Thermodynamics: NEET notes

1. System, surroundings and state functions

NCERT § "Thermodynamic Terms"

• The system is the part of the universe under study; everything else is the surroundings, and the two together make up the universe.
• An open system exchanges both energy and matter with its surroundings (reactants in an open beaker); a closed system exchanges energy but not matter (a sealed flask); an isolated system exchanges neither (an ideal thermos flask).
• The state of a system is fixed by measurable state variables such as pressure, volume, temperature and amount.
• A state function depends only on the present state of the system, not on how that state was reached: p, V, T, U, H, S and G are state functions.
• Heat (q) and work (w) are path functions; their values depend on how the change is carried out, though their sum ΔU does not.
• Internal energy U is the total energy of the system (chemical, electrical, mechanical and other forms); only its change ΔU can be measured.
• In adiabatic changes no heat passes between system and surroundings (q = 0), so the work done on the system equals ΔU.
• An isothermal process takes place at constant temperature; for an ideal gas this means ΔU = 0.

2. Work, heat and the first law

NCERT § "The Internal Energy as a State Function"

• NCERT's sign convention: work that the surroundings do on the system counts as positive w, and work the system does on its surroundings counts as negative w.
• Likewise q is positive when heat flows into the system and negative when heat leaves it.
• First law: ΔU = q + w. Energy of an isolated system stays constant; energy can change form but is not created or destroyed.
• If a gas absorbs 100 J of heat and does 300 J of work on the surroundings, ΔU = +100 + (−300) = −200 J.
• For heat exchanged at constant volume and with no other work, w = 0 and ΔU = qᵥ.
• Adiabatic work done on a system raises its internal energy by exactly that amount: ΔU = w_ad.
• Heat and work are two different ways of transferring energy; neither is stored in the system.

3. Pressure-volume work

NCERT § "Applications"

• For expansion or compression against a constant external pressure, w = −pₑₓ(V_f − V_i) = −pₑₓΔV.
• In expansion ΔV is positive, so w is negative (the system does work); in compression ΔV is negative, so w is positive.
• A reversible process proceeds through a series of equilibrium states, with the external pressure differing from the internal pressure only infinitesimally at every step.
• Reversible isothermal expansion of an ideal gas: w_rev = −2.303 nRT log(V_f/V_i).
• Reversible expansion does more work on the surroundings than an irreversible expansion between the same two states.
• Free expansion is expansion into a vacuum (pₑₓ = 0), so no work is done; for an ideal gas ΔU is also zero because it has no intermolecular attractions.
• For isothermal changes of an ideal gas ΔU = 0, so q = −w: irreversible q = pₑₓ(V_f − V_i), reversible q = 2.303 nRT log(V_f/V_i), free expansion q = 0.
• Work of 1 L bar equals 100 J.

4. Enthalpy, heat capacity and extensive properties

NCERT § "Enthalpy, H"

• Enthalpy is defined as H = U + pV; at constant pressure its change equals the heat absorbed, ΔH = q_p.
• ΔH = ΔU + pΔV; for reactions involving gases this becomes ΔH = ΔU + Δn_gRT, where Δn_g = moles of gaseous products − moles of gaseous reactants.
• Liquids and solids are left out of Δn_g; their volume change is negligible.
• If Δn_g = 0 (e.g. H₂(g) + I₂(g) → 2HI(g)), ΔH = ΔU; if Δn_g < 0, ΔH is smaller (more negative) than ΔU, and if Δn_g > 0, ΔH is larger than ΔU.
• ΔH negative means an exothermic reaction (heat released); ΔH positive means endothermic (heat absorbed).
• Extensive properties depend on the amount of matter (mass, volume, U, H, heat capacity); intensive properties do not (temperature, pressure, density, molar heat capacity).
• The ratio of two extensive properties is intensive; for example molar volume V/n and density m/V.
• Heat capacity: q = CΔT; molar heat capacity C_m = C/n; specific heat capacity c relates to mass by q = m c ΔT.
• For an ideal gas, C_p − C_v = R, where these are molar heat capacities at constant pressure and constant volume.

