Thermodynamics - Class 11 Chemistry

Thermodynamics

Overview: Energy changes in chemical reactions, Laws of Thermodynamics, Enthalpy, Entropy, and Gibbs Free Energy.

1. First Law of Thermodynamics

Law of Conservation of Energy. Energy can neither be created nor destroyed.

ΔU = q + w

q: Heat (+ absorbed, - released).
w: Work (+ on system, - by system).
ΔU: Change in Internal Energy.

2. Enthalpy (H)

Heat content of system at constant pressure.

H = U + PV

ΔH = ΔU + PΔV = ΔU + Δn_gRT

Exothermic: ΔH is negative (Heat released).
Endothermic: ΔH is positive (Heat absorbed).

3. Hess's Law

Standard Enthalpy of Reaction is sum of enthalpies of intermediate reactions. Path independent (State function).

Δ_rH = ΣΔ_fH(products) - ΣΔ_fH(reactants)

4. Entropy (S) & Second Law

Entropy: Measure of disorder or randomness. ΔS = q_rev / T.

Second Law: Entropy of universe increases in a spontaneous process.

ΔS_total = ΔS_sys + ΔS_surr > 0

5. Gibbs Free Energy (G)

Available energy to do useful work. Criteria for spontaneity.

G = H - TS

ΔG = ΔH - TΔS (Gibbs-Helmholtz Eq)

ΔG < 0: Spontaneous.
ΔG > 0: Non-spontaneous.
ΔG = 0: Equilibrium.
Standard Free Energy: ΔG° = -RT ln K.

Numericals - Thermodynamics

Numericals

Work Done (Expansion)

Q1. Gas expands from 2 L to 10 L against constant pressure of 1 bar. Calc work in Joules.

w = -P_ext ΔV

w = -1 bar × (10 - 2) L = -8 L bar.

1 L bar = 100 J.

w = -800 J.

(Work done by system is negative).

Internal Energy Change

Q2. System absorbs 500 J heat and does 200 J work. Calc ΔU.

q = +500 J (absorbed).

w = -200 J (work done BY system).

ΔU = q + w = 500 - 200.

ΔU = 300 J.

Enthalpy Change

Q3. For reaction N2 + 3H2 -> 2NH3, ΔH = -92 kJ. Calc ΔU at 298 K.

ΔH = ΔU + Δng RT

Δng = np - nr = 2 - (1+3) = -2.

-92000 = ΔU + (-2 × 8.314 × 298).

-92000 = ΔU - 4955.

ΔU = -92000 + 4955 = -87045 J = -87.045 kJ.

Standard Enthalpy of Formation

Q4. Calc enthalpy of combustion of CH4. Given ΔfH: CH4=-74, CO2=-393, H2O=-286.

CH4 + 2O2 -> CO2 + 2H2O

ΔH = [ΔfH(CO2) + 2ΔfH(H2O)] - [ΔfH(CH4) + 0]

= [-393 + 2(-286)] - [-74]

= [-393 - 572] + 74

= -965 + 74 = -891 kJ/mol.

Gibbs Free Energy

Q5. For a reaction, ΔH = -10 kJ, ΔS = -20 J/K. Spontaneous at 300 K?

ΔG = ΔH - TΔS

ΔG = -10000 - (300 × -20)

ΔG = -10000 + 6000 = -4000 J.

Since ΔG < 0, reaction is Spontaneous.

Entropy Change

Q6. Liquid water vaporizes at 373 K. ΔvapH = 40.8 kJ/mol. Calc ΔS.

At equilibrium (Boiling point), ΔG = 0.

ΔS = ΔH / T

ΔS = 40800 / 373

ΔS = 109.38 J K^-1 mol^-1.

Bomb Calorimeter

Q7. Combustion of 1g graphite raises temp by 1K. C_cal = 20 kJ/K. Calc ΔU.

q = C ΔT = 20 × 1 = 20 kJ.

Heat released = 20 kJ. So ΔU for 1g = -20 kJ.

For 1 mol (12g), ΔU = 12 × -20 = -240 kJ/mol.

Equilibrium Constant

Q8. Calc K for reaction if ΔG° = -8.314 kJ at 300 K.

ΔG° = -RT ln K

-8314 = -8.314 × 300 × ln K

1000 = 300 ln K. ln K = 3.33.

K = e^3.33 ≈ 28.

Bond Enthalpy

Q9. Calc bond enthalpy of H-Cl given rxn H2 + Cl2 -> 2HCl is -184 kJ. B.E(H-H)=435, B.E(Cl-Cl)=242.

ΔH = ΣBE(rect) - ΣBE(prod)

-184 = [435 + 242] - [2 × BE(H-Cl)]

-184 = 677 - 2x

2x = 677 + 184 = 861.

x = 430.5 kJ/mol.

Work (Isothermal Reversible)

Q10. 1 mol gas expands rev from 10L to 100L at 300K.

w = -2.303 nRT log(V2/V1)

w = -2.303 × 1 × 8.314 × 300 × log(100/10)

w = -5744 × log(10) = -5744 J.

