The determination of thermodynamic functions of the reactions in commercial alkaline-manganese dioxide galvanic

cell (Duracell®)Ahmad Alhazeem, Roberto Hernandez, Christopher Rinschler and Danielle Baginsky

Department of Chemistry, The Pennsylvania State University, University Park, PA 16802Submitted: February 14, 2013 (CHEM 457, Section 5)

The thermodynamic functions ΔrG, K, ΔrS and ΔrH of the reaction inside an alkaline cell

were determined by measuring the voltage at different temperatures. The functions ΔrG (-

309100.8 J) and K (1.02x1054) were first found by recording the temperature and voltage

at standard conditions. The results obtained of voltage at diferent temperatures were then

graphed and used to calculate ΔrS (-16.6±1.13 J) and ΔrH (-314,077.2±21266.4 J) by

using the slope of the graph in equations 3 and 4. The ΔrH value was 12.3% within the

literature value, which is reasonable despite the experimental limitations.

Introduction

The basis topic of this experiment, electrochemistry, is about the study of

reactions in which charged particles (ions or electrons) cross the interface between two

phases of matter, typically a metallic phase (the electrode) and a conductive solution (the

electrolyte). A galvanic cell is an electrochemical cell in which the free energy of a

chemical reaction is converted into electrical energy1. Redox reactions inside the cell

cause an electric current to flow in an external circuit, where useful work can be done. So

when ‘batteries’ are being used like switching on an electric torch or staring a car engine

electrical energy is provided by the redox reactions happening inside electrochemical

cells2.

Galvanic cells are classified as either primary or secondary cells in which the

main difference is that a primary cell may be used only once and a secondary cell may be

recharged by passing an electric current through it in the opposite direction to the current

flow during discharge2. In these cells ions flow through the electrolyte and electrons flow

in the electrodes where the anode is the site of oxidation and the cathode is the site of

reduction. The cell is used in this experiment is an alkaline dry cell, shown in Figure 1,

where the anode is a paste of powdered zinc with an electrolyte of potassium hydroxide,

and the cathode is manganese dioxide in the same electrolyte. The electrode reactions that

occur are zinc is oxidized to zinc oxide at the anode and manganese dioxide is reduced to

manganese (III) oxide at the cathode. The alkaline cell battery can be used for a variety of

devices but it is commonly known as a ‘torch battery’2.

The purpose of this experiment is to determine the thermodynamic functions of

the electrochemistry happening inside the cell so equations are needed to relate those two

sections. The free energy change for the process shows the maximum amount of

electrical work that can be obtained and its relation to the cell potential (E) is shown in

equation 1 where F is the Faraday constant and v is the number of moles of electrons

involved in balance equation3.

−vFE=∆r G (1)

When a voltaic cell produces an electric current, reactants are converted to

products causing the cell potential to decrease and eventually reach zero where

equilibrium is achieved. This situation can be analyzed by the Nernst equation shown in

equation 2 relating the cell potential to the equilibrium constant (K) that shows the extent

of reaction3.

lnK= vF Eo

RT (2)

Using equation 1 and a thermodynamic relationship, equation 3 shows that the

standard cell potential can also be related to entropy, which is the measure of the

dispersal of the energy in the system.

dEdT

=∆r S

vF (3)

Enthalpy, which is the amount of heat energy used or released in a system, can

then be obtained using the Gibbs free energy equation as shown in equation 4.

∆ r H=∆r G+T ∆ r S (4)

Figure 1. Diagram of a dry alkaline cell

Experimental

Details of the experiment are explained in the lab manual4, which is basically

about measuring the voltage of a commercial alkaline dry cell (AA 1.5 Volt Duarcell®

PC1500 Procell® alkaline battery) at different temperatures. The temperature in this

experiment is measured using a digital thermometer and the voltage is measured using a

digital multimeter (Hewlet Packard 34401A multimeter). The alkaline dry cell is placed

in a dewar filled with ethanol at an intitial temperature of 30°C and then it is cooled down

to about 0°C by adding dry ice to the ethanol while recording the temperature and voltage

at regular intervals of about 5°C. The Varistat is also used to regulate the temperature to a

suitable value that can be recorded within the approximate intervals. The temperature and

voltage was also recorded at standard conditions in order to calculate ΔrG. The setup of

this experiment also uses a reference battery with the measured battery increasing the

precision of the measurements.

Results and Discussion

The alkaline galvanic cell was first placed at an intitial temperature of 30°C where

the first voltage was recorded. The temperature was then decreased at inertvals of about

5°C while recording the results of voltage until the temperature reached close to 0°C.

There were seven sets of results obtained at different temperatures that were graphed so

that the slope can be used to calculate the thermodynamic functions ΔrS and ΔrH.

The results of the experiment are shown in Table 1 that were then used to plot E

vs. T shown by the graph in Figure 2. The trend of the results show that as the

temperature increases the cell potential decreases which is proven by the Nernst equation

shown in equation 2 earlier in the introduction where reactants are converted to products

causing the cell potential to decrease and eventually reach zero achieving equilibrium.

