1. Lead-Acid Battery 1

1. Lead-Acid Battery 1 The basic electrochemical reaction equation 2 in a lead-acid battery can be written as follows:

Pb + 2H2SO4 + PbO2 <---- Charging + PbSO4 + 2H2O + PbSO4 Discharging----> 1.1 Discharging the Lead-Acid Battery During the discharge portion of the reaction, lead dioxide (positive plate) and lead (negative plate) react with sulfuric acid to create lead sulfate, water and energy. 1.2 Charging the Lead-Acid Battery

During the recharge phase of the reaction, the cycle is reversed: the lead sulfate and water are electro-chemically converted to lead, lead oxide and sulfuric acid by an external electrical charging source. 1.3 Problems of Lead-Acid Battery The biggest problem in lead-acid cells is sulfation due to chronic undercharging. Here the sulfate ions have entered into deep bonds with the lead on the cell's plates. The sulfate ions can bond with the lead at three successively deeper energy levels. Level One is the bond we use when we normally charge and discharge the cell. After a month or so at Level One, some of the bonds form Level Two bonds which require more electric power to break. After several months of being at Level Two bond, the sulfate ions really cozy up to the lead and form Level Three bonds. Level Three bonds are not accessible electrically. No amount of recharging will break Level Three bonds. The longer the lead sulfate bond stays at a level the more likely it is to form a closer acquaintance and enter the next deeper level. This is why it is so important to fully, regularly, and completely, recharge lead-acid cells. 1.4 Lead-Acid Battery Equalization Charges If the loss in capacity is due to Level Two bonding, then a repeated series of equalizing charges will break the Level Two bonds. Under equalization the Level Two bonds will first be transformed into Level One bonds, and then the sulfate ion can be kicked loose of the lead entirely and reenter the electrolyte solution. If your lead-acid cells have lost capacity, then a regime of equalizing charges is the first procedure to try. An equalization charge is a controlled overcharge of an already fully recharged cell. First recharge the cell and then continue to charge the cell at a C/20 rate for five to seven hours. During equalization charges, the cell voltage will become very high, about 2.7 VDC per cell. This overcharge contains the necessary power to break the Level Two bonds and force them to Level One. Once they reach Level One, the bond is easily broken and the sulfate ions reenter into solution in the electrolyte. 1.5 Lead-Acid Battery Care 3 The Lead acid battery is made up of plates, lead, and lead oxide (various other elements are used to change density, hardness, porosity, etc.) with a 35% sulfuric acid and 65% water solution. This solution is called electrolyte which causes a chemical reaction that produce electrons. When you test a battery with a hydrometer you are measuring the amount of sulfuric acid in the electrolyte. If your reading is low, that means the chemistry that makes electrons is lacking. So where did the sulfur go? It is stuck to the battery plates and when you recharge the battery the sulfur returns to the electrolyte.

State of Charge Specific Gravity 100% *75% 50% 25% Discharged 1.265 1.225 1.190 1.155 1.120 12V 12.7 12.4 12.2 12.0 11.9 Voltage 6V 6.3 6.2 6.1 6.0 6.0 *Sulfation of Batteries starts when specific gravity falls below 1.225 or voltage measures less than 12.4 (12v Battery) or 6.2 (6 volt battery). Sulfation hardens the battery plates reducing and eventually destroying the ability of the battery to generate Volts and Amps. The alternator is a battery charger. It works well if the battery is not deeply discharged. The alternator tends to overcharge batteries that are very low and the overcharge can damage batteries. 2. THERMODYNAMICS First Law of Thermodynamics : You can t create or destroy energy Second Law of Thermodynamics: Energy spontaneously disperses from being localized to becoming spread out if it is hindered. Third Law of Thermodynamics: The entropy of a perfect crystal is zero when the temperature of the crystal is equal to absolute zero (0K). Thermodynamic Properties of Selected Substances 4 For one mole at 298K and 1 atmosphere pressure Substance (form) Enthalpy f H (kj) Gibbs f G (kj) Entropy (J/ K Specific heat C P (J/K) Volume V(cm 3 ) Al (s) 0 0 28.33 24.35 9.99 Al 2 SiO 5 (kyanite) -2594.29-2443.88 83.81 121.71 44.09 Al 2 SiO 5 (andalusite) -2590.27-2442.66 93.22 122.72 51.53 Al 2 SiO 5 (sillimanite) -2587.76-2440.99 96.11 124.52 49.90 Ar (g) 0 0 154.84 20.79... C (graphite) 0 0 5.74 8.53 5.30 C (diamond) 1.895 2.900 2.38 6.11 3.42 CH 4 (g) -74.81-50.72 186.26 35.31... C 2 H 6 (g) -84.68-32.82 229.60 52.63... C 3 H 8 (g) -103.85-23.49 269.91 73.5... C 2 H 5 OH (l) -277.69-174.78 160.7 111.46 58.4

