Thermodynamic Quantities Derived from emf Studies of Concentraton Cells of Al \((NO_3)_3\) and \(CuSO_4\)

Abstract

This study explores the usefulness of concentration cells for determining thermodynamic quantities from electromotive force (emf) measurements. The thermodynamic quantities investigated include the Gibbs free energy change, entropy change and enthalpy change. Two different concentration cells were constructed for this purpose. The cell notations are represented as follows: \(\mathrm{Al}\left|\mathrm{Al}\left(\mathrm{NO}_3\right)_3\left(0.01 \mathrm{~mol} . \mathrm{dm}^{-3}\right) \| \mathrm{Al}\left(\mathrm{NO}_3\right)_3\left(0.001 \mathrm{~mol} . \mathrm{dm}^{-3}\right)\right| \mathrm{Al}\) and \(\mathrm{Cu}\left|\mathrm{CuSO}_4\left(0.01 \mathrm{~mol} . \mathrm{dm}^{-3}\right)\right|\left|\mathrm{CuSO}_{43}\left(0.001 \mathrm{~mol} . \mathrm{dm}^{-3}\right)\right| \mathrm{Cu}\). The emf of the concentration cells were obtained from a voltmeter at five different temperatures ( \(298.15,308.15,318.15,328.15\) and 338.15 K ). The emf values showed a progressive increase with temperature in both half-cells. The emf values ranged from 2.830 mV to 5.700 mV in the \(\mathrm{Al}\left(\mathrm{NO}_3\right)_3\) concentration cell and 4.200 mV to 8.300 mV in the \(\mathrm{CuSO}_4\) concentration cell. The values of the entropy change and enthalpy change extrapolated from the plot of Gibbs free energy change versus temperature for the concentration cells were respectively, \(-0.0547(\mathrm{~J} / \mathrm{k} . \mathrm{mol})\) and \(-1.7605(\mathrm{~J} / \mathrm{mol})\) for \(\mathrm{Al}\left(\mathrm{NO}_3\right)_3\) and was \(-0.1694(\mathrm{~J} / \mathrm{k} . \mathrm{mol})\) and \(-3.793(\mathrm{~J} / \mathrm{mol})\) for \(\mathrm{CuSO}_4\). The values of the Gibbs free energy change in the concentration cells over the measured temperature range was from \(-2.980 \times 10^5 \mathrm{~J} / \mathrm{mol}\) to \(-5.380 \times 10^5 \mathrm{~J} / \mathrm{mol}\) in the \(\mathrm{Al}\left(\mathrm{NO}_3\right)_3\) and from \(-8.380 \times 10^5 \mathrm{~J} / \mathrm{mol}\) to \(-1.610 \times 10^6 \mathrm{~J} / \mathrm{mol}\) in the \(\mathrm{CuSO}_4\) respectively.