FreeEnergyLesson6

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LESSON 6: REVISION - FUNDAMENTAL EQUATIONS

Definition of Gibbs energy:


G = H -TS (6.1)


Equilibrium criterion at constant P and T:


dG = 0 (6.2)


Definition of Helmholtz energy:


A = U -TS (6.3)


Equilibrium criterion at constant V and T:


dA = 0 (6.4)


Alternative definition of Gibbs energy:


G = U - TS +PV (6.5)


Change in internal energy:


dU = TdS -PdV (6.6)


Change in Gibbs energy:


dG = - SdT + VdP (6.7)


Change in Gibbs energy with pressure for a solid or a liquid:


ΔG = V(P - P°) (6.8)


Change in Gibbs energy with pressure for a gas:


ΔG = RT In (P/P°) (6.9)


The chemical equation:


0 = ΣiViBi                 (6.10)

The change in Gibbs energy by a chemical reaction:


ΔrG = ΔrG° + RT In IIi(PCO/P°)Vi (6.11)


The equilibrium constant:


K = IIi(PCO/P°)Vi(6.12)


Relation between Gibbs energy and equilibrium constant:


ΔrG° = - RTlnK (6.13)


Relations between In K and ΔrH°:


dinK /dT = ΔrH°/RT2 (6.14)


dinK /d(I/T) = -ΔrH°/R (6.15)


Definition of fugacity:


ΔG = ΔG° + RT In (f/P°) (6.16)


Fugacity approaches the pressure when the pressure approaches zero:


6limitpto0.jpg(f/P)=1             (6.17)


The equilibrium constant for a reaction between real gases:


K= IIi(fi/P°)Vi (6.18)