5. Calorimetry

NCERT § "Measurement of ΔU and ΔH: Calorimetry"

• Energy changes are measured by calorimetry: the reaction is run in a vessel immersed in a known amount of liquid, and the heat released or absorbed is found from the temperature change and the calorimeter's heat capacity.
• A bomb calorimeter is a sealed steel vessel of constant volume, so no pressure-volume work is done and it measures ΔU.
• In a bomb calorimeter the sample is burnt in pure oxygen, and the heat given out is found from the rise in temperature of the surrounding water.
• Reactions carried out at constant (atmospheric) pressure in a simple calorimeter give q_p, which is ΔH.
• To convert a bomb calorimeter ΔU into ΔH, use ΔH = ΔU + Δn_gRT with gaseous species only.

6. Reaction enthalpy, standard states and thermochemical equations

NCERT § "Enthalpy Change, ΔrH of a Reaction – Reaction Enthalpy"

• Reaction enthalpy ΔᵣH = Σ(enthalpies of products) − Σ(enthalpies of reactants), each multiplied by its coefficient.
• Standard state means the substance taken pure and under 1 bar, at whatever temperature is specified; tabulated values are mostly for 298 K and carry the ° sign.
• A thermochemical equation is a balanced equation with physical states written in and its ΔᵣH value; the coefficients stand for moles.
• Multiplying an equation by a number multiplies ΔᵣH by the same number; reversing the equation reverses the sign of ΔᵣH.
• Standard enthalpy of fusion, vaporisation and sublimation are enthalpy changes for melting, boiling or subliming one mole of a substance; for water ΔfusH° = 6.00 kJ mol⁻¹ at 273 K and ΔvapH° = 40.79 kJ mol⁻¹ at 373 K.
• Sublimation equals fusion followed by vaporisation at the same temperature, so ΔsubH° = ΔfusH° + ΔvapH°.
• Standard enthalpy of formation ΔfH° is the enthalpy change for making one mole of a compound out of its elements, each taken in its most stable form (reference state).
• ΔfH° of an element in its reference state is zero; for carbon the reference state is graphite.
• Using formation data: ΔᵣH° = Σ aᵢΔfH°(products) − Σ bᵢΔfH°(reactants).

7. Hess's law

NCERT § "Hess's Law of Constant Heat Summation"

• Because enthalpy is a state function, the total enthalpy change of a reaction is the same whether it happens in one step or in several.
• Thermochemical equations can therefore be added, subtracted and scaled like algebraic equations to obtain an unknown ΔᵣH.
• A classic use is finding ΔfH° of CO from the combustion enthalpies of carbon to CO₂ and of CO to CO₂, because carbon cannot be converted cleanly to CO alone.
• Combustion data give formation enthalpies: for a hydrocarbon, ΔcH° = Σ ΔfH°(CO₂ and H₂O formed) − ΔfH°(hydrocarbon), since ΔfH° of O₂ is zero.
• When combining equations, carry each species' physical state; H₂O(l) and H₂O(g) have different ΔfH° values.

8. Enthalpies of combustion, atomisation, bonds, lattices, solution and dilution

NCERT § "Enthalpies for Different Types of Reactions"

