FreeEnergyLesson6

=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:

(f/P)=1            (6.17)

The equilibrium constant for a reaction between real gases:

K= IIi(fi/P°)Vi            (6.18)