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Temperature Dependence on EMF
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Using an electrochemical cell containing cadmium-mercury amalgam, cadmium, and cadmium sulfate, the dependence of electromotive force (emf) on temperature was measured at temperatures near 20C and constant ambient pressure. The emf was measured using a precision digital voltmeter and checked for accuracy with a Weston cell.
Introduction & Theory
An electromotive force, or emf, may be generated in an electrochemical cell by separating a spontaneous reaction into two half-reactions and forcing the electrons involved to travel through a circuit to complete the reaction. The physical location of the half-reaction that produces excess electrons is called the anode, and the location lacking electrons is termed the cathode. In the cell used in this experiment, the half-reaction at the anode is
A cell such as that described above, when operating reversibly, isothermally, and isobarically with only electrical work and expansion work has an increase in free energy given by the following equation
At constant temperature and pressure, the Gibbs-Helmholtz equation gives us the following relationship for a change in state
The general procedure given in the text(1) was followed, however a specialized cell was used instead of the beaker as suggested. In addition, a precision digital volt meter was used instead of a potentiometer described, and the temperature of a single bath was varied to determine the dependence of electromotive force on temperature.
Table 1 - Summary of Results
|Temperature (K)||Cell Voltage (Volts)||Standard Voltage (Volts)|
Averaging the voltages at each temperature and charting yields
Chart 1 - emf (V) vs Temperature (K)
Linear regression of the data yields (/T)p equal to -1.50x10-3 volts K-1 and a correlation coefficient of -0.695. By interpolation, the estimated value of the emf at 298.15 K is 0.5708 volts.
As shown in eqs. (1) and (2), two Faradays of electricity pass through the cell in this reaction. Using the emf calculated above for the cell at 25C (298.15 K), substitution into eq. (4) yields
At 25C, H evaluates to -196000 J
Cadmium has a molecular weight of 112.4 g mole-1 and mercury has a molecular weight of 200.9 g mole-1. Dividing the weights of materials used in making the amalgam by the appropriate molecular weight yields a composition of 2.39x10-3 mole Cd and 6.76x10-2 mole Hg. This is equivalent to 3.42 mole% Cd and 96.6 mole% Hg. The quantity X2 is then equal to 3.42 mole% and the activity a2 may be also be assumed to be 0.00342. The following equation gives the standard free energy change for the Cd(s)=Cd(Hg) at 298.15 K
For a spontaneous reaction, S>0. The results obtained for this experiment indicate a negative S for a spontaneous reaction, and as a result are clearly invalid. The chart of emf vs temperature shows a general decrease in voltage as temperature increases, while the rate of both half reactions should be increasing with temperature causing increased voltages.
Probably the largest contributor to the error was motion of the amalgam in the J electrode. This was caused by motions of the stir bar in the cell, as well as forces from the current of the stirrer water bath outside of the cell. These factors were increased by the magnetic stirring mechanism not being exactly level and a general lack of stability in the supports.
Drift in the metering equipment was negligible, varying by only 0.0393 percent over the course of the experiment (as measured by the Weston cell).
Another possible source of error in the experiment is the assumption in the calculation that X2 is constant. As the cell reacts, X2 will increase. For experiments (such as this one) done over relatively short time periods with high impedance metering equipment, this increase is negligible.
An "amalgam" with X2 = 1 would be pure cadmium, not an amalgam at all. As a result, the reaction would be Cd(s)=Cd(s), with no change in state. Consequently, there would be no change in free energy and G would be zero. In this experiment, a change of state did occur and the reactants had a different free energy than the products, hence a non-zero value for G .
1. D.P. Shoemaker, C.W. Garland, J.W. Nibler, Experiments in Physical Chemistry, 6th ed., The McGraw-Hill Companies (1996).