Class 11 Chemistry Notes Chapter 6 (Thermodynamics) – Chemistry Part-I Book

Alright class, let's begin our detailed study of Chapter 6: Thermodynamics. This is a crucial chapter, not just for your Class 11 understanding, but also because its concepts frequently appear in various government examinations. Pay close attention to the definitions, laws, and formulas.

Chapter 6: Thermodynamics - Detailed Notes

1. Introduction

• Thermodynamics: The branch of science dealing with heat, work, and other forms of energy, and their interconversions. It primarily deals with macroscopic properties of systems.
• Importance: Helps predict the feasibility (spontaneity) of a process and the extent to which it can occur under given conditions.

2. Basic Terminology

• System: The specific part of the universe under investigation (e.g., a reaction mixture in a beaker).
• Surroundings: Everything else in the universe outside the system.
• Boundary: The real or imaginary surface separating the system from the surroundings.
• Types of Systems:
  • Open System: Can exchange both energy (heat/work) and matter with the surroundings (e.g., boiling water in an open beaker).
  • Closed System: Can exchange energy but not matter with the surroundings (e.g., boiling water in a sealed container).
  • Isolated System: Cannot exchange either energy or matter with the surroundings (e.g., water in a perfectly insulated thermos flask - an ideal concept).

3. State of the System & State Functions

• State Variables: Properties required to describe the condition (state) of a system (e.g., Pressure (P), Volume (V), Temperature (T), amount (n)). These are macroscopic properties.
• State Function (or State Variable): A property whose value depends only on the current state of the system, irrespective of the path taken to reach that state.
  • Examples: P, V, T, Internal Energy (U), Enthalpy (H), Entropy (S), Gibbs Free Energy (G).
  • Change in a state function (e.g., ΔU) depends only on the initial and final states (ΔU = U_final - U_initial).
• Path Function: A property whose value depends on the path followed during a process.
  • Examples: Heat (q), Work (w).

4. Thermodynamic Processes

• Isothermal Process: Temperature remains constant (ΔT = 0). For ideal gas, ΔU = 0.
• Adiabatic Process: No heat exchange between system and surroundings (q = 0).
• Isobaric Process: Pressure remains constant (ΔP = 0).
• Isochoric Process: Volume remains constant (ΔV = 0). Work done (PΔV) is zero.
• Reversible Process: A process carried out infinitesimally slowly so that the system remains in equilibrium with the surroundings at each stage. It can be reversed by an infinitesimal change in conditions. Maximum work is obtained. (Ideal concept).
• Irreversible Process: A process carried out rapidly; the system is not in equilibrium during the change. All natural processes are irreversible.

5. Internal Energy (U)

• The sum of all forms of energy associated with a system (kinetic and potential energies of molecules - translational, vibrational, rotational, electronic, nuclear).
• It's a state function and an extensive property (depends on the amount of substance).
• Absolute value cannot be determined, but change (ΔU) can be measured.
• ΔU = U_final - U_initial

6. First Law of Thermodynamics (Law of Conservation of Energy)

• Statement: Energy can neither be created nor destroyed, only converted from one form to another. The energy of an isolated system is constant.
• Mathematical Expression: ΔU = q + w
  • ΔU = Change in internal energy
  • q = Heat absorbed by the system
  • w = Work done on the system
• Sign Conventions (Important!):
  • q: Positive (+) if heat is absorbed by the system; Negative (-) if heat is released by the system.
  • w: Positive (+) if work is done on the system (compression); Negative (-) if work is done by the system (expansion).

7. Work (w)

• Energy transfer due to factors other than temperature difference.
• Pressure-Volume (PV) Work: Work done during expansion or compression of gases.
  • w = - P_ext ΔV
    • P_ext = External pressure against which expansion/compression occurs.
    • ΔV = Change in volume (V_final - V_initial).
  • If ΔV > 0 (expansion), w is negative (work done by the system).
  • If ΔV < 0 (compression), w is positive (work done on the system).
• Free Expansion: Expansion against zero external pressure (vacuum). P_ext = 0, so w = 0.
• Work in Reversible Isothermal Expansion (Ideal Gas): w_rev = -nRT ln(V_f / V_i) = -nRT ln(P_i / P_f)
• Work in Irreversible Isothermal Expansion (Ideal Gas): w_irrev = -P_ext (V_f - V_i)
• Note: |w_rev| > |w_irrev| for expansion.

