Thermodynamics

Chemistry · Class 11

Lesson 12 of 12 · 18 min

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Must-know facts

20 facts

  1. 1Open: energy + matter exchange; closed: energy only; isolated: neither.
  2. 2State functions: p, V, T, U, H, S, G; path functions: q and w.
  3. 3NCERT sign convention: w > 0 when work is done on the system; q > 0 when heat is absorbed by the system.
  4. 4ΔU = q + w.
  5. 5w = −pₑₓΔV; w_rev (isothermal, ideal gas) = −2.303 nRT log(V_f/V_i).
  6. 6Free expansion of an ideal gas: w = 0, q = 0, ΔU = 0.
  7. 7Isothermal ideal gas: ΔU = 0 and q = −w.
  8. 8Adiabatic: q = 0, so ΔU = w_ad.
  9. 9ΔH = ΔU + Δn_gRT, counting gaseous species only.
  10. 10Bomb calorimeter (constant volume) measures ΔU; constant-pressure calorimetry measures ΔH.
  11. 11C_p − C_v = R for one mole of ideal gas.
  12. 12ΔfH° of an element in its reference state = 0 (carbon: graphite).
  13. 13ΔsubH° = ΔfusH° + ΔvapH°.
  14. 14ΔᵣH (gas phase) ≈ Σ bond enthalpies broken − Σ bond enthalpies formed.
  15. 15Lattice enthalpy of NaCl = +788 kJ mol⁻¹, obtained by a Born-Haber cycle.
  16. 16ΔS = q_rev/T; spontaneous if ΔS_total > 0.
  17. 17ΔG = ΔH − TΔS; spontaneous at constant T and p if ΔG < 0.
  18. 18Crossover temperature T = ΔH/ΔS.
  19. 19ΔᵣG° = −2.303 RT log K.
  20. 20Third law: S → 0 for a pure perfect crystal as T → 0 K; ΔsolH = ΔlatticeH + ΔhydH.

Common traps

Where marks are lost

Writing w = +pΔV (the older physics-style convention) in chemistry problems.

NCERT uses w = −pₑₓΔV with ΔU = q + w; work done by the gas on expansion is negative.

Counting water or other liquids in Δn_g.

Only gaseous moles count; for CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), Δn_g = 1 − 3 = −2.

Plugging ΔS in J K⁻¹ mol⁻¹ straight into ΔG = ΔH − TΔS with ΔH in kJ.

Convert first: 120 J K⁻¹ mol⁻¹ = 0.120 kJ K⁻¹ mol⁻¹.

Assuming every exothermic reaction is spontaneous.

Spontaneity is decided by ΔG (or ΔS_total), not by ΔH alone; ΔH < 0 with ΔS < 0 fails at high temperature.

Calling heat or work a state function because ΔU is.

Only their sum is path-independent; q and w separately depend on the path.

Reversing the bond-enthalpy formula (products minus reactants).

Bond enthalpies are energies to break bonds, so use broken (reactants) minus formed (products).

Forgetting that a free expansion does no work.

Against zero external pressure w = −0 × ΔV = 0, whatever the volume change.

Taking heat capacity as intensive.

Heat capacity grows with the amount of substance and is extensive; molar and specific heat capacities are intensive.

Thinking spontaneous means fast.

Spontaneity is about direction, not rate; a spontaneous reaction can be extremely slow.

Formulas

15 to know

First law

ΔU = q + w

NCERT convention: q > 0 when heat enters the system; w > 0 when work is done on the system.

Work against constant external pressure

w = −pₑₓ(V_f − V_i)

Negative for expansion, positive for compression. 1 L bar = 100 J.

Reversible isothermal work (ideal gas)

w_rev = −2.303 nRT log(V_f/V_i)

Equivalently −2.303 nRT log(p_i/p_f); R = 8.314 J K⁻¹ mol⁻¹.

Enthalpy

H = U + pV ; ΔH = q_p

Heat exchanged at constant pressure.

ΔH and ΔU

ΔH = ΔU + Δn_gRT

Δn_g = moles of gaseous products − moles of gaseous reactants.

Heat and heat capacity

q = CΔT = n C_m ΔT = m c ΔT

C extensive; C_m (J K⁻¹ mol⁻¹) and c (J K⁻¹ g⁻¹) intensive.

Molar heat capacities of an ideal gas

C_p − C_v = R

R = 8.314 J K⁻¹ mol⁻¹.

Reaction enthalpy from formation data

ΔᵣH° = Σ aᵢΔfH°(products) − Σ bᵢΔfH°(reactants)

ΔfH° of elements in reference states is zero.

Reaction enthalpy from bond enthalpies

ΔᵣH° = Σ bond enthalpies(reactants) − Σ bond enthalpies(products)

Valid for gas-phase reactions; gives approximate values.

Enthalpy of solution of an ionic solid

ΔsolH = ΔlatticeH + ΔhydH

NaCl: +788 + (−784) = +4 kJ mol⁻¹.

Sublimation enthalpy

ΔsubH° = ΔfusH° + ΔvapH°

At the same temperature.

Entropy change

ΔS = q_rev / T

Unit J K⁻¹ (J K⁻¹ mol⁻¹ for molar values).

Total entropy criterion

ΔS_total = ΔS_sys + ΔS_surr > 0

= 0 at equilibrium.

Gibbs energy

ΔG = ΔH − TΔS

ΔG < 0 spontaneous at constant T and p; crossover T = ΔH/ΔS.

Gibbs energy and K

ΔᵣG° = −RT ln K = −2.303 RT log K

R = 8.314 J K⁻¹ mol⁻¹; keep ΔᵣG° in J mol⁻¹ when R is in J.

Key terms

15 terms

Isolated system
A system that exchanges neither energy nor matter with its surroundings.
State function
A property whose change depends only on initial and final states.
Internal energy
Total energy stored in a system; only its change is measurable.
Adiabatic process
A change in which no heat passes between system and surroundings.
Reversible process
A change carried out through a series of near-equilibrium steps, which can be reversed by an infinitesimal change.
Enthalpy
H = U + pV; its change equals heat exchanged at constant pressure.
Extensive property
A property that scales with the amount of matter, like volume or enthalpy.
Intensive property
A property independent of amount, like temperature or density.
Standard state
Pure form of a substance at 1 bar and a stated temperature, usually 298 K.
Standard enthalpy of formation
Enthalpy change when a compound's elements, each in its reference state, combine to give one mole of that compound.
Hess's law
Total enthalpy change is the same whatever the route between the same initial and final states.
Lattice enthalpy
Enthalpy needed to break one mole of an ionic solid into gaseous ions.
Enthalpy of dilution
Enthalpy change when more solvent is added to an existing solution; it depends on the starting concentration.
Entropy
A state function measuring randomness; ΔS = q_rev/T.
Gibbs energy
G = H − TS; its decrease at constant T and p marks a spontaneous change.
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