This document summarizes an experiment to determine the thermodynamic parameters (ΔG, K, ΔS, ΔH) of reactions in an alkaline-manganese dioxide (AA Duracell) battery. The ΔG was calculated to be -303.4±0.2 kJ/mol. K was measured to be 3.7×10^53 ± 3.7×10^50. ΔS was calculated to be -23.0±0.01 J/Kmol. ΔH was experimentally determined to be 310.3±0.4 kJ/mol, which was within 0.55% of the theoretical value calculated from formation energies. Errors may have arisen from measuring external rather

1. The determination of thermodynamic functions of the reactions in
commercial alkaline-manganese dioxide galvanic cell
Rashid Alsuwaidi, Chris Lieb, Chris Russell and Ralph Eachus
Department of Chemistry, The Pennsylvania State University, University Park, PA 16802
Submitted: February 3, 2014 (CHEM 457, Section 2)
Abstract
The thermodynamic parameters; Δ G, K, ΔS and ΔH which are the Gibbs ,equilibrium constant
,entropy and enthalpy respectively, were calculated for a commercial alkaline-manganese
dioxide galvanic cell. The Δ G was calculated to be -303.4±0.2kJ/mol.The K was measured to be
3.7×10^53 ± 3.7×10 ^50.ΔS was calculated to be -23.0±0.01J/Kmol.The experimental ΔH was
calculated to be 310.3±0.4kJ/mole and compared to the ΔH calculated from the enthalpies of
formation ∆ 𝑓H˚, which was 312kJ/mol.The percent difference was calculated to be 0.55%.
Introduction
A galvanic cell is a simple device which converts chemical energy to electric energy. This occurs
due to redox reactions were reactant are oxidized and the other reduced. In this experiment a AA
Duracell battery was used, which consists of Zinc at the negative terminal which is oxidized and
magnesium dioxide at the positive terminal which is reduced. It uses potassium hydroxide as an
electrolyte which allows high electron mobility at a low freezing point.1 The reaction is shown
below:
Zn(s) + 2OH-(aq) → ZnO(s) + H2O (l) + 2e- (E° = -0.76 V)
2MnO2(s) + H2O (l) + 2e- → Mn2O3(s) + 2OH-(aq) (E° = +.80 V)
Zn(s) + 2MnO2(s) → ZnO(s) + Mn2O3(s) (E° = 1.56 V)
The most common batteries are based on Lithium, lead and nickel with most consumer products
using Lithium –ion batteries. Lithium-ion batteries are mostly used in portable products such as
digital cameras, laptops and phones because it has a high energy density, small size and
inexpensive but has a short battery life. If you’re going to be operating at subzero temperatures

2. then lead-based batteries are better, inexpensive and have a high specific power but it will be
slow to charge, bulky and not environmentally friendly. Batteries can be discharged in over a
wide range of temperatures, while charging has a limited range so it is best to charge a battery at
room temperature to maintain its performance and increase its shelf life. Cold temperatures
increases a batteries internal resistance so it is better to reduce the current when charging.
The purpose of the experiment was to determine parameters Δ G, K, ΔS and ΔH for a AA
Duracell battery and to also compare ΔH to the enthalpy of formation ∆ 𝑓H˚ of the redox reaction
in the battery.
(1) ∆G = -vFE
The Gibbs free energy is calculated using Equation 1.The symbols v, F and E represent the
number of electron involved in the redox reaction, Faradays constant which is 9.6×10 ^4 C/mol
and the electromotive force(V) respectively.
(2) ln K =
𝑣𝐹𝐸
𝑅𝑇
Equation 2 is used to calculate the equilibrium constant K. The ideal gas constant is represented
by R which is 8.314 J/molK, while T is the temperature of the reaction in Kelvin.
(3)
𝑑𝐸
𝑑𝑇
=
∆ 𝑆
𝑣𝐹
By applying the thermodynamic relationship
𝑑𝐺
𝑑𝑇
= −𝑆 in Equation 1 you will arrive at
Equation 3 which was used to calculate ΔS in J/molK. The temperature coefficient of the cell is
represented by
𝑑𝐸
𝑑𝑇
.

3. (4) ∆ 𝐻 = ∆𝐺 + 𝑇∆ 𝑆
The enthalpy of the AA Duracell battery was calculated using Equation 4 in J/mol by using the
values calculated from Equation 1 and 3.
Experimental
The voltage was measured at various temperatures, which was done using two AA Duracell
batteries and a Hewlett Packard 34401A multimeter which has an uncertainty of
±.001mV.1Temperature and voltage are recorded of the battery before being placed in a Dewar
filled with ethanol. Precision is improved by using a reference battery maintained at 0˚C which is
connected in parallel to the measured battery. The positive end of the battery being measured is
connected to the positive end of the voltmeter. Using alligator clips, connect the negative leads
of the measured and reference battery. The reference battery is transferred to the reference
Dewar which is maintained at 0˚C.The positive end of the reference battery is connected to the
negative end (black) of the voltmeter. The voltage of the battery being measured will be recorded
at various temperatures in the range of -25 to 40 ˚C in a Dewar filled with ethanol. The first
reading was recorded at 27.7˚C while trying to maintain the same temperature for 10 minutes
before recording the voltage. Dry ice was added at 4˚C increments to get the second reading.
This was done until 7 data points were collected.
Results
The data collected as shown in Table 1 were then plotted as shown in Figure 1.The measured
temperatures was subtracted from the reference temperature to calculate the actual temperature.
The electromotive force (E˚) was calculated by adding the ∆V and the voltage of battery which
was 1.6062V.