8. Enthalpy (H)

• A thermodynamic state function, defined as H = U + PV.
• Useful for processes occurring at constant pressure (common in chemistry labs).
• Change in Enthalpy (ΔH):
  • ΔH = H_final - H_initial
  • At constant pressure: ΔH = ΔU + PΔV
  • Since ΔU = q + w = q - P_extΔV, if P = P_ext (constant pressure), then ΔU = q_p - PΔV.
  • Substituting in ΔH equation: ΔH = (q_p - PΔV) + PΔV => ΔH = q_p
  • Therefore, the change in enthalpy at constant pressure is equal to the heat absorbed or released by the system at constant pressure.
• Relationship between ΔH and ΔU for Reactions involving Gases:
  • Assuming ideal gas behavior: PV = nRT
  • ΔH = ΔU + Δ(PV)
  • If T is constant: ΔH = ΔU + Δ(n_gRT) = ΔU + RT Δn_g
  • ΔH = ΔU + Δn_g RT
    • Δn_g = (Total moles of gaseous products) - (Total moles of gaseous reactants)
    • R = Ideal gas constant (usually 8.314 J K⁻¹ mol⁻¹)
    • T = Absolute temperature in Kelvin (K)
• Extensive Property: Depends on the amount of substance.

9. Heat Capacity (C)

• Amount of heat required to raise the temperature of a substance by 1°C (or 1 K).
• Molar Heat Capacity (C_m): Heat capacity per mole (J K⁻¹ mol⁻¹).
• Specific Heat Capacity (c_s or s): Heat capacity per gram (J K⁻¹ g⁻¹).
• Relationship: q = C ΔT = n C_m ΔT = m c_s ΔT
• Heat Capacity at Constant Volume (C_v): Heat required to raise the temperature of one mole by 1K at constant volume.
  • At constant volume, ΔV = 0, so w = 0. From First Law, ΔU = q_v.
  • C_v = (∂U / ∂T)_v (or approximately ΔU / ΔT for 1 mole) => ΔU = n C_v ΔT
• Heat Capacity at Constant Pressure (C_p): Heat required to raise the temperature of one mole by 1K at constant pressure.
  • At constant pressure, ΔH = q_p.
  • C_p = (∂H / ∂T)_p (or approximately ΔH / ΔT for 1 mole) => ΔH = n C_p ΔT
• Relationship between C_p and C_v for an Ideal Gas:
  • C_p - C_v = R (Mayer's Relation)

10. Calorimetry: Measurement of ΔU and ΔH

• Bomb Calorimeter: Used to measure ΔU (heat change at constant volume, q_v). Reaction occurs in a sealed 'bomb'. q_reaction = - q_calorimeter = - C_cal ΔT (where C_cal is heat capacity of calorimeter). Since ΔV=0, q_v = ΔU.
• Coffee-Cup Calorimeter: Used to measure ΔH (heat change at constant pressure, q_p). Simpler setup, open to atmosphere. q_reaction = - q_solution = - (m s ΔT)_solution. Since P is constant, q_p = ΔH.

11. Enthalpy Changes of Reactions (Δ_rH)

• Standard Enthalpy of Reaction (Δ_rH°): Enthalpy change when reactants in their standard states are converted to products in their standard states.
  • Standard State: Pure substance at 1 bar pressure and specified temperature (usually 298 K). For solutions, concentration is 1 M.
• Types of Reaction Enthalpies:
  • Standard Enthalpy of Formation (Δ_fH°): Enthalpy change when 1 mole of a compound is formed from its constituent elements in their most stable standard states (reference states). Δ_fH° of elements in their reference state is zero (e.g., O₂(g), C(graphite), H₂(g)).
    • Δ_rH° = Σ ν_p Δ_fH°(products) - Σ ν_r Δ_fH°(reactants) (ν = stoichiometric coefficients)
  • Standard Enthalpy of Combustion (Δ_cH°): Enthalpy change when 1 mole of a substance undergoes complete combustion in excess oxygen under standard conditions. Usually exothermic (Δ_cH° is negative).
  • Enthalpy of Atomization (Δ_aH°): Enthalpy change when 1 mole of a substance breaks down into its constituent atoms in the gaseous phase. (e.g., CH₄(g) → C(g) + 4H(g)).
  • Bond Enthalpy (Δ_bondH°): Average enthalpy change required to break 1 mole of a specific type of bond between atoms in the gaseous state. Always positive (energy required).
    • For reactions involving breaking and forming bonds:
      Δ_rH° ≈ Σ (Bond enthalpies of reactants) - Σ (Bond enthalpies of products)
      (Note: This is an approximation, especially for liquids/solids).
  • Enthalpy of Solution (Δ_solH°): Enthalpy change when 1 mole of a substance dissolves in a specified amount of solvent. Can be endo- or exothermic.
  • Lattice Enthalpy (Δ_latticeH°): Enthalpy change when 1 mole of an ionic compound dissociates into its gaseous ions. Always positive. (e.g., NaCl(s) → Na⁺(g) + Cl⁻(g)). Cannot be measured directly, calculated using Born-Haber cycle.
  • Enthalpy of Hydration (Δ_hydH°): Enthalpy change when 1 mole of gaseous ions gets hydrated (dissolved in water). Usually negative.
  • Enthalpy of Neutralization: Enthalpy change when 1 mole of H⁺ ions from an acid reacts with 1 mole of OH⁻ ions from a base to form 1 mole of water. For strong acid-strong base, it's constant ≈ -57.1 kJ/mol.

