Class 11 Chemistry · NCERT chapter 6 · 7 topics · free to read
System, Surroundings & State Functions
A thermodynamic system is the part of the universe under study; everything else is the surroundings. Systems can be open (exchanges mass + energy), closed (energy only), or isolated (neither). Properties are either state functions (depend only on current state: U, H, S, G) or path functions (depend on how you got there: q, w). Properties are extensive (depend on amount: U, H, S, V) or intensive (don't: T, P, density).
Universe = System + Surroundings
Types of Systems
Thermodynamic systems are classified by what they can exchange with their surroundings: matter, energy, both, or neither.
A system is the specific part of the universe you're studying. Everything outside is the surroundings. The real boundary between them is called the wall or boundary. What matters is what the boundary allows through.
Open — exchanges both energy AND matter
Hot coffee in an open cup (heat + vapour escape)
Closed — exchanges only energy, NOT matter
Gas in a piston-cylinder (heat flows, gas stays)
Isolated — exchanges NEITHER energy nor matter
Ideal thermos flask (nothing crosses boundary)
NCERT defines the universe = system + surroundings
The boundary can be real (container wall) or imaginary (a region of space)
An adiabatic wall does not allow heat transfer; a diathermal wall does
A truly isolated system is an idealization — no real system is perfectly isolated
State Functions vs Path Functions
State functions depend only on the current state of the system (initial and final), not on how the system reached that state. Path functions depend on the route taken.
A state function (or state variable) depends ONLY on the current state of the system — not on how you got there. Think of altitude: whether you climbed or took a helicopter, your altitude at the top is the same. A path function depends on the specific route — the distance you walked IS different for each path.
State functions: U (internal energy), H (enthalpy), S (entropy), G (Gibbs energy), T , P , V , n
Path functions: q (heat) and w (work) — they depend on the process taken
For state functions: X = X_ final - X_ initial — path doesn't matter
For a cyclic process (returning to the same state): U = 0 , H = 0 , but q 0 and w 0
Extensive vs Intensive Properties
Extensive properties scale with the amount of substance (mass, volume, energy). Intensive properties are independent of the amount (temperature, pressure, density).
Take a glass of water at 25°C. Pour half into another glass. Each half is still at 25°C (temperature didn't halve). But each half has half the volume, half the mass, half the internal energy. Temperature is intensive; volume, mass, energy are extensive.
Mass ( m )
Temperature ( T )
Volume ( V )
Pressure ( P )
Internal energy ( U )
Density ( )
Enthalpy ( H ), Entropy ( S )
Molar heat capacity ( C_m )
Heat capacity ( C )
Refractive index, viscosity
Extensive / Extensive = Intensive. Example: mass/volume = density (intensive)
NCERT explicitly lists this classification — expect a direct MCQ
Quick recall
Is heat capacity ( C ) extensive or intensive? What about specific heat capacity ( c )?
C (total heat capacity) is extensive — it doubles if you double the amount. Specific heat capacity c (per gram) and molar heat capacity C_m (per mole) are intensive — they don't depend on the amount.
First Law of Thermodynamics
Energy can neither be created nor destroyed — only converted. Mathematically: ΔU = q + w. For expansion work against a constant external pressure: w = −P_ext ΔV. At constant volume, ΔU = q_V. At constant pressure, ΔH = q_P. Enthalpy H = U + PV is the 'constant-pressure energy'.
U = q + w
Internal Energy & the First Law
The internal energy U of a system is the total of all molecular kinetic and potential energies. The first law says ΔU = q + w: the change in internal energy equals heat absorbed plus work done on the system.
Internal energy ( U ) is the sum of ALL forms of energy inside the system — translational, rotational, vibrational kinetic energies of molecules, plus intermolecular potential energies. We can never know the absolute value of U , but we CAN measure U .
U = q + w
Here q = heat absorbed BY the system and w = work done ON the system. This is the IUPAC sign convention used by NCERT.
