# 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 = Σ(6.10)_{i}V_{i}B_{i}

The change in Gibbs energy by a chemical reaction:

** Δ _{r}G = Δ_{r}G° + 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 _{r}G° = - RTlnK** (6.13)

Relations between In K and Δ_{r}H°:

**dinK /dT = Δ _{r}H°/RT^{2} ** (6.14)

**dinK /d(I/T) = -Δ _{r}H°/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)