12. Hess's Law of Constant Heat Summation

• Statement: The total enthalpy change for a reaction is the same, whether the reaction takes place in one step or in several steps.
• Basis: Enthalpy is a state function.
• Application: Allows calculation of enthalpy changes for reactions that cannot be measured directly, by combining enthalpy changes of other known reactions.

13. Spontaneity

• Spontaneous Process: A process that has a natural tendency to occur under given conditions without external intervention. May be fast or slow. (e.g., rusting of iron, dissolution of sugar in water).
• Non-Spontaneous Process: A process that cannot occur on its own; requires external energy input.
• Enthalpy change (ΔH < 0) favors spontaneity but is not the sole criterion (e.g., melting of ice above 0°C is spontaneous but endothermic). Need another factor: Entropy.

14. Entropy (S)

• A measure of the degree of randomness or disorder of a system.
• State function and extensive property. Units: J K⁻¹ mol⁻¹.
• Generally, S(gas) > S(liquid) > S(solid).
• Entropy increases when:
  • Phase transition from solid → liquid → gas.
  • Temperature increases.
  • Number of moles of gas increases in a reaction.
  • A substance dissolves.
• Change in Entropy (ΔS): ΔS = S_final - S_initial
• Entropy change during phase transition: ΔS_trans = ΔH_trans / T_trans (at constant T and P)
• Second Law of Thermodynamics: The entropy of the universe (system + surroundings) always increases during a spontaneous process.
  • ΔS_total = ΔS_system + ΔS_surroundings > 0 (for spontaneous process)
  • ΔS_total = 0 (for reversible process / equilibrium)
• Calculating ΔS_surroundings: ΔS_surr = -q_sys / T_surr = -ΔH_sys / T (at constant P and T)

15. Gibbs Free Energy (G)

• A thermodynamic state function that combines enthalpy and entropy to provide a single criterion for spontaneity at constant temperature and pressure.
• Defined as: G = H - TS
• Change in Gibbs Free Energy (ΔG): At constant T, ΔG = ΔH - TΔS
• Criterion for Spontaneity (at constant T and P):
  • ΔG < 0: Process is spontaneous.
  • ΔG > 0: Process is non-spontaneous (reverse process is spontaneous).
  • ΔG = 0: System is in equilibrium.
• Effect of Temperature on Spontaneity (using ΔG = ΔH - TΔS):
  • If ΔH < 0, ΔS > 0: ΔG always negative, spontaneous at all T.
  • If ΔH > 0, ΔS < 0: ΔG always positive, non-spontaneous at all T.
  • If ΔH < 0, ΔS < 0: ΔG negative at low T (enthalpy driven), spontaneous at low T.
  • If ΔH > 0, ΔS > 0: ΔG negative at high T (entropy driven), spontaneous at high T.
• Standard Gibbs Energy Change (Δ_rG°): Gibbs energy change for a reaction when all reactants and products are in their standard states.
  • Δ_rG° = Σ ν_p Δ_fG°(products) - Σ ν_r Δ_fG°(reactants)
  • Δ_fG° = Standard Gibbs energy of formation (defined similarly to Δ_fH°). Δ_fG° for elements in reference state is zero.
• Relationship between Δ_rG° and Equilibrium Constant (K):
  • Δ_rG° = - RT ln K
  • If Δ_rG° < 0, K > 1 (products favored at equilibrium).
  • If Δ_rG° > 0, K < 1 (reactants favored at equilibrium).
  • If Δ_rG° = 0, K = 1.