Formulas & Facts - Thermodynamics

Equations & Formulas

Concept	Formula
First Law	ΔU = q + w
Work (Irrev)	w = -P_extΔV
Work (Rev ISO)	w = -2.303 nRT log(V2/V1)
Enthalpy	ΔH = ΔU + Δn_gRT
Heat Capacity	C_p - C_v = R
Entropy	ΔS = q_rev / T
Gibbs Free Energy	ΔG = ΔH - TΔS
Standard Free Energy	ΔG° = -2.303 RT log K
Kirchhoff's Eq	ΔH2 - ΔH1 = ΔCp (T2 - T1)

50 NEET Facts

Key points for Thermodynamics.

1. Extensive Property Depends on mass/size (e.g., Mass, Vol, H, U, G, S). Additive.

2. Intensive Property Independent of mass (e.g. Temp, Pressure, Density, Molarity, EMF). Non-additive.

3. State Function Depends only on initial and final state (e.g. P, V, T, H, U, G, S).

4. Path Function Depends on path taken (e.g. Work, Heat).

5. Adiabatic Process No heat exchange. q = 0.

6. Isothermal Process Temp constant. ΔT = 0, ΔU = 0 (ideal gas).

7. Isobaric Process Pressure constant. ΔP = 0.

8. Isochoric Process Volume constant. ΔV = 0, w = 0.

9. Cyclic Process Returns to initial state. ΔH = ΔU = 0.

10. Reversible Process Infinitely slow. Pext ~ Pint. Equilibrium at all steps. Max work.

11. Irreversible Process Fast, finite time. Real processes.

12. Work done on vacuum Free expansion. Pext=0. w=0. q=0. ΔU=0. ΔT=0.

13. Heat Capacity Heat to raise temp by 1 C.

14. Specific Heat Heat to raise temp of 1g by 1 C. Intensive.

15. Molar Heat Capacity Heat to raise temp of 1 mol by 1 C. Cm = c × M.

16. Phase Transition Temp remains constant. Entropy increases (Solid->Liq->Gas).

17. ΔH Fusion Solid to Liquid. Always positive (Endo).

18. Standard State 1 bar pressure. Specific temp (usually 298K).

19. Enthalpy of Element In standard state is taken as Zero (e.g., O2, C(graphite), Na(s)).

20. Bond Dissociation Energy Energy to break bond. Always positive.

21. Born Haber Cycle for NaCl Sublimation + IE + Dissociation + EA + Lattice Energy = ΔfH.

22. Spontaneity Condition ΔSuniverse > 0.

23. Gibbs Energy Criteria At const T, P: ΔG < 0 is Spontaneous.

24. Endo Reaction Spontaneous? Yes, if ΔS is very positive and T is high enough (TΔS > ΔH).

25. Exo Reaction Non-spontaneous? Yes, if ΔS is negative and T is high (TΔS term dominates).

26. Third Law Entropy of perfectly crystalline substance at 0 K is Zero.

27. Residual Entropy Substances like CO, NO have entropy > 0 at 0 K due to disorder.

28. Entropy of Gas S(gas) >> S(liq) > S(solid).

29. Boiling Egg Entropy increases (Denaturation of protein -> disorder).

30. Stretching Rubber Band Entropy decreases (Chains align). (Spontaneity driven by ΔH).

31. Atomization Enthalpy Enthalpy change breaking bonds to form atoms. Always +ve.

32. Solution Enthalpy ΔsolH = ΔlatticeH + ΔhydrationH. If ΔHyd > ΔLattice, exo, soluble.

33. Combustion Enthalpy Always negative (Exothermic).

34. Neutralization Enthalpy Strong Acid + Strong Base = -57.1 kJ/mol (const). Form water.

35. Weak Acid Neutralization Heat released is LESS than 57.1 kJ because some heat used for ionization.

36. Efficiency (Carnot) η = (T2 - T1) / T2 = w / q2.

37. Cp/Cv Ratio Gamma (γ). Mono=1.66, Di=1.4, Poly=1.33.

38. Expansion cooling Adiabatic expansion leads to cooling (Work done at expense of Internal Energy).

39. Gibbs Energy & Work -ΔG = W_non_expansion (Useful work max).

40. Coupling Reactions Non-spontaneous rxn coupled with spontaneous one to occur (ATP hydrolysis).

41. Standard Hydrogen electrode ΔG = 0. E = 0.

42. Entropy of Mixing ΔS_mix is always positive for ideal gases.

43. Diamond to Graphite Graphite is more stable. ΔG < 0. But rate is very slow (Kinetics).

44. Bomb Calorimeter Measures ΔU (Constant Volume).

45. Coffee Cup Calorimeter Measures ΔH (Constant Pressure).

46. ΔG vs K K > 1 then ΔG < 0. K < 1 then ΔG> 0.

47. Trouton's Rule ΔvapS ~ 88 J/K mol for most liquids.

48. ΔfH of O3 Not zero. O3 is not standard form.

49. Thermodynamic Scale of T Kelvin scale. Independent of working substance.

50. Clausius Inequality dS >= dq/T.

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