Free Energy & Chemical Thermodynamics

Question 1

Free Energy

Answer 1

Energy available for work

Question 2

Enthalpy

Answer 2

Energy of system plus work needed to make room for it.

H = U + PV

Question 3

Helmholtz Free Energy

Answer 3

System with constant temperature and volume.
Total energy needed to create the system minus the heat you can get for free from environment at temperature T.

F = U - TS

Question 4

Gibbs Free Energy

Answer 4

System with constant P and T.
System’s energy minus the heat term plus the atmospheric work.

G = U - TS + PV

Question 5

Change in Helmholtz Free Energy

Answer 5

ΔF = ΔU - T ΔS = Q + W - TΔS

At constant temperature:
ΔF <= W

Question 6

Change in Gibb’s Free Energy

Answer 6

ΔG = ΔU - T ΔS + P ΔV = Q + W - T ΔS + P ΔV

So ΔG = ΔH - T ΔS

W = -P ΔV + Wother

So at constant T, P:
ΔG <= Wother

Question 7

Thermodynamic Potentials

Answer 7

U, H, F, and G

Question 8

Thermodynamic Identities Given Enthalpy & Free Energy

Answer 8

Enthalpy:

dU = TdS - PdV + udN
dH = dU + PdV + VdP

dH = TdS + VdP + udN

Helmholtz Free Energy:

dF = dU - TdS - SdT
dF = -SdT - PdV + udN

Gibb’s Free Energy:

dG = dU + PdV - TdS
dG = -SdT + VdP + udN

Question 9

Free Energy as a Force Toward Equilibrium
Relationship between:

1. Entropy, Volume, Energy
2. Helmholtz Free Energy, Temperature, Volume
3. Gibb’s Free Energy, Temperature, Pressure

Answer 9

1. At constant energy and volume, entropy tends to increase.
2. At constant temperature and volume, Helmholtz free energy tends to decrease.

dStotal = dS - 1/T dU = -1/T(dU-TdS) = -1/T dF

3. At constant temperature and pressure, Gibb’s free energy tends to decrease.

dStotal = dS - 1/T dU - P/T dV = -1/T(dU-TdS +PdV) = -1/T dF

Question 10

Gibb’s Free Energy & Chemical Potential

Answer 10

If you add one particle to a system, holding the temperature and pressure fixed, the Gibbs free energy of system increases by u.

u = (dG/dN) T, P

G = Nu
(u is the Gibbs free energy per particle)

Question 11

Extensive versus Intensive Properties

Answer 11

If a quantity doubles when you double the # of particles, it is an extensive quantity.

Extensive: V, N, S, U, H, F, G, mass
Intensive: T, P, u, density