Metal-Acid Batteries

Summary: This lecture looks at two examples of metal-acid batteries, utilizing the Nernst equation and Pourbaix diagrams to gain an understanding of the system’s open circuit voltage (OCV) behavior. Metal-acid batteries Example 1: Fruit battery Conditions: Zinc metal anode, Copper metal Cathode, Citric acid electrolyte (pH=3 for grapefruit, pH=2 for lemon) Anodic reaction: Zn → Zn 2+ + 2 e − ∆φ AΘ = −0.76 V (1.1) ∆φCΘ = 0V (1.2) ∆φCΘ = 0.34 V (1.3) Potential cathodic reactions: 2H + + 2 e − → H 2 Cu 2+ + 2 e − → Cu As always, the Θ denotes standard conditions. Reaction 1.3 can immediately be eliminated as the concentration of Cu 2+ would be extremely low in the fruit. The effect that this low concentration would have on the battery’s OCV will be explored later. The overall battery reaction is given as 1.4 below. Zn+ 2 H + → Zn 2+ + H 2 ∆φ Θ = ∆φCΘ − ∆φ AΘ = 0.76 V Applying the Nernst equation to this system, yields the following potentials for each half reaction. 1 (1.4) Anode: 2 k BT  aZn2+ ae− ln  ∆V = −0.76 + 2e  aZn    (1.5) Cathode: 2 2 k BT  aH + ae− ∆ V =0 + ln  2e  aH 2    (1.6) For the overall cell, subtract the anode ΔV from the cathode ΔV. = VO 0.76 + 2 k BT  aH + aZn ln  2e  aH 2 aZn2+    (1.7) Knowing that aZn = 1 for a solid metal electrode, 1.6 can be simplified. 2 k BT  a H + = VO 0.76 + ln  2e  aH 2 aZn2+    (1.8) In the dilute limit, the activities of each species can be estimated by their concentrations or partial pressures normalized by the standard condition concentration or partial pressure (1M or 1atm), respectively; this results in dimensionless concentrations and pressures. So, 1.8 can be rewritten in terms of measurable dimensionless quantities. = VO 0.76 + 2 k BT  c H + ln  2e  pH 2 cZn2+    (1.9) Define p H 2 = − log10 ( pH 2 ) and p Zn = − log10 (c Zn2+ ) and evaluate at room temperature (~25oC). VO = 0.76 − 0.06 p H + 0.03p H 2 + 0.03p Zn (1.10) If we had decided to try to use the copper reaction for the cathode (1.3), the resulting OCV would be given as follows (again using the activity of the solid metal is 1 and defining p Zn = − log10 (cCu 2+ ) ). k T  c 2+ VO = 1.1 + B ln  Cu 2e  cZn2+  1.1 − 0.03p Cu + 0.03p Zn  =  (1.11) Any small amount of copper ions in solution would be depleted almost immediately, at which point the OCV would diverge to −∞ . Thus, it is clear that copper cannot be responsible for the cathodic reaction. 2 Example 2: Lead-Acid Battery Anode reaction Pb + SO42− → PbSO4 + 2e − ∆φ AΘ = −0.356 V (1.12) Cathode reaction PbSO4 + 2H 2O → PbO2 + SO42− + 4H + + 2e − 1.685 V ∆φCΘ = (1.13) Lead Electrodeposition and Dissolution ∆φ Θ = 0.126 V Pb ↔ Pb 2+ + 2e − PbO2 + 4 H + + 2e − → Pb 2+ + 2H 2O ∆φ Θ = 1.45 V (1.14) (1.15) The ∆φ in reactions 1.13 and 1.15 have strong dependencies on electrolyte pH as given by equations 1.16 and 1.17 below. ∆= φ 1.685 − 0.12 p H (1.16) ∆φ= 1.45 − 0.12 p H (1.17) The overall cell voltage as a function of pH is given by equation 1.18 below. VO = ∆φC − ∆φ A = 2.041− 0.12 p H (1.18) A similar battery utilizing the Pb-PbO2 coupling could function in the absence of the SO42− anion, but such a battery would require lead ions to be added from solution directly onto the lead electrode which is an unstable process. In the presence of sulfuric acid (H2SO4), there is a twofold benefit for the battery. First, the voltage increases in more acidic environments (low pH). Second, the PbSO4 forms a protective layer on the two electrodes as shown below, allowing for stable and reversible electrochemistry. 3 Determining the stable species in the battery at a given voltage is easiest to conceptualize with the aid of a Pourbaix diagram, which plots the ∆φ for redox reactions vs pH of the chemical environment. Taking the first reaction (1.12) as an example, at voltages below -0.356V, any lead species will be reduced to lead metal. At voltages higher, some other species will be stable; this depends on whether that higher voltage falls within region I, II, III, or IV. The table below summarizes the favored species in each of the regions (I-IV) Region I In the presence of SO42- in H2O PbO2 In the presence of only H2O PbO2 II PbSO4 PbO2 III PbSO4 Pb2+ IV PbSO4 Pb V Pb Pb 4