As a part of a study to measure the dissociation constant of acetic acid, Harnedand

Chapter 22, Problem 22-19

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As a part of a study to measure the dissociation constant of acetic acid, Harnedand Ehlers 16 needed to measure EO for the following cell:(a) Write an expression for the potential of the cell.(b) Show that the expression can be arranged to giveo RTE = E - F In YH,O'Yu mll,o' muwhere mH;O' and mn are the molal (mole solute per kilogram solvcnt) concentrations.(c) Under what circumstances is this expression valid:(d) Show that the expression in (b) may be writtenE + 2k log m = E" - 2k log Ywhere k = In lORTI F.(e) A considerably simplificd version of the Debye:!:Iilckel cxpression that isvalid for very dilutc solutions is log Y = -0.5 \I'm + bm, wherc c \s a constant.Show that the expression for the cell potcntial in (d) may be written asE + 2klogm - kvm = E" - 2kcm(f) The previous expression is a "limiting law" that becomes linear as the concentrationof the electrolyte approaches zero. The equation assumes the formy = ax + b, where y = E + 2klogm - kvm; x = m, the slope; a =,-2kc;and the y-intercept b = F'. Harned and Ehlers very accurately measured thepotential of the cell without liquid junction presented at the beglOOing of theproblem as a function of concentration of HCI (molal) and temperature andobtained the data in the following table. For example, they measured the potentialof the cell at 25'C with an HCl conccntration of 0.01 m and obtained avalue of 0.46419 volts.Construct a plot of E + 2k log m -- k \1m versus m. and note that the plot isquite linear at low concentration. Extrapolate the line to the y-intcrcept, andestimate a value for En Compare your value with the value of Harned andEhlers, and explain any difference. Also compare the value to the one shownin Table 22-1. The simplest way to carry out this exercise is to place the datain a spreadsheet. and use the Exccl function INTERCEPT(known_y's,known_x's) to determine the extrapolated value for En" Use only the datafrom 0.005-0.01 m to find the intcrcept.(g) Enter the data for all temperatures into the spreadsheet and determine valuesfor EO at all temperatures from ye to 35"C. Altcrnatively, you maydownload an Excel sprcadsheet containing the entire data table. Use yourweb browser to conncct to http://www.thomsonedu.com/chemistry/skoog.and select your course, Instrumcntal Analysis. Finally, navigate to the linksfor Chapter 22, and click on the spreadsheet link for this problem.(h) Two typographical errors in the preceding table appeared in the originalpublished paper. Find the errors, and correct them. How can you justifythese 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 ratherthan molarity or weight molarity? Explain whether it matters which of theseconcentration units are used.