C 6 H 12 O 6 (glucose) -1268-910 212 115... CO (g) -110.53-137.17 197.67 29.14... CO 2 (g) -393.51-394.36 213.74 37.11... H 2 CO 3 (aq) -699.65-623.08 187.4...... HCO - 3 (aq) -691.99-586.77 91.2...... Ca 2+ (aq) -542.83-553.58-53.1...... CaCO 3 (calcite) -1206.9-1128.8 92.9 81.88 36.93 CaCO 3 (aragonite) -1207.1-1127.8 88.7 81.25 34.15 CaCl 2 (s) -795.8-748.1 104.6 72.59 51.6 Cl 2 (g) 0 0 223.07 33.91... Cl - (aq) -167.16-131.23 56.5-136.4 17.3 Cu (s) 0 0 33.150 24.44 7.12 Fe (s) 0 0 27.28 25.10 7.11 H 2 (g) 0 0 130.68 28.82... H (g) 217.97 203.25 114.71 20.78... H + (aq) 0 0 0 0... H 2 O (l) -285.83-237.13 69.91 75.29 18.068 H 2 O (g) -241.82-228.57 188.83 33.58... He (g) 0 0 126.15 20.79... Hg (l) 0 0 76.02 27.98 14.81 N 2 (g) 0 0 191.61 29.12... NH 3 (g) -46.11-16.45 192.45 35.06... Na + (aq) -240.12-261.91 59.0 46.4-1.2 NaCl (s) -411.15-384.14 72.13 50.50 27.01 NaAlSi 3 O 8 (albite) -3935.1-3711.5 207.40 205.10 100.07 NaAlSi 2 O 6 (jadeite) -3030.9-2852.1 133.5 160.0 60.40 Ne (g) 0 0 146.33 20.79... O 2 (g) 0 0 205.14 29.38... O 2 (aq) -11.7 16.4 110.9...... OH - (aq) -229.99-157.24-10.75-148.5... Pb (s) 0 0 64.81 26.44 18.3 PbO 2 (s) -277.4-217.33 68.6 64.64... PbSO 4 (s) -920.0-813.0 148.5 103.2... SO 2-4 (aq) -909.27-744.53 20.1-293...

HSO 4 - (aq) -887.34-755.91 131.8-84... SiO 2 (α quartz) -910.94-856.64 41.84 44.43 22.69 H 4 SiO 4 (aq) -1449.36-1307.67 215.13 468.98... Data from Schroeder, Daniel V., An Introduction to Thermal Physics, Addison-Wesley, 2000. Definitions Enthalpy Change 5 The heat content of a chemical system is called the enthalpy (symbol: H) The enthalpy change ( H) is the amount of heat released or absorbed when a chemical reaction occurs at constant pressure. H = H (products) - H (reactants) H is specified per mole of substance as in the balanced chemical equation for the reaction The units are usually given as kj mol -1 (kj/mol) or sometimes as kcal mol -1 (kcal/mol) 1 calorie (1 cal) = 4.184 joules (4.184 J) Energy changes are measured under standard laboratory conditions 25 o C (298K) & 101.3kPa (1 atmosphere) Type of Exothermic Reaction Energy Energy is released. absorbed Energy is a product of the reaction. or Reaction vessel becomes warmer. released Temperature inside reaction vessel increases. Relative Energy of Energy of the reactants is greater than the reactants energy of the products & products Sign of H = H H (products) - H (reactants) = negative (-ve) Writing the equation Energy Profile N 2 (g) + 3H 2 (g) -----> 2NH 3 (g) + 92.4 kj N 2 (g) + 3H 2 (g) ---> 2NH 3 (g) H=-92.4 kj mol -1 Energy of reactants (N 2 & H 2 ) is greater than the energy of the products (NH 3 ). Energy is released. H is negative. H is measured from the energy of reactants to the energy of products on the Energy Profile diagram. Endothermic Energy is absorbed. Energy is a reactant of the reaction. Reaction vessel becomes cooler. Temperature inside reaction vessel decreases. Energy of the reactants is less than the energy of the products H = H (products) - H (reactants) = positive (+ve) 2NH 3 (g) + 92.4 kj -----> N 2 (g) + 3H 2 (g) 2NH 3 g ---> N 2 (g) + 3H 2 (g) H=+92.4 kj mol -1 Energy of reactants (NH 3 ) is less than the energy of the products (N 2 & H 2 ). Energy is absorbed. H is positive. H is measured from the energy of reactants to the energy of products on the Energy Profile diagram. Enthalpy comes from the Greek heat inside

