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The equilibrium potential can be described by the Nernst equation: ′1aa mol of Cl2 and H2 are denoted aCl2 and aH2 , respectively. Eeq = E0 + Cl2 H2 , [5] a2HCl(aq) ln where f = F/(R(T +273.15)) [V-1], R = 8.314 J is the universal gas constant, F = 2 f mol·K 96485 C is Faraday’s constant, and T is the temperature in degrees Celsius. The activities ′′ E0 is the temperature-dependent equilibrium potential when all activities are unity. E0 must be chosen so that Eeq = 1.358 V at the standard temperature, pressure, and concen- tration of 25 ◦C, 1 atm, and 1 M, respectively (10). Assuming the difference between ′ reactant and product entropies is independent of temperature, E0 is a linear function of temperature, whose slope is given by the entropy of formation divided by 2 f : E0′ = 1.7364 − 0.00126(T + 273.15). [6] aHCl(aq) is the mean ionic activity of aqueous hydrochloric acid, which depends on T and the concentrations of the ionic species. For dilute or ideal solutions, the activity is directly proportional to the concentration according to Henry’s law. For non-ideal concentrated solutions, however, the activity coefficient can vary significantly, and the activity deviates from Henry’s law behavior. In the model, we define the activity in the following way: a =γ m, [7] HCl(aq) m m0 where γm is the unitless activity coefficient, which depends on temperature and concentra- tion, m is the molality in mol , and m0 is the reference molality of 1 mol . Partanen et kg solvent kg al. have studied in depth the concentration and temperature dependence of the activity of hydrochloric acid (11). They present an “extended” Hu ̈ckel equation that approximates the activity to a precision corresponding to 3 mV in the equilibrium potential over the molality range of 0 to 16 mol, and a temperature range of 0 to 50 ◦C. γm is presented as a function kg of the solution molality, m, and temperature, T in Celsius (Eq. 12 in ref. 11): −3A √m lnγm = φ√ +h1 m m0 m 2 m0 m 7/2 m0 −ln(1+2MH2Om), [8] where MH O = 0.0180 kg is the molecular weight of water, Aφ = 0.39205 (mol·kg-1)-1/2, 1+B m 2 mol +b2,γ +b3,γ B=1.4(mol·kg-1)-1/2,h1 =0.33866−0.001283T,b2,γ =0.006,andb3,γ =−9.7×10−5, where the latter three are unitless. To convert molality to molarity, M mol solute , we use the following expression: L solution m= 1000M [9] ρHCl(aq) −MHClM g kg where MHCl = 36.461 mol is the molecular weight of HCl, and ρHCl(aq) m3 is the density of the acid solution. The density itself is a function of temperature and concentration, and 8PDF Image | Regenerative Hydrogen Chlorine Fuel Cell for Grid-Scale
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