Question

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4. Consider the equilibrium in which solid calcium carbonate decomposes to the oxide plus carbon dioxide CaCO3(s) CaO(s) + CO2(g) Write down an expression for the equilibrium constant of this reaction in terms of the partial pressure of CO2. The standard enthalpies of formation of CaCO3(s), CO2(g) and CaO(s) are -1207.6 kJ mol", -393.5 kJ mol' and -634.9 kJ mol? respectively, and the standard entropies are 91.7JK'mol, 213.8JK' mol and 38.1 J K mol' (all at 298 K). Assuming that these values are independent of temperature, compute AH”, AS and AG at 800 K; hence find the equilibrium pressure of carbon dioxide at this temperature.

Answer 1

It is a heterogeneous equilibrium | CaCO3 (S) + CaO S + CO2 (0) That occurs when a reaction in the reactants and products are in different phases. The concentrations of solid substances remain constant, so they are not included in the equilibrium expression. So: K. = [CO] For a balance in which gases intervene we have to: Partial pressure K= K, = PCO,

Calculate AHºrxm) AS rxn , AG and K, at 800 k : Data: Sº CO2 = 213.8 J/Kxmol Sº CaCO3(s) = 91.7J/Kxmol sº Caos = 38.11 J/Kxmol AH, CO2 = -393.5 kJ/mol AH, CaCO3 (5) = -1207.6 kJ/mol AH,Cao s) = - 634.9 kJ/mol AHºrn = En AH°f(products) - EnaHºf(reactants) AH°rxn = [ (AH°,CO2(g) + (AH°,Cao (s))] - [ (AH°,CaCO3(s)] AH®x = [ (-393.5 kJ) + (-634.9)]kJ/mol ]- [ -1207.6 kJ/mol] AH®x = - 1028.40 kJ/mol + 1207.6 kJ/mol AH°man = 179.2 kJ/mol = 179200 J/mol

AS°rxn = n. 5° (products) - En, Sºreactants) AS° x1 = [ (8°CO2(g) + (SºCaO(-)) - [ (SºCaCO3(e)] AS n = [ 213.8 J/Kxmol + 38.11 J/Kxmol] - [ 91.7J/Kxmol)] AS = 251.91J/Kxmol - 91.7J/Kxmol 15°mn = 160.21J/Kxmol AGʻrxn = AH°xn- T AS°xn AGºrxn = 179200 J/mol - 800 K (160.21J/Kxmol) AG°xn = 179200 J/mol - (128168 J/mol ) | AGM = 51032 J/mol AGM = -RTINK 51032 Hmot = - 8.31 J/molxkx 800 K Ink In K = 51032 6648 HK = 27.7 е е K = 4.5x 104 so: K. = 4.5x104 ----> PCO2(g) = 4.5x104 atm