The decrease of the cell potential however is not that much as the temperature increases

since the slope of the graph is quite small. The results graphed in Figure 2 is considered

to have a strong correlation since the R2 value of 0.97757 is very close to 1 showing that

the results were consistent and no critical errors occurred.

Table 1. Voltage of alkaline cell at different temperatures

T (°C) E (mV) (±0.001)

30 8.957

25.7 9.481

20.2 10.059

15.2 10.542

11.2 10.875

6.2 11.198

1.5 11.391

270 275 280 285 290 295 300 3050

0.002

0.004

0.006

0.008

0.01

0.012f(x) = − 8.666517186484E-05 x + 0.0353920443956143R² = 0.977572701022584

E vs. T

Temperature (K)

E (V

)

Figure 2. E vs. T of alkaline cell

During the experiment the temperature and voltage were recorded at standard

conditions by placing the appropriate leads of the voltmeter to the battery holder. This

was then used to calculate the Gibbs free energy (ΔrG) and equilibrium constant (K) of

the reaction inside the cell. Equations 1 and 2 were used for the calculations that were

found to be -309100.8 J for ΔrG and 1.02x1054 for K. Since the value of ΔrG was negative

and K was much greater than 1, this shows that the reactions was product-favored at

equilibrium and spontaneous at standard conditions which is expected for a commercial

alkaline battery where reactants are converted to products when an electric current is

produced.

The recordings of temperature and voltage obtained from the experiment were

then plotted in a graph that had a slope value of -0.0000867±0.00000587. This value was

then used to calculate the thermodynamic function of entropy (ΔrS) and enthalpy (ΔrH).

Equation 3 was first used in order to calculate the entropy (ΔrS) of the electrochemical

reaction, which was found to be -16.6±1.13 J. The value of ΔrS along with the value

calculated for ΔrG previously were then plugged into equation 4 that gave a ΔrH of -

314,077.2±21266.4 J which is within 12.3 % of the literature value of ΔfH° -279.6 kJ.

This difference between those two values is due to the fact that the literature value is

obtained from bulk values whereas the result from the experiment is obtained from only

one alkaline cell.

The ΔrH value obtained from this experiment is be considered to be reasonable

being only 12.3% from the literature value which is caused from limitations that can not

be controlled during the experiment. Most of the errors that occur in this experiment are

to due problems with the temperature of the system. The first error was that the

temperature that was being measured for this experiment was from the outside of the

alkaline cell whereas the reaction was occurring inside the cell. This means that the

temperature being measured is not the absolute actual temperature of the electrochemical

reaction. The second error was that the temperature fluctuates when adding dry ice to

cool it down and using the Varistat to heat it up which decreases the accuracy of the

results since the battery needs to thermally equilibrate at each cooling data point for 10

minutes before recording the temperature and voltage.

The value of ΔrH is important since shows how much energy is contained inside

the galvanic cell before it is used or released in the system as heat when an electric

current is produced. The experiment can be considered a success since a reasonable value

for ΔrH has been obtained that was close to the literature value despite the experimental

limitations. The experiment might be improved by using a more suitable method to

control the temperature of the system instead of dry ice and the Varistat, like having

temperature sensors inside the dewar that can be control the temperature inside digitally

from a screen on the outside. Also to improve the accuracy of the results the temperature

of the reaction inside the cell needs to be measured by possibly having a wire inside the

cell without interrupting the electro chemical reactions taking place.

Conclusion

So in conclusion the thermodynamic functions ΔrG, K, ΔrS and ΔrH of the

reaction inside an alkaline cell were determined by measuring the voltage at different

temperatures. The functions ΔrG (-309100.8 J) and K (1.02x1054) were first found by

recording the temperature and voltage at standard conditions then plugging the values

into equations 1 and 2. The results obtained of voltage at diferent temperatures were then

graphed and used to calculate ΔrS (-16.6±1.13 J) and ΔrH (-314,077.2±21266.4 J) by

using the slope of the graph in equations 3 and 4. The ΔrH value was 12.3% within the

literature value, which is reasonable despite the experimental limitations. One of the main

sources of error on this experiment was the measurement and control of temperature of

the alkaline cell that might be solved by having a digital method of controlling the

temperature instead of using dry ice and the Varistat. This experiment shows how much

energy is contained inside a commercial alkaline cell and how the voltage is affected by

changes in temperature.

Acknowledgement

The author would like to acknowledge the group members mentioned in the first page,

Dr. Milosavljevic and our CHEM 457 teaching assistant for their assistant with the

completion of all aspects of this study including data collection and analysis.

References

(1) Patra, B. B., Samantray, B. Engineering Chemistry I (for BPUT); Dorling Kindersley:

India, 2011.

(2) Clugston, M, Flemming, R. Advanced Chemistry; Oxford University Press: Oxford,

2000.

(3) Kotz, J, Treichel, P, Townsend, J. Chemistry and Chemical Reactivity, Seventh Edition;

Thomson Brooks/Cole: Belmont, 2009.

(4) Milosavljevic, B.H. Lab Packet for CHEM 457: Experimental Physical Chemistry,

Gravimetric Determination of the Gas Constant. University Press: University Park, 2009.