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3436 Paths tSouSsutastianianbalbeleEEnneergrgyy Then, when we introduce the thermodynamical data from Tab. 1 into (5), the standard reaction enthalpy ΔHr of the VRB reaction (1) becomes: ΔHr=ΔHf,VO2+ +ΔHf,V3+ +ΔHf,H2O −ΔHf,V2+ −ΔHf,VO2+ −2ΔHf,H+ (7) = −155.6 kJ/mol and similarly, the standard reaction entropy ΔSr is obtained when these thermodynamical data are introduced into (6): Formula State V2+ aq V3+ aq VO2+ aq VO2+ aq H2O aq H+ aq ΔSr=Sf,VO2+ +Sf,V3+ +Sf,H2O −Sf,V2+ −Sf,VO2+ −2Sf,H+ = −121.7 J/mol · K (8) ΔHf [kJ/mol] (-226) (-259) -486.6 -649.8 -285.8 0 ΔGf [kJ/mol] -218 -251.3 -446.4 -587.0 -237.2 0 Sf [J/mol · K] (-130) (-230) -133.9 -42.3 69.9 0 Table 1. Thermodynamical data for some vanadium compounds at 298.15 K. Values in parentheses are estimated (Van herle, 2002; Bard et al., 1985). The conservation of energy relates the change in free energy resulting from the transfer of n moles of electrons to the difference of potential E: ΔG = −nFE [J/mol] (9) Therefore, we obtain the standard potential E when we introduce ΔG (4) with the values of the standard reaction enthalpy (7) and entropy (8) into the reformulated (9): Δ G Δ H r − T Δ S r E =− nF =− nF [V] (10) So, we have determined from the thermodynamical principles that the standard potential E is 1.23 V at 25◦C . The characteristic curve of the equilibrium potential E is illustrated in Fig. 3 for a single cell as a function of the state of charge SoC. We can also observe the relation between E, SoC and the protons and vanadium concentrations.PDF Image | Understanding the Vanadium Redox Flow Batteries
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