Equilibrium_Thermo

# Equilibrium_Thermo - Temperature Dependence of Equilibrium...

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Temperature Dependence of Equilibrium Constant The Gibbs free energy of a system in the absence of external electric and magnetic fields is defined as G = U + PV - TS Total differentiationof this fundamental relationship yields dG = dU + PdV + VdP - TdS - SdT At constant pressure and temperature, this reduces to dG = dU + PdV - TdS Recalling that at constant pressure dU + PdV = dH dG = dH - TdS The net change in Gibbs free energy in a reaction is thus D G 0 =D H 0 - T D S 0 The Gibbs energy change determines the spontaneity of reactions : only processes with negative D G o are spontaneous. This can be rationalized by considering a a reacting system and its surroundingand writing the relationship as - D G 0 T =- D H sys 0 T +D S sys 0 The heat released or absorbed in a reversible reaction is related to the reaction enthalpy d Q = dH - VdP At constant pressure, all reaction enhalpy in an exothermic reaction is converted to the heat of the surrounding, leading to the increase in the entropy of the surrounding. Thus - D G 0 T =D S surr 0 +D S sys 0 We see that - D G 0 T represents the total entropy change of the universe. D S universe 0 =D S surr 0 +D S sys 0 Assuming a thermodynamically closed universe only processes that can occur are the ones that increse the entropy of the universe H the second law L . Because temperature must be positive, the entropy of the universe increases only when D G 0 of a process is negative. In chemistry, the equilibrium is usually defined via the equilibrium constant, which is related to the reaction Gibbs free energy D G 0 =- RT ln K eq We will now analyze how dG 0 and K eq depend on intensive variables such as temperature and pressure. Such analysis reveals that the temperature

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Equilibrium_Thermo - Temperature Dependence of Equilibrium...

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