Thermodynamics Class 11 Chemistry Notes

• System types: open (matter + energy exchange), closed (energy only), isolated (neither).
• State functions (H, U, V, P, T) depend only on the current state, not the path; path functions (q, w) depend on how the change happens.
• Work done by a gas:
• $w=-P_{\text{ext}}\Delta V$
• .
• Sign convention: heat absorbed by the system q > 0, work done on the system w > 0.

• For an ideal gas,
• $\Delta U=n{C}_V\Delta T$
• .
• Adiabatic process (q = 0):
• $\Delta U=w$
• .
• Isothermal process (ΔT = 0):
• $\Delta U=0$
• , so
• $q=-w$
• .

• Enthalpy of formation: heat to form 1 mole of a compound from its elements.
• Standard enthalpy of reaction is measured at 298 K and 1 bar.
• Calorimetry measures heat using
• $q=mc\Delta T$
• .

Example: A reaction is exothermic with $\Delta H=-20\text{kJ}$ and $\Delta S=+50\text{J/K}$ at 300 K. Is it spontaneous?

Solution: $\Delta G=-20-0.050\times 300=-20-15=-35\text{kJ}$. Since $\Delta G<0$, the process is spontaneous.

Exercises (NCERT Q5.1–Q5.22)

• 5.1) Choose the correct answer. A thermodynamic state function is a quantity: (i) used to determine heat changes. (ii) whose value is independent of path. (iii) used to determine pressure–volume work. (iv) whose value depends on temperature only.
• 5.2) For a process to occur under adiabatic conditions, the correct condition is: (i) ΔT = 0. (ii) Δp = 0. (iii) q = 0. (iv) w = 0.
• 5.3) The enthalpies of all elements in their standard states are: (i) unity. (ii) zero. (iii) less than zero. (iv) different for each element.
• 5.4) The standard combustion change in internal energy of methane is −X kJ mol⁻¹. Which relation gives its standard enthalpy change? (i) ΔH° = ΔU°. (ii) ΔH° > ΔU°. (iii) ΔH° < ΔU°. (iv) ΔH° = 0.
• 5.5) At 298 K, the enthalpies of combustion of methane, graphite and dihydrogen are −890.3 kJ mol⁻¹, −393.5 kJ mol⁻¹ and −285.8 kJ mol⁻¹, respectively. The enthalpy of formation of CH₄(g) is: (i) −74.8 kJ mol⁻¹. (ii) −52.27 kJ mol⁻¹. (iii) +74.8 kJ mol⁻¹. (iv) +52.26 kJ mol⁻¹.
• 5.6) A reaction A + B → C + D + q is found to have a positive entropy change. The reaction will be: (i) possible at high temperature. (ii) possible only at low temperature. (iii) not possible at any temperature. (iv) possible at any temperature.
• 5.7) In a process, 701 J of heat is absorbed by a system and 394 J of work is done by the system. What is the change in internal energy?
• 5.8) The reaction of cyanamide, NH₂CN(s), with dioxygen was carried out in a bomb calorimeter. Its ΔU was −742.7 kJ mol⁻¹ at 298 K. Calculate the enthalpy change for the reaction:
• 5.9) Calculate the heat needed to raise the temperature of 60.0 g of aluminium from 35 °C to 55 °C. The molar heat capacity of Al is 24 J mol⁻¹ K⁻¹.
• 5.10) Calculate the enthalpy change when 1.0 mol of water at 10.0 °C freezes to ice at −10.0 °C. The enthalpy of fusion at 0 °C is 6.03 kJ mol⁻¹.
• 5.11) The enthalpy of combustion of carbon to CO₂ is −393.5 kJ mol⁻¹. Calculate the heat released when 35.2 g of CO₂ is formed from carbon and dioxygen.
• 5.12) The standard enthalpies of formation of CO(g), CO₂(g), N₂O(g) and N₂O₄(g) are −110, −393, +81 and +9.7 kJ mol⁻¹, respectively. Find ΔᵣH° for N₂O₄(g) + 3CO(g) → N₂O(g) + 3CO₂(g).
• 5.13) For N₂(g) + 3H₂(g) → 2NH₃(g), ΔᵣH° = −92.4 kJ mol⁻¹. What is the standard enthalpy of formation of NH₃(g)?
• 5.14) Calculate the standard enthalpy of formation of CH₃OH(l) from these data:
• 5.15) Calculate the enthalpy change for CCl₄(g) → C(g) + 4Cl(g), and then calculate the C–Cl bond enthalpy in gaseous CCl₄. Given ΔᵥₐₚH°(CCl₄) = 30.5 kJ mol⁻¹, ΔfH°(CCl₄(g)) = −135.5 kJ mol⁻¹, ΔₐH°(C) = 715.0 kJ mol⁻¹ and ΔₐH°(Cl₂) = 242 kJ mol⁻¹.
• 5.16) For an isolated system, ΔU = 0. What will be ΔS?
• 5.17) For 2A + B → C at 298 K, ΔH = 400 kJ mol⁻¹ and ΔS = 0.2 kJ K⁻¹ mol⁻¹. At what temperature does the reaction become spontaneous if ΔH and ΔS remain constant?
• 5.18) For 2Cl(g) → Cl₂(g), what are the signs of ΔH and ΔS?
• 5.19) For 2A(g) + B(g) → 2D(g) at 298 K, ΔU° = −10.5 kJ and ΔS° = −44.1 J K⁻¹. Calculate ΔG° and predict whether the reaction may occur spontaneously.
• 5.20) The equilibrium constant for a reaction is 10. Find ΔG° at 300 K when R = 8.314 J K⁻¹ mol⁻¹.
• 5.21) Comment on the thermodynamic stability of NO(g) from these data:
• 5.22) Calculate the entropy change of the surroundings when 1.00 mol of H₂O(l) is formed under standard conditions, given ΔfH° = −286 kJ mol⁻¹ at 298 K.