4. Table 1. Voltage of alkaline cell at different temperatures
TREF TMEAS TACTUAL DELTA
V
E(V)
24.2 27.2 27.5 -10.293 1.595907
24.5 23.1 23.5 -9.798 1.596402
24.6 19.2 19.6 -9.288 1.596912
24.6 15.2 15.7 -8.82 1.59738
24.7 11.2 11.8 -8.355 1.597845
24.8 6.7 7.3 -7.891 1.598309
24.8 3.4 4 -7.569 1.598631
Figure.1:Electromotive force vs. temperature
Using Equations 1 and 2 the Δ G and K were calculated to be -303.4±0.2kJ/mole and
3.7×10^53± 3.7×10^50 respectively.2From Figure.1, the best fit line gave us a linear plot with an
error of R2=0.9977 which indicates our results are consistent. The equation of the best fit line has
a slope of -0.00012 ± 2.53×10^-6 which represents the temperature coefficient
𝑑𝐸
𝑑𝑇
.This is used

5. in Equation 3 to calculate the ∆ 𝑆 which was -23.0±0.01 J/molK. Using the values from
Equation 1 and 3 in Equation 4 the experimental ΔH was calculated to be 310.3±0.4kJ/mol
which was 0.55% within the theoretical value of 312kJ/mole calculated from the enthalpies of
formation ∆ 𝑓H˚.3
Discussion
The ΔrH calculated had a percent difference of 0.55% compared to the theoretical value, so a
reasonable value was obtained, while the errors were probably due to things we had no control
over. The 0.55% difference in the values was possibly due to the way the temperatures were
being measured since we can’t measure the internal temperature directly, we had to record the
external temperature of the battery, which is why it must equilibrate for 10 minutes before
recording the temperature and voltage. The error could be reduced if the temperature was
allowed to equilibrate longer to 15 to 20 minutes. In addition; the temperature cannot always be
maintained at the desired temperature using dry ice and it fluctuates. To fix this problem, a
solution with a higher heat capacity such as water could be used, so that the temperature would
not decrease or increase quickly and be maintained at the desired temperature for longer periods,
while the battery equilibrates. When the experiment was conducted the heat from our bodies
might have also contributed to the errors. To have a 1mV precision meant that anything above
99mV that was recorded on the voltmeter will not be accurate so the ∆V was calculated at each
temperature by subtracting the voltage of the measured and reference battery. The ∆V is added to
the initial voltage of the battery to get a precision of 1mV.As the temperature decreases the rate
of the reaction decreases, which causes the internal resistance of the battery to increase but it will
last longer. As the temperature increases the rate of the reaction increases and the internal
resistance decreases but it will shorten the battery life. The temperature range we used showed
only slight changes in the electromotive force, so a higher temperature range such as 40 to 60˚C
or a very low temperature range such as -20 to 0˚C could be tested to see if the results will be
similar. The optimum temperature for the battery is at 25˚C because being colder or hotter would
reduce its performance.

6. Conclusion
To conclude; the Δ G was calculated to be -303.4±0.2kJ/mol. The K was measured to be 3.7×10
^53 ± 3.7×10 ^50.The ΔS was calculated to be -23.0±0.01J/Kmol. The ΔH was calculated to be
310.3 ± 0.4kJ/mol. The experimental ΔH had a percent difference of 0.55% compared to the
theoretical value of 312kJ/mole which was reasonable. The main sources of error where from
recording the external temperatures of the battery instead of the internal and the difficulties in
maintaining the desired temperature using dry ice to equilibrate. This experiment allowed us to
calculate the thermodynamic parameters; ΔG, K, ΔS and ΔH; in addition, showed how the
voltage of the battery is effected by temperature changes.
Acknowledgement
I would like to acknowledge Chris Lieb, Chris Russell and Ralph Eachus, who were the group
members that assisted in performing the experiment and data analysis. In addition; Dr.
Milosavljevic, teaching assistants Mr. Yuguang (Chris) Lee and Ms. Jennifer Tan.
Reference
1. Milosavljevic, B.H. Lab Packet for CHEM 457: Experimental Physical Chemistry, The
determination of thermodynamic functions of the reactions in commercial alkaline-manganese
dioxide galvanic cell. University Press: University Park, 2014.
2. Peter Kissinger, & William R. Heineman. (Eds.). (1996). Laboratory Techniques in Electro
analytical Chemistry (5th Ed.). New York, NY: Marcel Dekker.
3. Denis Hanson, Vi Maeers and Harley Weston, What is Percentage Difference?
http://mathcentral.uregina.ca/about/ (accessed January 30, 2014).

7. Appendix
1.
Regression Statistics
Multiple R 0.998829
R Square 0.99766
Adjusted R Square0.997192
Standard Error5.29E-05
Observations 7
ANOVA
df SS MS F Significance F
Regression 1 5.96E-06 5.96E-06 2131.588 9E-08
Residual 5 1.4E-08 2.8E-09
Total 6 5.98E-06
CoefficientsStandard Errort Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept 1.599165 4.43E-05 36116.54 3.09E-22 1.599051 1.599279 1.599051 1.599279
X Variable 1-0.00012 2.53E-06 -46.1691 9E-08 -0.00012 -0.00011 -0.00012 -0.00011