• Standard enthalpy of combustion ΔcH° is the enthalpy change per mole of a substance burnt completely in oxygen, all species in standard states; combustion is always exothermic.
• Enthalpy of atomisation is the enthalpy change when all the bonds in one mole of a substance are broken to give separate gaseous atoms; for H₂ it is 435.0 kJ mol⁻¹, and for CH₄ it is 1665 kJ mol⁻¹.
• Bond dissociation enthalpy applies to one specific bond in a diatomic or particular molecule; for polyatomic molecules a mean bond enthalpy is used (C–H in CH₄: 1665/4 = 416 kJ mol⁻¹).
• Estimating reaction enthalpy for gas-phase reactions: ΔᵣH° = Σ bond enthalpies of reactants − Σ bond enthalpies of products (bonds broken minus bonds formed).
• Mean bond enthalpies give only approximate reaction enthalpies because a given bond's strength varies from molecule to molecule.
• Lattice enthalpy is the enthalpy needed to pull one mole of an ionic solid fully apart into its gaseous ions; for NaCl it is +788 kJ mol⁻¹.
• Lattice enthalpy cannot be measured directly; it is found from a Born-Haber cycle, which applies Hess's law to steps such as sublimation, ionisation, dissociation and electron gain.
• Enthalpy of solution ΔsolH is the enthalpy change for dissolving one mole of a substance in a stated amount of solvent; for an ionic solid, ΔsolH = ΔlatticeH + ΔhydH. For NaCl, +788 − 784 = +4 kJ mol⁻¹, so dissolving it barely changes the temperature.
• ΔsolH is positive for most ionic salts, so their solubility in water rises with temperature; a very high lattice enthalpy can stop a salt dissolving at all.
• Enthalpy of dilution is the enthalpy change when extra solvent is added to a solution; it depends on the starting concentration and on how much solvent is added. For HCl, going from HCl·25 aq to HCl·40 aq gives −72.79 − (−72.03) = −0.76 kJ mol⁻¹.

9. Spontaneity and entropy

NCERT § "Spontaneity"

• A spontaneous process can proceed on its own without outside help once started; spontaneity says nothing about how fast it happens.
• A negative ΔH favours spontaneity but does not guarantee it: some endothermic processes, such as dissolving certain salts, are spontaneous.
• Entropy S measures the degree of randomness or disorder of a system; it is a state function.
• Entropy increases from solid to liquid to gas, on dissolving a solid, and generally when a reaction produces more gas molecules.
• For a reversible transfer of heat q_rev at temperature T, ΔS = q_rev/T; the same amount of heat raises entropy more at low temperature than at high temperature.
• A process is spontaneous when the total entropy change is positive: ΔS_total = ΔS_sys + ΔS_surr > 0.
• At equilibrium ΔS_total = 0.
• For an isolated system ΔU = 0, and entropy is the driving force: ΔS > 0 for a spontaneous change.
• Third law: as the temperature approaches 0 K, the entropy of a pure, perfectly crystalline substance approaches zero. Solutions and supercooled liquids keep some entropy at 0 K. The law lets absolute entropies of pure substances be worked out from thermal data.

10. Gibbs energy and spontaneity

NCERT § "Gibbs Energy and Spontaneity"

• Gibbs energy is defined as G = H − TS; at constant temperature ΔG = ΔH − TΔS.
• At constant temperature and pressure, ΔG < 0 means spontaneous, ΔG > 0 means non-spontaneous (the reverse is spontaneous), and ΔG = 0 means equilibrium.
• ΔH < 0 and ΔS > 0: ΔG is negative at all temperatures, always spontaneous.
• ΔH > 0 and ΔS < 0: ΔG is positive at all temperatures, never spontaneous.
• ΔH < 0 and ΔS < 0: spontaneous only at low temperature, when |ΔH| > |TΔS|.
• ΔH > 0 and ΔS > 0: spontaneous only at high temperature, when TΔS > ΔH.
• The temperature at which ΔG changes sign is T = ΔH/ΔS, assuming both stay roughly constant; convert ΔS to kJ K⁻¹ mol⁻¹ before dividing into ΔH in kJ mol⁻¹.

11. Gibbs energy and equilibrium

NCERT § "Gibbs Energy Change and Equilibrium"

• At equilibrium ΔᵣG = 0, and the standard Gibbs energy change is related to the equilibrium constant by ΔᵣG° = −RT ln K = −2.303 RT log K.
• A negative ΔᵣG° gives K > 1, favouring products; a positive ΔᵣG° gives K < 1, favouring reactants.
• K = e^(−ΔᵣG°/RT); remember to express ΔᵣG° in J mol⁻¹ when R is 8.314 J K⁻¹ mol⁻¹.
• ΔᵣG° can be found from ΔᵣH° − TΔᵣS°, so enthalpy and entropy data let you calculate K.
• Strongly endothermic reactions can still reach a large K at high temperatures if ΔᵣS° is large and positive.

Must-know facts

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

Common traps

Formulas

Key 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.