Answers at a glance

1. 1
   Q5.1 → A state function has a path-independent value, so the correct option is (ii).
2. 2
   Q5.2 → An adiabatic process satisfies q = 0, so the correct option is (iii).
3. 3
   Q5.3 → The standard enthalpy of every element in its standard state is 0 kJ mol⁻¹, so option (ii) is correct.
4. 4
   Q5.4 → ΔH° = ΔU° − RT, so ΔH° < ΔU° and option (iii) is correct.
5. 5
   Q5.5 → The enthalpy of formation of CH₄(g) is −74.8 kJ mol⁻¹, so option (i) is correct.
6. 6
   Q5.6 → The reaction is possible at any temperature, so the corrected fourth option (iv) is correct.
7. 7
   Q5.7 → The change in internal energy is ΔU = +307 J.
8. 8
   Q5.8 → The standard reaction enthalpy at 298 K is ΔH° = −741.5 kJ mol⁻¹.
9. 9
   Q5.9 → The required heat is 1.07 kJ for the 60.0 g sample.
10. 10
    Q5.10 → The enthalpy change from liquid water at 10 °C to ice at −10 °C is −7.151 kJ mol⁻¹.
11. 11
    Q5.11 → Forming 35.2 g of CO₂ releases 314.8 kJ of heat, corresponding to ΔH = −314.8 kJ for the sample.
12. 12
    Q5.12 → The standard reaction enthalpy is ΔᵣH° = −777.7 kJ mol⁻¹.
13. 13
    Q5.13 → The standard enthalpy of formation of NH₃(g) is −46.2 kJ mol⁻¹.
14. 14
    Q5.14 → The standard enthalpy of formation of CH₃OH(l) is −239 kJ mol⁻¹.
15. 15
    Q5.15 → The reaction enthalpy is +1304 kJ mol⁻¹, and the C–Cl bond enthalpy is 326 kJ mol⁻¹.
16. 16
    Q5.16 → For the expected spontaneous change, ΔS is positive; ΔS = 0 only for an ideal reversible change.
17. 17
    Q5.17 → The reaction is spontaneous for T > 2000 K; at 2000 K it is at equilibrium.
18. 18
    Q5.18 → Both enthalpy and entropy decrease, so ΔH < 0 and ΔS < 0.
19. 19
    Q5.19 → ΔG° ≈ +0.16 kJ for the reaction as written, so it is not spontaneous under the stated standard conditions.
20. 20
    Q5.20 → The standard Gibbs energy change is ΔG° = −5.744 kJ mol⁻¹.
21. 21
    Q5.21 → NO(g) is unstable relative to its elements, while its conversion to the lower-enthalpy NO₂(g) is energetically favoured.
22. 22
    Q5.22 → The entropy change of the surroundings is ΔS(surr) = +959.73 J mol⁻¹ K⁻¹.

MCQ Questions

1 Mark Questions

1. 1
   Define enthalpy (H). (Ans: H = U + PV — the heat content of a system at constant pressure)
2. 2
   State the first law of thermodynamics. (Ans: energy can neither be created nor destroyed; ΔU = q + w)
3. 3
   What is a spontaneous process? (Ans: a process that occurs on its own without any external driving force at a given temperature and pressure)
4. 4
   Define entropy. (Ans: a measure of disorder/randomness of the system; ΔS = q_rev/T)

2 Mark Questions

1. 1
   Differentiate between exothermic and endothermic reactions. (Ans: heat released vs absorbed; ΔH < 0 vs ΔH > 0)
2. 2
   State Hess's law of constant heat summation. (Ans: the total enthalpy change of a reaction is the same whether it occurs in one step or in several steps)
3. 3
   What is the relation between ΔH and ΔU for a reaction at constant pressure? (Ans: ΔH = ΔU + Δn_g RT)

3 Mark Questions

1. 1
   Using the first law, derive ΔH = ΔU + PΔV and explain the conditions under which ΔH = ΔU. (Ans: at constant pressure; equal when no gaseous volume change — Δn_g = 0)
2. 2
   Calculate the standard enthalpy of the reaction N₂(g) + 3H₂(g) → 2NH₃(g) if bond enthalpies are N≡N = 946, H–H = 436, N–H = 391 kJ mol⁻¹. (Ans: ΔH = 2(946) + 3(436) − 6(391) = −92 kJ mol⁻¹)
3. 3
   State the second law of thermodynamics and explain its relationship to entropy and spontaneity. (Ans: total entropy of the universe increases in a spontaneous change)

5 Mark Questions

1. 1
   Define Gibbs free energy. Derive ΔG = ΔH − TΔS and explain the criteria of spontaneity (ΔG < 0 spontaneous, ΔG = 0 equilibrium, ΔG > 0 non-spontaneous) with examples of the four sign combinations of ΔH and ΔS.
2. 2
   Explain Hess's law with a full worked example (e.g. ΔH°f of CO from the combustion of C and CO), and define the standard enthalpies of formation, combustion and neutralisation with one numerical application of each.