I.

Free Energy

1. Processes at constant T and p, the Gibbs free energy

2. Processes at constant T and V, Helmholtz free energy

3. Relationship between G and A

4. Free energy changes in chemical reactions

Where: Kp is the standard pressure equilibrium constant ( depend on T)

5. The Gibbs free energy of mixing

Notice that since χa,b < 1 both ln terms will be less than zero. Thus ∆Gmix < 0 is negative. This confirms that the
mixing of ideal gases is spontaneous.

Example 1

Calculate the Gibbs free energy of mixing. Note that this is being worked out using the case 2 approach. A
container is divided into 2 equal compartments. One contains 3 mol of H 2 at 25C. The other contains 1 mol of N 2
at 25C. Calculate the ∆G of mixing.

Answer:

II.Application of Free Energy to Phase Transitions

1. The liquid-vapor and solid-vapor boundaries, The Clausius-Clapeyron equation

 another way to write the Clausius-Clapeyron equation is

2. The solid-liquid boundary, The Clapeyron equation

Example 1.

The normal boiling point of benzene is 80.1oC and the enthalpy of vaporization is ∆Hvap = 30.8kJ/mol. Calculate
the boiling point of benzene at 100 torr.

Answer

Example 2. Many of the highest mountains in the world are in excess of 25,000 feet. At these altitudes p = 250
torr. Calculate the freezing point and boiling point of water at this pressure.

Given:

• the density of ice is: ρice = 0.92g/cm3

• the density of water is: ρwater = 1.00g/cm3

• ∆Hfusion = 6.01kJ/mol

• ∆Hvaporation = 40.7kJ/mol

Answer: Use the Clapeyron equation for fusion and the Clausius-Clapeyron equation for vaporization. The
Clapeyron equation gives
Example 3. The melting point of Na is 97.8 oC at 1 atm.

The densities of solid Na and liquid Na are

Na(s)ρ = 0.929g/cm3

Na(l)ρ = 0.952g/cm3 . Also ∆Hfus = 3 kJ/mol, ∆Vfus = -0.6cm3/mol . Calculate the melting point of Na at p=120
atm.

Answer:

III. The fundamental equations of thermodynamics

Note : The thermodynamic boat

IV. Thermodynamic Relation.

1. Redlich and Kwong Equation.

 2. Peng–Robinson equation of state

3. Van der Waals equation of state

Example 4.

Iodine crystals sublime according to the reaction at 25°C. I2(s) ⇄ I2(g).

Find the temperature at which solid iodine crystals and gaseous iodine will exist in equilibrium. Change in
enthalpy for the reaction, ΔH° = 9.41 kcal/mole and ΔS, the change in entropy, = 20.6 cal°K −1 mole−1.

Answer:

Example 5.

Kp has the value 10−5 for the equilibrium CO2(g) + H2(g) = CO(g) + H2O(g)

at 25C, and ΔS, the entropy change, is − 10 cal/deg mole for the reaction as written (ΔH° and ΔS° do not change
much with temperature. One mole of CO, 2 moles of H2, and 3 moles of CO2 are introduced into a 5-liter flask at
25C.

Calculate

(a) ΔG°, the free energy change, at 25°C,

(b) the equilibrium pressure

(c) the moles of each species present at equilibrium

(d) Kp at 100°C.

Answer:
Example 6.

Estimate the degree of dissociation at equilibrium for the following reaction

H2O (g) → H2 (g) + 1/2O2 (g).

The standard Gibbs energy of reaction for the decomposition is ∆G = 118 kJ/mol at 2300K. Make reasonable
simplifications or assumptions about α.

Answer:

Mock Test:

QUESTIONS

Q1. (5 marks) True or False

• isobaric means ∆G = 0

• isothermal mean ∆T = 0

• isentropic means ∆H = 0

• isometric means ∆U = 0
• adiabatic means dq = 0

Answer:

Q2. ( 30 marks) Give the definition of 1st, 2nd and 3rd Thermodynamic Law. Give 3 examples for each Law.

Q3. (10 marks) If one treats a fluid using the Van der Waals Equation of State, what is the expression for the
isothermal reversible work for a process from (P1,V1) to (P2,V2)

Answer:

Q4. ( 5 marks) A dwelling requires 6*105 Btu per day to maintain its temperature at 700 F when the outside
temperature is 320 F.

(a) If an electric heat pump is used to supply this energy, determine the minimum theoretical work input for one
day of operation, in Btu/day.

(b) Evaluating electricity at 8 cents per kW.h, determine the minimum theoretical cost to operate the heat pump,
in $/day

Answer:

Q5. ( 10 marks) For the following chemical transformation, the value of KP = 2.3x1012 at T=298oK:

2NO(g) + O2 (g)  2NO2 (g)

Consider that initially, there are 2 moles of NO(g) and 1 mole of O2 (g). What extent of reaction optimizes the
total Gibbs free energy of this system? Consider the gases to be ideal and make necessary approximations to
arrive at an expression for the extent of reaction in terms of the total pressure, P, and the equilibrium constant, K P
given above. Note the magnitude of KP in thinking about what approximation to invoke in your solution.

Answer:
Q6. ( 5 marks) True or False

1. Equilibrium state variables and functions depend on the path a system takes to achieve the
equilibrium.

2. Work is a state function.

3. An adiabatic boundary prevents heat interactions between a system and its surroundings.

4. Thermodynamics directly tells us information about the kinetics (timescales) needed to

observe changes.

5. Entropy is a molecular property but is not a macrosopic property.

Q7. ( 10 marks)

One mole of H2O (liquid) is super-cooled to -2.25 Celsius at 1 bar pressure. The equilibrium freezing
temperature at this pressure is 0.0 Celsius. The transformation H2O (liquid) → H2O (solid) is suddenly observed
to occur. Show that the transformation (i.e., freezing) is spontaneous at this state point. Consider the
surroundings to be at constant temperature of -2.25 Celsius. The following information may be useful

Q8. ( 20 marks) Consider the reversible reaction:

Assumptions: solids are not volatile and gases are ideal. Enthalpies of formation have little temperature
dependence (though this will be a big assumption)

Determine Standard Free Energy.

Answer

Q9. ( 5 marks)

The standard Gibbs free energy of reaction for the decomposition of water

H2O (g) → H2(g) + 1/2O2 (g) is 135.2 kJ/mol at 2000K. Suppose steam at 200 kPa is passed through a tube
furnace at that temperature. Calculate the mole fraction of O 2 present in the output gas stream.

Answer:

Q10. ( 5 marks)

Methane gas enters empty a steady ? Low composition chamber at 250C and 1 atm and is burned with 50%
excess air, which also enters at 250C and 1atm. After combusition, the products are allowed to cool to 250C.
Determine the heat transfer per kmol of CH4.

kJ kJ kJ kJ kJ
Hints: cair = 1 ; cmethane = 35.6 ;cO2 = 32 ;cCO2 = 38 ; cwater = 75
kmol . K kmol . K kmol . K kmol . K kmol . K
Using the energy balance!!!.