Lesson 12 of 12 · 18 min
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Must-know facts
20 facts
- 01Open: energy + matter exchange; closed: energy only; isolated: neither.
- 02State functions: p, V, T, U, H, S, G; path functions: q and w.
- 03NCERT sign convention: w > 0 when work is done on the system; q > 0 when heat is absorbed by the system.
- 04ΔU = q + w.
- 05w = −pₑₓΔV; w_rev (isothermal, ideal gas) = −2.303 nRT log(V_f/V_i).
- 06Free expansion of an ideal gas: w = 0, q = 0, ΔU = 0.
- 07Isothermal ideal gas: ΔU = 0 and q = −w.
- 08Adiabatic: q = 0, so ΔU = w_ad.
- 09ΔH = ΔU + Δn_gRT, counting gaseous species only.
- 10Bomb calorimeter (constant volume) measures ΔU; constant-pressure calorimetry measures ΔH.
- 11C_p − C_v = R for one mole of ideal gas.
- 12ΔfH° of an element in its reference state = 0 (carbon: graphite).
- 13ΔsubH° = ΔfusH° + ΔvapH°.
- 14ΔᵣH (gas phase) ≈ Σ bond enthalpies broken − Σ bond enthalpies formed.
- 15Lattice enthalpy of NaCl = +788 kJ mol⁻¹, obtained by a Born-Haber cycle.
- 16ΔS = q_rev/T; spontaneous if ΔS_total > 0.
- 17ΔG = ΔH − TΔS; spontaneous at constant T and p if ΔG < 0.
- 18Crossover temperature T = ΔH/ΔS.
- 19ΔᵣG° = −2.303 RT log K.
- 20Third law: S → 0 for a pure perfect crystal as T → 0 K; ΔsolH = ΔlatticeH + ΔhydH.
Common traps
Where marks are lost
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.