Entropy 6 is defined as the degree of freedom that particles of matter have. The letter S is used to symbolize entropy. Gases have greater entropy than pure liquids, which have greater entropy than pure solids. Solutions have greater entropy than pure liquids as the particles in a solution are more separated and solvent molecules separate the solute particles: S > S > S > S gas soln liq solid Entropy is merely the way to measure the energy that spreads out in a process (as a function of temperature). Entropy change, S, measures how much energy is spread out in a system, or how spread out is the energy of a system (both always involving T). As an example of reversible process, melting ice to water at 273 K where S = q/t. So, in that equation, it's easy to see that q (the enthalpy of fusion) is how much "heat" energy was spread out in the ice to change it to water. The absolute entropy is obtained by integrating entropy change from absolute zero to T. The enthalpy data in the table are relative data ( H), which compare each compound with its elements. The data are relative because there is no absolute zero on the enthalpy scale. All we can measure is the heat given off or absorbed by reaction. Thus, all we can determine is the difference between the enthalpies of the reactants and the products of a reaction. We therefore define the enthalpy of formation of the elements in their most thermodynamically stable states as zero and report all compounds as either more or less stable than their elements. The entropy data are different. The third law defines absolute zero on the entropy scale. As a result, the absolute of any element or compound can be measured by comparing it with a perfect crystal at absolute zero. The entropy data are therefore given as absolute numbers, S 0. The Gibbs free energy 7 of a system, represented by the letter G, is defined as the energy of a system that is free to do work at constant temperature and pressure. Mathematically, it is defined as: Where: G=H-TS G is the free energy H is the enthalpy

T is the temperature S is the entropy of the system The change in free energy is calculated as: G = H - T S 3. Electrolysis of Water 8 By providing energy from a battery, water (H 2 O) can be dissociated into the diatomic molecules of hydrogen (H 2 ) and oxygen (O 2 ). This process is a good example of the application of the four thermodynamic potentials. The electrolysis of one mole of water produces a mole of hydrogen gas and a half-mole of oxygen gas in their normal diatomic forms. A detailed analysis of the process makes use of the thermodyamic potentials and the first law of thermodynamics. This process is presumed to be at 298K and one atmosphere pressure, and the relevant values are taken from a table of thermodynamic properties. Quantity H 2 O H 2 0.5 O 2 Change Enthalpy -285.83 kj 0 0 H = 285.83 kj Entropy 69.91 J/K 130.68 J/K 0.5 x 205.14 J/K T S = 48.7 kj

