beginning of this problem. Their results are shown in the following table.

Potential Measurements of Cell Pt,H2(1 atm) k HOAc(cHOAc),NaOAc(cNaOAc),NaCl(cNaCl),AgCl(sat’d) k Ag without Liquid Junction as a Function of Ionic Strength (Molality) and Temperature (°C)

The notation for molal concentration up to this point in our discussion of the Harned and Ehlers paper has been in terms of the variables mx, where × is the species of interest. Do these symbols represent molal analytical concentrations, molal equilibrium concentrations, or both? Explain. Note that the symbols for concentration in the table adhere to the convention that we have used throughout this book, not the notation of Harned and Ehlers.

(g) Calculate the ionic strength of each of the solutions using the expression for the Ka of acetic acid to calculate [H3O+], [OAc−], and [HOAc] with the usual suitable approximations and a provisional value of Ka = 1.8 × 10-5. Use the potentials in the table at 25°C to calculate values for K' with the expression in part (d). Construct a plot of K' versus μ and extrapolate the graph to infinite dilution (μ = 0) to find a value for Ka at 25°C. Compare the extrapolated value to the provisional value used to calculate m. What effect does the provisional value of Ka have on the extrapolated value of Ka? You can perform these calculations most easily using a spreadsheet.

(h) If you have made these computations using a spreadsheet, determine the dissociation constant for acetic acid at all other temperatures for which data are available. How does Ka vary with temperature? At what temperature does the maximum in Ka occur?