Problem

Challenge Problem: As a part of a study to measure the dissociation constant of acetic aci...

Challenge Problem: As a part of a study to measure the dissociation constant of acetic acid, Harned and Ehlers3 needed to measure E0 for the following cell: Pt, H2(1 atm) | HCl(m), AgCl(sat’d) | Ag

(a) Write an expression for the potential of the cell.
(b) Show that the expression can be written as E = E0 – RT/F in (γH3O+)(γCl2)mH3O+mCl2
where γH3O+ and γCl2 are the activity coefficients of hydronium ion and chloride ion, respectively, and mH3O+ and mCl2 are their respective molal (mole solute/kg solvent) concentrations.
(c) Under what circumstances is this expression valid?
(d) Show that the expression in (b) may be writen E + 2k log m = E0 - 2k log γ , where k = ln 10RT/F. What are m and γ?
(e) A considerably-simplified version of the Debye-Hückel expression that is valid for very dilute solutions is log γ = 20.5 + bm,where b is a constant. Show that the expression for the cell potential in (d) may be written as
E + 2k log m - k = E0 - 2kcm.
(f) The previous expression is a “limiting law” that becomes linear as the concentration of the electrolyte approaches zero. The equation assumes the form y 5 ax 1 b, where
y = E + 2k log m - k, × = m, the slope a = 22kc, and the y-intercept b = E0. Harned and Ehlers very accurately measured the potential of the cell without liquid junction presented at the beginning of the problem as a function of concentration of HCl (molal) and temperature and obtained the data in the table below. For example, they measured the potential of the cell at 25°C with an HCl concentration of 0.01 m and obtained a value of 0.46419 volts.
Potential Measurements of Cell Pt,H2(1 atm) k HCl(m), AgCl(sat’d) k Ag without Liquid Junction as a Function of Concentration (Molal) and Temperature (°C)
Construct a plot of E + 2k log m - k versus m and note that the plot is quite linear at low concentration. Extrapolate the line to the y-intercept and estimate a value for E0. Compare your value with the value determined by Harned and Ehlers and explain any difference. Also compare the value to the one shown in Table. The simplest way to carry out this exercise is to place the data in a spreadsheet and use the Excel function INTERCEPT(known_y’s, known_x’s) to determine the extrapolated value for E0. Use only the data from 0.005 to 0.01 m to find the intercept.
(g) If you have used a spreadsheet to carry out the data analysis in (f), enter the data for all temperatures into the spreadsheet and determine values for E0 at all temperatures from 5°C to 35°C. Alternatively, you may download an Excel spreadsheet containing the entire data table from our companion website.
(h) There are two typographical errors in the table above that appeared in the original published paper. Find the errors, and correct them. How can you justify these corrections? What statistical criteria can you apply to justify your action? In your judgment, is it likely that these errors have been detected previously? Explain your answer.
(i) Why do you think that these workers used molality in their studies rather than molarity or weight molarity? Explain whether it matters which of these concentration units are used.