(a) Derive a general relation for (E/p)T,n for electrochemical cells employing reactants

Chapter 7, Problem 7.21

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(a) Derive a general relation for (E/p)T,n for electrochemical cells employing reactants in any state of matter. (b) E. Cohen and K. Piepenbroek (Z. Physik. Chem. 167A, 365 (1933)) calculated the change in volume for the reaction TlCl(s) + CNS(aq)TlCNS(s) + Cl(aq) at 30C from density data and obtained rV = 2.666 0.080 cm3 mol1. They also measured the emf of the cell Tl(Hg) | TlCNS(s) |KCNS_KCl | TlCl | Tl(Hg) at pressures up to 1500 atm. Their results are given in the following table: p/atm 1.00 250 500 750 1000 1250 1500 E/mV 8.56 9.27 9.98 10.69 11.39 12.11 12.82 From this information, obtain (E/p)T,n at 30C and compare to the value obtained from rV. (c) Fit the data to a polynomial for E against p. How constant is (E/p)T,n? (d) From the polynomial, estimate an effective isothermal compressibility for the cell as a whole.