Chapter 5: Chemical Thermodynamics

5.1 Thermodynamic Terms

System and Surroundings

• System: The part of the universe under study
• Surroundings: Everything else in the universe

\[ \text{Universe} = \text{System} + \text{Surroundings} \]

Types of Systems

State Functions and Path Functions

• State functions: Depend only on the state, not the path (e.g., \(U\), \(H\), \(S\), \(G\), \(P\), \(V\), \(T\))
• Path functions: Depend on the path (e.g., work \(w\), heat \(q\))

Extensive and Intensive Properties

Extensive properties depend on the amount of matter. Intensive properties do not.

5.2 Internal Energy (U)

The internal energy of a system is the total energy (kinetic + potential) of all particles.

• \(U\) is a state function — we can measure only the change \(\Delta U\), not absolute \(U\).

\[ \Delta U = U_{\text{final}} - U_{\text{initial}} = q + w \]

where \(q\) = heat absorbed by the system, \(w\) = work done on the system.

Work

For gases, the work of expansion/compression against a constant external pressure:

\[ w = -P_{\text{ext}} \Delta V \]

For reversible processes:

\[ w = -nRT \ln\frac{V_f}{V_i} \]

Sign convention (IUPAC):

• Work done on the system → \(w > 0\)
• Work done by the system → \(w < 0\)
• Heat absorbed by the system → \(q > 0\)
• Heat released by the system → \(q < 0\)

5.3 First Law of Thermodynamics

“Energy can neither be created nor destroyed; it can only be transformed from one form to another.”

\[ \Delta U = q + w \]

Special Cases

1. At constant volume (\(\Delta V = 0\)): \(w = 0\), so \(\Delta U = q_V\)
2. At constant pressure: \(\Delta H = q_P\)

5.4 Enthalpy (H)

\[ H = U + PV \]

For a process at constant pressure:

\[ \Delta H = \Delta U + P\Delta V \]

For reactions involving gases:

\[ \Delta H = \Delta U + \Delta n_g RT \]

where \(\Delta n_g\) = (moles of gaseous products) − (moles of gaseous reactants)

Heat Capacity

• Heat capacity at constant volume: \(C_V = \frac{q_V}{\Delta T} = \frac{\Delta U}{\Delta T}\)
• Heat capacity at constant pressure: \(C_P = \frac{q_P}{\Delta T} = \frac{\Delta H}{\Delta T}\)

For an ideal gas:

\[ C_P - C_V = R = 8.314;\text{J mol}^{-1}\text{K}^{-1} \]

5.5 Measurement of ΔU and ΔH — Calorimetry

Bomb Calorimeter (Constant Volume)

Used to measure \(\Delta U\) for combustion reactions.

5.6 Enthalpy Changes for Various Types of Reactions

Standard Enthalpy of Formation (\(\Delta_f H^\circ\))

Enthalpy change when one mole of a compound is formed from its elements in their standard states at 1 bar and specified temperature (usually 298 K).

\[ \Delta_r H^\circ = \sum \Delta_f H^\circ(\text{products}) - \sum \Delta_f H^\circ(\text{reactants}) \]

By convention: \(\Delta_f H^\circ\) of elements in their standard state = 0

Standard Enthalpy of Combustion (\(\Delta_c H^\circ\))

Enthalpy change when one mole of a substance undergoes complete combustion in O₂.

\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \quad \Delta_c H^\circ = -890.3;\text{kJ/mol} \]

Other Important Enthalpy Changes

5.7 Hess’s Law of Constant Heat Summation

“The total enthalpy change for a reaction is the same whether the reaction takes place in one step or in a series of steps.”

This is because \(H\) is a state function.

Application — Born-Haber Cycle:

Used to calculate lattice enthalpy of ionic compounds indirectly.

5.8 Bond Enthalpy

The enthalpy of a reaction can be estimated from bond enthalpies:

\[ \Delta_r H^\circ \approx \sum (\text{B.E. of bonds broken}) - \sum (\text{B.E. of bonds formed}) \]

Bonds broken → endothermic (\(+\)); Bonds formed → exothermic (\(-\))

5.9 Second Law of Thermodynamics

The second law introduces the concept of entropy (\(S\)) — a measure of the disorder or randomness of a system.