16. Third Law of Thermodynamics

• Statement: The entropy of a perfectly crystalline solid approaches zero as the absolute temperature approaches zero (0 K).
• Allows calculation of absolute entropies of substances at different temperatures.

Key Formulas Summary:

• ΔU = q + w
• w = -P_ext ΔV
• H = U + PV
• ΔH = ΔU + PΔV (const P)
• ΔH = q_p
• ΔU = q_v
• ΔH = ΔU + Δn_g RT
• C_p - C_v = R
• ΔH = n C_p ΔT
• ΔU = n C_v ΔT
• Δ_rH° = Σ ν_p Δ_fH°(products) - Σ ν_r Δ_fH°(reactants)
• Δ_rH° ≈ Σ (Bond enthalpies reactants) - Σ (Bond enthalpies products)
• ΔS_total = ΔS_sys + ΔS_surr > 0 (spontaneous)
• ΔG = ΔH - TΔS
• ΔG < 0 (spontaneous at const T, P)
• Δ_rG° = - RT ln K

Multiple Choice Questions (MCQs)

1. Which of the following is NOT a state function?
   (a) Internal Energy (U)
   (b) Enthalpy (H)
   (c) Work (w)
   (d) Entropy (S)

2. For an adiabatic process, which condition is correct?
   (a) ΔT = 0
   (b) ΔP = 0
   (c) q = 0
   (d) w = 0

3. The first law of thermodynamics is essentially the law of:
   (a) Conservation of mass
   (b) Conservation of energy
   (c) Conservation of momentum
   (d) Increasing entropy

4. For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), the relationship between ΔH and ΔU at constant temperature is:
   (a) ΔH = ΔU + 2RT
   (b) ΔH = ΔU - 2RT
   (c) ΔH = ΔU + RT
   (d) ΔH = ΔU - RT

5. The standard enthalpy of formation (Δ_fH°) is zero for:
   (a) O₃(g)
   (b) Br₂(l)
   (c) C(diamond)
   (d) H₂O(l)

6. Hess's law is based on:
   (a) Enthalpy being a path function
   (b) The first law of thermodynamics
   (c) Enthalpy being a state function
   (d) The second law of thermodynamics

7. For a process to be spontaneous at constant temperature and pressure, the condition is:
   (a) ΔH < 0
   (b) ΔS > 0
   (c) ΔG < 0
   (d) ΔU < 0

8. The entropy change (ΔS) is expected to be positive for which of the following processes?
   (a) 2H₂(g) + O₂(g) → 2H₂O(l)
   (b) N₂(g) + 3H₂(g) → 2NH₃(g)
   (c) CaCO₃(s) → CaO(s) + CO₂(g)
   (d) Freezing of water

9. The relationship ΔG° = - RT ln K implies that:
   (a) If ΔG° > 0, then K > 1
   (b) If ΔG° < 0, then K < 1
   (c) If ΔG° = 0, then K = 0
   (d) If ΔG° < 0, then K > 1

10. In the expansion of an ideal gas into a vacuum (free expansion), which of the following is true?
    (a) q = 0, w = 0, ΔU = 0
    (b) q > 0, w < 0, ΔU = 0
    (c) q < 0, w > 0, ΔU < 0
    (d) q = 0, w < 0, ΔU < 0

Answers to MCQs:

1. (c) Work (w)
2. (c) q = 0
3. (b) Conservation of energy
4. (b) ΔH = ΔU - 2RT (Δn_g = 2 - (1+3) = -2)
5. (b) Br₂(l) (Bromine is liquid in its standard state)
6. (c) Enthalpy being a state function
7. (c) ΔG < 0
8. (c) CaCO₃(s) → CaO(s) + CO₂(g) (Increase in moles of gas, increase in disorder)
9. (d) If ΔG° < 0, then K > 1
10. (a) q = 0 (usually assumed insulated or happens fast), w = 0 (P_ext = 0), therefore ΔU = q + w = 0

Remember to thoroughly revise these concepts and practice numerical problems based on the formulas. Good luck with your preparation!