(a) Derive a general relation for \((\partial E / \partial p)_{T n}\) for
electrochemical cells employing reactants in any state of matter. (b) E. Cohen
and \(\mathrm{K}\). Piepenbroek (Z. Physik. Chem. 167A, 365 (1933)) calculated
the change in volume for the reaction
\(\mathrm{TlCl}(\mathrm{s})+\mathrm{CNS}^{-}(\mathrm{aq}) \rightarrow
\mathrm{TlCNS}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq})\) at \(30^{\circ}
\mathrm{C}\) from density data
and obtained \(\Delta_{1} \mathrm{~V}=-2.666 \pm 0.080 \mathrm{~cm}^{3}
\mathrm{~mol}^{-1}\). They also measured the emf of the cell
\(\mathrm{Tl}(\mathrm{Hg})|\mathrm{TICNS}(\mathrm{s})|
\mathrm{KCNS}:|\mathrm{KCl}| \mathrm{TlCl} \mid \mathrm{Tl}(\mathrm{Hg})\) at
pressures up to \(1500 \mathrm{~atm}\).
Their results are given in the following table:
$$
\begin{array}{llllllll}
\text { p/atm } & 1.00 & 250 & 500 & 750 & 1000 & 1250 & 1500 \\
E / \mathrm{mV} & 8.56 & 9.27 & 9.98 & 10.69 & 11.39 & 12.11 & 12.82
\end{array}
$$
From this information, obtain \((\partial E / \partial p)_{T n}\) at \(30^{\circ}
\mathrm{C}\) and compare to the value obtained from \(\Delta_{1} \mathrm{~V} .\)
(c) Fit the data to a polynomial for \(\mathrm{E}\) against \(\mathrm{p}\). How
constant is \((\partial E / \partial p)_{T, n} ?\)
(d) From the polynomial, estimate an effective isothermal compressibility for
the cell as a whole.