“In any spontaneous process, the total entropy of the universe always increases.”

\[ \Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0 \]

For a reversible process at constant temperature:

\[ \Delta S = \frac{q_{\text{rev}}}{T} \]

Entropy Changes

• \(\Delta S > 0\): Increase in disorder (e.g., melting, vaporization, dissolution, gas expansion)
• \(\Delta S < 0\): Increase in order (e.g., freezing, condensation)

5.10 Gibbs Energy (G)

\[ G = H - TS \]

At constant T and P:

\[ \Delta G = \Delta H - T\Delta S \]

Criteria for Spontaneity

Equilibrium Condition

\[ \Delta G = 0 \quad \text{(at equilibrium)} \]

\[ \Delta G^\circ = -RT \ln K \]

where \(K\) is the equilibrium constant.

5.11 Third Law of Thermodynamics (Brief Introduction)

“The entropy of a perfectly crystalline substance at absolute zero (0 K) is zero.”

\[ S_{0,\text{K}} = 0 \quad \text{(for a perfect crystal)} \]

This law provides a reference point for calculating absolute entropy values.

Practice Questions

Multiple Choice Questions (MCQs)

1. For an adiabatic process, the correct expression is:

 (a) \(\Delta U = q\)

 (b) \(\Delta U = w\)

 (c) \(\Delta U = q + w\)

 (d) \(q = 0, \Delta U = w\)

2. The enthalpy of combustion of carbon to CO₂ is −393.5 kJ/mol. The heat released upon formation of 35.2 g of CO₂ from carbon and dioxygen gas is:

 (a) −393.5 kJ

 (b) −314.8 kJ

 (c) +314.8 kJ

 (d) −787.0 kJ

3. A reaction has \(\Delta H = -40;\text{kJ}\) and \(\Delta S = -120;\text{J/K}\). The reaction is spontaneous at:

 (a) all temperatures

 (b) temperatures below 333 K

 (c) temperatures above 333 K

 (d) no temperature

4. The relationship between \(\Delta H\) and \(\Delta U\) for the reaction \(2\text{C}(s) + 3\text{H}_2(g) \rightarrow \text{C}_2\text{H}_6(g)\) is:

 (a) \(\Delta H = \Delta U + 2RT\)

 (b) \(\Delta H = \Delta U - 2RT\)

 (c) \(\Delta H = \Delta U\)

 (d) \(\Delta H = \Delta U + RT\)

5. For which of the following reactions is \(\Delta H = \Delta U\)?

 (a) \(\text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{Cl}_2(g)\)

 (b) \(\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)\)

 (c) \(\text{H}_2(g) + \text{I}_2(g) \rightarrow 2\text{HI}(g)\)

 (d) \(2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g)\)

Short Answer Questions (2–3 Marks)

6. State Hess’s law. Why is it a consequence of the first law of thermodynamics?

7. Calculate the standard enthalpy of formation of CH₃OH(l) using the following data:

\[ \text{CH}_3\text{OH}(l) + \frac{3}{2}\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \quad \Delta_c H^\circ = -726;\text{kJ/mol} \]

\[ \Delta_f H^\circ[\text{CO}_2(g)] = -393.5;\text{kJ/mol}, \quad \Delta_f H^\circ[\text{H}_2\text{O}(l)] = -285.8;\text{kJ/mol} \]

8. What is the sign of entropy change (\(\Delta S\)) for the following processes?

 (i) Freezing of water

 (ii) Evaporation of ethanol

 (iii) Dissolving NaCl in water

9. Explain why \(C_P > C_V\) for gases.

10. Define: (i) Standard enthalpy of atomization (ii) Lattice enthalpy

Long Answer Questions (5 Marks)

11. (a) State and explain the first law of thermodynamics. Derive the relationship between \(\Delta H\) and \(\Delta U\).

 (b) Calculate the \(\Delta U\) for the reaction: \(2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g)\), given \(\Delta H = -198;\text{kJ}\) at 298 K.

12. (a) Explain the Gibbs energy equation and how it determines the spontaneity of a reaction.

 (b) A reaction has \(\Delta H = 52;\text{kJ}\) and \(\Delta S = 165;\text{J/K}\). At what temperature will it become spontaneous?

Assertion-Reason Questions

13. Assertion (A): An endothermic reaction can be spontaneous.

Reason (R): Increase in entropy can drive a reaction forward.

14. Assertion (A): State functions are path-independent.

Reason (R): The value of a state function depends only on the present state, not on how that state was reached.

Answer Key