# 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)