3.014 MATERIALS LABORATORY MODULE – BETA 1 NOVEMBER 16 – 21, 2005 LEAD ACID STORAGE CELL OBJECTIVES: • Understand the relationship between Gibbs Free Energy and Electrochemical Cell Potential. • Derive Nernst Equation (Cell Potential versus Activity of reacting species) for lead acid cell • Verify the effect of Temperature on the Cell Potential of the lead acid cell. • Verify the effect of Activity (or concentration) of reacting species on the Cell Potential of the lead acid cell. • Examine the effect of Electrode Composition on the Cell Potential of the lead acid cell. BACKGROUND: A lead acid cell is a basic component of a lead acid storage battery (e.g., a car battery). A 12.0 Volt car battery consists of six sets of cells, each producing 2.0 Volts. A lead acid cell is an electrochemical cell, comprising of a lead grid as an anode (negative terminal) and a second lead grid coated with lead oxide, as a cathode (positive terminal), immersed in sulfuric acid. The concentration of sulfuric acid in a fully charged auto battery measures a specific gravity of 1.265 – 1.285. This is equivalent to a molar concentration of 4.5 – 6.0 M.[1] The cell potential (open circuit potential or battery voltage) is a result of the electrochemical reactions occurring at the cell electrode interfaces. The electrochemical reactions that convert chemical energy into electrical energy in a lead acid cell, are shown in equations 1 and 2. [2,3] –2Pb + SO4 --------------> PbSO4 + 2 e-1 (1) Oxidation (anode)-1 -2PbO2 + 4H+1 + 2 e + SO4 -----------------> PbSO4 + 2H2O (2) Reduction (Cathode) Reactions 1 and 2, are half-cell reactions occurring simultaneously, at the anode and cathode. The cell voltage is dependent on several factors, such as electrode chemistry, temperature and electrolyte concentration. The Nernst equation establishes the relationship between the cell voltage and these various parameters. [2,3] NERNST EQUATION FOR THE ELECTROCHEMICAL REACTIONS IN A LEAD ACID STORAGE CELL [4,5] The Nernst equation is a fundamental equation in electrochemical reactions which expresses the electrochemical cell potential in terms of reactants and products of the reaction. It can be derived based on Gibbs Free Energy Criterion for chemical reactions. The maximum amount of electrical energy (or work done) that can be delivered, by an electrochemical cell (or battery) in a given state, nFE, depends on the change in Gibbs Free Energy, ∆G as shown in equation 3. ∆G = - nFE (3) where n is the number of moles of electrons exchanged in an electrochemical reaction, F is the Faraday’s constant (96,485 C / mole), and E is the cell potential. For cell conditions, in a standard state, ∆G0 = - nFE0 (4) 0 0where, E represents standard electrochemical cell potential, and ∆G represents the Gibbs Free Energy changes in the standard state. For a general chemical reaction, the changes in Gibbs Free Energy is related to the reactants and products of reaction, as shown in equations 5 and 6. 0∆G - ∆G = RT ln [ a products / a reactants] (5) or 0∆G - ∆G = 2.303 x RT log[ a products / a reactants] (6) 0where, ∆G and ∆G, represent changes in the free energy of products and reactants in non-standard and standard states, respectively, R is the gas constant (8.314 J/deg.mole), T is the absolute temperature, a products and a reactants are the activities of products and reactants, respectively.Equations, 3, 4 and 6, establishes the NERNST equation, which relates the cell potential in any state, to the standard cell potential, and the products and reactants of the electrochemical reaction. 0 E – E = - [2.303 x RT / nF] x {log[ a products / a reactants]} (7) 0Or E = E - [2.303 x RT/nF] x { log[ a products / a reactants]} (8) The Nernst equation for the lead acid cell can be written by adding the two half-cell reactions given in equations 1 and 2. Overall reaction: PbO2 + Pb + 2SO4 -2 + 4H+1 ----------------------> 2 PbSO4 + 2 H20 (9) Or PbO2 + Pb + 2H2SO4 -------------------> 2PbSO4 + 2H2O (10) Note: The affect of sulfuric acid concentration on the electrode potential, is clearly seen in equation 10, which is a simpler form of equation 9. Using equation 8, the Nernst equation for the lead acid cell is, 0 2 2 2E = E - [2.303 RT / nF] x { log [ a PbSO4 * a H2O] / [aPbO2 * a Pb * a H2SO4]} Where a s’ are the activities of the reactants and the products of the cell. R = 8.314 J / K-mole, is the gas constant T, is the absolute temperature (K) Since aPbSO4 = 1, aH2O = 1, a PbO2 = 1, a Pb = 1 [The activity of a pure solid = 1, activity of water = 1] 0 2E = E – [2.303 RT / nF] x { log [ 1 / aH2SO4]} 0E = E – [2.303 RT / nF] x { - 2 log a H2SO4} 0E = E + [2 * 2.303 RT / n F] x {log a H2SO4} (11)-2Note: n= 2 n = # of moles of electrons involved in the oxidation-reduction reactions in equations, 1 and 2, above. Equation 11, clearly shows the effect of temperature and the activity (or concentration) of H+ and SO4 ions in H2SO4, on the cell potential. Note: 1. The activity of a reacting species is related to the electrolyte concentration a H2SO4 = γ H2SO4 * C H2SO4 Where γ H2SO4 is defined as an activity coefficient for the reacting species, and C H2SO4 is the acid concentration, usually expressed as MOLALITY (or MOLAL concentration). 2. The activity coefficient is generally temperature and concentration dependent, and is experimentally determined. The values for H2SO4 is provided in the handout. -3 For very dilute solutions, << 1.0 x 10 M,  γ may be approximated to unity. MATERIALS: ELECTRODES: Pb and lead oxide from Leoch Battery Technology Company, LTD. Pb, Sn and Pb-Sn (50% by mass) wires ELECTROLYTE: Sulfuric Acid (96%) from Mallinckrodt EXPERIMENT: Assemble a lead acid cell in a 600 mL beaker with a cap to support the electrodes and a thermocouple. Connect the lead (Pb) anode to the negative terminal of a digital multimeter, and the lead oxide cathode to the positive terminal of the multimeter. Fill the beaker with the desired concentration of sulfuric acid to the 200 mL level. Note: The maximum concentration of acid, 3.0M used here, is lower than the nominal concentrations, 4.5 – 6.0 M reported for auto batteries. The 3.0 M acid cell produces a potential above 2.0 volts, and is adequate for the demonstrating our objectives. 1. Measure cell