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Formula State V2+ V3+ VO2+ VO2+ H2O H+ Aqueous Aqueous Aqueous Aqueous -259.0* -649.8 0.0 -230.0* -42.3 0.0 -251.3 -587.0 0.0 Study of redox flow battery systems for residential applications The standard enthalpy of reaction can be determined by subtracting the standard enthalpy of formation, ∆Hof,j, of the reagents from standard enthalpy of formation of the products (Equation 2.4): ∆𝐻𝑟° = ∆𝐻°𝑓,VO2+ + ∆𝐻°𝑓,V3+ + ∆𝐻°𝑓,H2O − ∆𝐻°𝑓,V2+ − ∆𝐻°𝑓,VO2+ − 2∆𝐻°𝑓,H+ (2.4) Using the values from Table 2.1, a standard reaction enthalpy of -155.6 kJ mol-1 is obtained for discharging step. Likewise, the standard entropy of reaction can also be determined by subtracting the standard entropy of formation, ∆Sof,j, of the reagents from standard entropy of formation of the products (Equation 2.5): ∆𝑆𝑟° = 𝑆°𝑓,VO2+ + 𝑆°𝑓,V3+ + 𝑆°𝑓,H2O − 𝑆°𝑓,V2+ − 𝑆°𝑓,VO2+ − 2𝑆°𝑓,H+ (2.5) By using again Table 2.1, a standard reaction entropy of -121.7 J mol-1 K-1 is obtained for discharging step. By solving Equations 2.3 and 2.2, a standard potential of 1.237 V is obtained [19, 20]. Table 2.1 – Thermodynamic data for vanadium ion species at a temperature of 298.15 K [19, 20, 25]. ∆Hfo (kJ mol-1) Sfo (J mol-1 K-1) ∆Gfo (kJ mol-1) -226.0* -130.0* -218.0 Aqueous -486.6 -133.9 -446.4 Aqueous -285.8 69.9 -237.2 *Estimated values [20]. If the effect of temperature is considered, the standard potential is proportional to temperature at a constant pressure. The theoretical variation of standard potential with temperature can be estimated from Equation (2.6) by using it to calculate the linear regression slope [19, 23]. However, the negative experimental slope is lower than the theoretical slope, with a value of -1.62 mV K-1 between 5 oC and 50 oC [19]. 𝜕𝐸° = − 1 (𝜕∆𝐺°) ≅ ∆𝑆𝑟° = -1.26 mV K-1 (2.6) 𝜕𝑇 𝑛𝐹 𝜕𝑇 𝑛𝐹 Chapter 2: Vanadium redox flow battery 8PDF Image | Tubular Vanadium Air Redox‐flow battery
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