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:

Δ_rG = Δ_rG° + RT In II_i(P_CO/P°)^V_i (6.11)

The equilibrium constant:

K = II_i(P_CO/P°)^V_i(6.12)

Relation between Gibbs energy and equilibrium constant:

Δ_rG° = - RTlnK (6.13)

Relations between In K and Δ_rH°:

dinK /dT = Δ_rH°/RT² (6.14)

dinK /d(I/T) = -Δ_rH°/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= II_i(f_i/P°)^Vi (6.18)