ΔH=H (products) -H (reactants) =H (H2) +H (0.5O2) -H (H2O) =0+0-(-285.83)=285.83kJ TΔS The process must provide the energy for the dissociation plus the energy to expand the produced gases. Both of those are included in the change in enthalpy included in the table above. At temperature 298K and one atmosphere pressure, the system work is W = P V = (101.3 x 10 3 Pa)(1.5 moles)(22.4 x 10-3 m 3 /mol)(298k/273k) = 3715 J Where: P=101.3x10 3 Pa(Pascal)= 1 atm; V=22.4x10-3 m 3 /mol @ T=273K and P=1 atm Since the enthalpy H= U+PV, the change in internal energy U is then U = H - P V = 285.83 kj - 3.72 kj = 282.1 kj This change in internal energy must be accompanied by the expansion of the gases produced, so the change in enthalpy represents the necessary energy to accomplish the electrolysis. However, it is not necessary to put in this whole amount in the form of electrical energy. Since the entropy increases in the process of dissociation, the amount T S can be provided from the environment at temperature T. The amount which must be supplied by the battery is actually the change in the Gibbs free energy: G = H - T S = 285.83 kj - 48.7 kj = 237.1 kj Since the electrolysis process results in an increase in entropy, the environment "helps" the process by contributing the amount T S. The utility of the Gibbs free energy is that it tells you what amount of energy in other forms must be supplied to get the process to proceed. 4. Hydrogen Fuel Cell Hydrogen and oxygen can be combined in a fuel cell to produce electrical energy. A fuel cell uses a chemical reaction to provide an external voltage, as does a battery, but differs from a battery in that the fuel is continually supplied in the form of hydrogen and oxygen gas. It can produce electrical energy at a higher efficiency than just burning the hydrogen to produce heat to drive a

generator because it is not subject to the thermal bottleneck from the second law of thermodynamics. It's only product is water, so it is pollution-free. All these features have led to periodic great excitement about its potential, but we are still in the process of developing that potential as a pollution-free, efficient energy source (see Kartha and Grimes). Combining a mole of hydrogen gas and a half-mole of oxygen gas from their normal diatomic forms produces a mole of water. A detailed analysis of the process makes use of the thermodynamic potentials. This process is presumed to be at 298K and one atmosphere pressure, and the relevant values are taken from a table of thermodynamic properties. Quantity H 2 0.5 O 2 H 2 O Change Enthalpy 0 0-285.83 kj H = -285.83 kj Entropy 130.68 J/K 0.5 x 205.14 J/K 69.91 J/K T S = -48.7 kj

Energy is provided by the combining of the atoms and from the decrease of the volume of the gases. Both of those are included in the change in enthalpy included in the table above. At temperature 298K and one atmosphere pressure, the system work is W = P V = (101.3 x 10 3 Pa)(1.5 moles)(-22.4 x 10-3 m 3 /mol)(298k/273k) = -3715 J Since the enthalpy H= U+PV, the change in internal energy U is then U = H - P V = -285.83 kj - 3.72 kj = -282.1 kj The entropy of the gases decreases by 48.7 kj in the process of combination since the number of water molecules is less than the number of hydrogen and oxygen molecules combining. Since the total entropy will not decrease in the reaction, the excess entropy in the amount T S must be expelled to the environment as heat at temperature T. The amount of energy per mole of hydrogen which can be provided as electrical energy is the change in the Gibbs free energy: G = H - T S = -285.83 kj + 48.7 kj = -237.1 kj For this ideal case, the fuel energy is converted to electrical energy at an efficiency of 237.1/285.8 x100% = 83%! This is far greater than the ideal efficiency of a generating facility which burned the hydrogen and used the heat to power a generator! Although real fuel cells do not approach that ideal efficiency, they are still much more efficient than any electric power plant which burns a fuel. Comparison of electrolysis and the fuel cell process In comparing the fuel cell process to its reverse reaction, electrolysis of water, it is useful treat the enthalpy change as the overall energy change. The Gibbs free energy is that which you actually have to supply if you want to drive a reaction, or the amount that you can actually get out if the reaction is working for you. So in the electrolysis/fuel cell pair where the enthalpy change is 285.8 kj, you have to put in 237 kj of energy to drive electrolysis and the heat from the environment will contribute T S=48.7 kj to help you. Going the other way in the fuel cell, you can get out the 237 kj as electric energy, but have to dump T S = 48.7 kj to the environment.

Reference 9

REFERENCES 1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/leadacid.html 2. http://www.flex.com/~kalepa/technotes.htm 3. http://www.batterystuff.com/battery/battery_tutorial.htm 4. http://hyperphysics.phy-astr.gsu.edu/hbase/tables/therprop.html 5. http://www.ausetute.com.au/enthchan.html 6. http://members.aol.com/profchm/entropy.html 7. http://www.shodor.org/unchem/advanced/thermo/ 8. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/electrol.html 9. Fuel Cells FactFile Published by IEE, Jan 2003.