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 16802
Submitted: 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=∆rG (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=vFEoRT (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=∆rSvF (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.
∆rH=∆rG+T∆rS (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
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.