32 Experiment : Thermodynamics of Electrochemical Cells
Abstract
The electromotive force of a cell was measured at different temperature to obtain E E Volts . was found out to be ( 1.4 0.5) 10 4 . From that number, other T P T P K thermodynamics properties at 25C were calculated. G was calculated to be -308270 Joule Joule 150 . S was found out to be -26.8 10.3 . H was 316000 3000 mol Kelvin mol Joule . From the above numbers, irreversible heat and reversible heat was calculated to mol Joule Joule be -316000 3000 and -8000 3000 respectively. mol mol
Introduction
The objective of this experiment is to determine G, H and S in a cell reaction. A reaction needs to be carried out reversibly in a cell and the measurement of reversible cell potential with respect to temperature needs to be done in order to determine G, H and S. In this experiment, the following reaction was carried out in a cell: Zn(s) + Ag2O(s) ZnO(s) + 2 Ag(s) The cell potential was determined at different temperature (25oC, 35oC and 45oC) to get
E T
. The voltmeter needs to be calibrated for offset error and gain error. The
P
corrected values was then used to get the thermodynamic properties.
Data and Calculations
Calibration : Calculation of offset error and gain error
Calibration Offset (V) V observed (V) V true (V) Gain Readings 0.0001 1.0188 1.01927 0.99944
Table 1. Values measured for calibration The offset value is obtained by shorting the voltmeter. The V observed is obtained by measuring the voltage of a standard cell of known voltage. From those values, the gain is calculated using this equation :
Gain
Vobserved Offset Vtrue
1.0188 0.0001 0.99944 1.01927
Sample calculation of the true (corrected) voltage : 25C water bath
Vtrue Vobserved Offset Gain 1.5967 0.0001 1.5975Volts 0.99944
Temperature (K) 318.15 308.15 298.15 288.15
Vobserved (Volts) 1.5937 1.5951 1.5967 1.5978
Vtrue (Volts) 1.5945 1.5959 1.5975 1.5986
V error (Volts) 0.0008 0.0008 0.0008 0.0008
Table 2. Result of the calculated voltage and its error. Note that the voltages above are the voltages after the system has equilibrated. This equilibration was verified by taking readings of voltmeter for every minute after equilibration is believed has been established. The error of the voltage is taken to be 0.05% of Vtrue.
Voltage vs Temperature
1.6000 1.5990
True Voltage (V)
1.5980 1.5970 1.5960 y = -1.3908E-04x + 1.6388E+00 1.5950 1.5940 1.5930 285 290 295 300 305 310 315 320 Temperature (K) y = -1.8993E-04x + 1.6541E+00 y = -8.3551E-05x + 1.6219E+00
Figure 1. The dependence of voltage on temperature. The best fit line is shown in solid line whereas the worst fit lines is shown in dashed lines.
Calculation of
E T
P
The of slope the best fit line in the voltage vs temperature is taken to be Therefore,
E T 1.3908 10
P 4
E T
.
P
Volts K
The error of the slope is the difference of the slopes of worst fit lines divided by 2.
E T
P
( 0.83551 ( 1.8993)) 10 2
E T ( 1.4 0.5) 10
P 4
4
5.319 10
5
Volts K
Therefore,
Volts K
Sample calculation of G, H, and S at 25C G = -nFE =
2 96485
(G) = nE(F) + nF(E)
Coulomb Joule 1.5975Volt = -308268.293 mol mol C mol 2 96485 Coulomb 0.0005Volt mol
= 2 1.5975Volts 0.008 = 154.083
Joule mol Joule mol
Therefore, G = -308270 150
Coulomb Volt Joule = -26.84 1.39 10 4 mol Kelvin mol Kelvin P E E (S) = n F + nF T P T P Volts C C Volt = 2 1.39 10 4 0.008 2 96485 5.319 10 5 Kelvin mol mol Kelvin Joule = 10.264 mol Kelvin
S = nF = 2 96485 Therefore, S = -26.8 10.3
E T
Joule mol Kelvin
H
= G + TS = -308268.293 + (298.15 Kelvin )(-26.84 = -316270.1224
Joule ) mol Kelvin
Joule mol (H) = (G) + T[(S)] Joule Joule = 154.083 + (298.15 Kelvin )(10.264 ) mol Kelvin mol Joule = 3214 mol
Therefore, H = 316000 3000
Joule mol
Sample calculation of qrev and qirr at 25C
qirr
= H = -316270.1224
Joule mol Joule mol Joule mol
qirr
= (H) = 3214.31625
Therefore,
qirr = -316000 3000
qrev qrev
= TS = (298.15 Kelvin )(-26.84 = T(S) = (298.15 Kelvin )(10.264
Joule Joule ) = -8001.829 mol Kelvin mol
Joule Joule ) = 3060 mol Kelvin mol
Therefore, qrev = -8000 3000
Joule mol
Calculation of cell potential, G, H, and S based on literature value and chemical reaction equation H298 G298 S -1 -1 kJ mol kJ mol kJ mol-1K-1 cr 0 0 42.55 Ag cr -31.05 -11.20 121.3 Ag2O cr 0 0 41.63 Zn cr -348.28 -318.30 43.64 ZnO Table 5. Heats of formation, Gibbs energy of formation and entropy values at 25C. Data is taken from D.D. Wagman et al, J. Physical Chemistry Reference Data (1982). state
Standard Electrode Potential Zn + 2 OH- ZnO + H2O + 2 eAg2O + H2O + 2 e- 2 Ag + 2 OHNet reaction: Zn + Ag2O ZnO + 2 Ag 1.245 V 0.344 V 1.589 V
H298 = (-1)(0) + (-1)(-31.05) + (-348.28) + 2(0) = -317.23 kJ mol-1 G298 = (-1)(0) + (-1)(-11.20) + (-318.30) + 2(0) = -307.10 kJ mol-1 S qirr qrev = (-1)(41.63) + (-1)(121.3) + (43.64) + 2(42.55) = -34.19 J mol-1 K-1 = H298 = -317.23 kJ mol-1 = TS = 298.15 K x (-34.19 J mol-1 K-1) = -10193.75 J mol-1
Results and calculation
Experimental value Cell potential Volts
E T
Literature value 1.589
Deviation (%) 0.53 -
1.5975
( 1.4 0.5) 10
4
P
Volts K
-
Joule -308270 150 -307100 0.38 mol Joule S -26.8 10.3 -34.19 21.61 mol Kelvin Joule H 316000 3000 -317230 0.39 mol Joule qirr -316000 3000 -317230 0.39 mol Joule qrev -8000 3000 -10193.75 21.51 mol Table 6. Comparison between experimental and literature value at 25C.
G
Discussion