U is a state function — U depends only on initial and final states
q and w are path functions — they depend on how the process is carried out
For a cyclic process (system returns to initial state): U = 0 , so q = -w
The first law is essentially the law of conservation of energy applied to thermodynamic systems
U is an extensive property — it doubles if the amount of substance doubles
Pressure-Volume Work
The most common form of work in chemistry is expansion/compression work against an external pressure. For irreversible expansion against constant P_ext: w = −P_ext ΔV. For reversible expansion: w = −nRT ln(V₂/V₁).
When a gas expands, it pushes against the surroundings, doing work. When compressed, surroundings do work on the gas. The general formula for work against constant external pressure:
w = -P_ ext V = -P_ ext (V_2 - V_1)
The negative sign ensures NCERT convention is satisfied: expansion ( V > 0 ) → w < 0 (system loses energy by doing work). Compression ( V < 0 ) → w > 0 (system gains energy).
Free expansion (into vacuum): P_ ext = 0 → w = 0 regardless of V
Irreversible expansion against constant P_ ext : w = -P_ ext (V_2 - V_1)
Reversible (isothermal) expansion of ideal gas: w = -nRT V_2 V_1 = -2.303 nRT V_2 V_1
Reversible work is the maximum work a system can do during expansion
Units: if P in atm and V in L → w in L·atm. Convert: 1 L·atm = 101.325 J
Quick recall
2 mol of an ideal gas expands isothermally and reversibly at 300 K from 10 L to 20 L. Calculate work done.
w = -nRT (V_2/V_1) = -2 8.314 300 (2) = -2 8.314 300 0.693 = -3458 J. Negative sign → work done BY the system (expansion).
Enthalpy
Enthalpy H = U + PV is defined to simplify calculations at constant pressure (which is how most chemistry happens — in open beakers). At constant pressure, ΔH = q_P. At constant volume, ΔU = q_V.
Most chemical reactions happen in open beakers at atmospheric pressure, not in sealed containers at constant volume. At constant pressure, some of the heat goes into PV work (gas expansion/contraction). Enthalpy accounts for this automatically:
H = U + PV
H = U + (PV) = U + P V (at constant P)
The beautiful result: at constant pressure, H = q_P (heat exchanged at constant pressure). At constant volume, U = q_V (heat exchanged at constant volume).
H is a state function and an extensive property
H = q_P — enthalpy change equals heat at constant pressure
U = q_V — internal energy change equals heat at constant volume
For reactions involving only solids and liquids: H U (negligible P V )
For reactions with gases: H = U + n_g RT where n_g = moles of gaseous products - moles of gaseous reactants
H = U + n_g RT
Quick recall
For the reaction N_2(g) + 3H_2(g) arrow 2NH_3(g) , if H = -92.4 kJ at 298 K, find U .
n_g = 2 - (1+3) = -2 . H = U + n_g RT . -92.4 = U + (-2)(8.314 10^ -3 )(298) . -92.4 = U - 4.95 . U = -92.4 + 4.95 = -87.45 kJ.
Enthalpy Changes
Standard enthalpy changes measure heat flow for specific processes at 1 bar and a specified temperature (usually 298 K). Key types: formation (ΔH_f°), combustion (ΔH_c°), bond dissociation, atomization, ionization, electron gain, solution, hydration, and lattice enthalpy. NCERT defines each precisely — knowing the exact definition is often the entire NEET question.
_r H^ = _f H^ (products) - _f H^ (reactants)
Standard Enthalpy of Formation
ΔfH° is the enthalpy change when 1 mole of a compound is formed from its constituent elements in their standard states at the specified temperature.
The standard enthalpy of formation ( _f H^ ) is the enthalpy change when 1 mole of a compound is formed from its elements in their standard states (most stable form at 1 bar). By definition, _f H^ of any element in its standard state is zero.
_f H^ must be for forming exactly 1 mole of the compound — adjust coefficients accordingly
_f H^ of ALL elements in standard state = 0 (by convention)
The superscript means standard conditions: 1 bar pressure
Standard state does NOT mean 298 K — it's a pressure specification. Temperature must be stated separately (usually 298 K)
_r H^ = _f H^ (products) - _f H^ (reactants)
This is the most powerful formula in thermochemistry. If you know _f H^ of every species, you can calculate _r H^ for ANY reaction without knowing the mechanism.
ΔcH° is the enthalpy change when 1 mole of a substance undergoes complete combustion in excess oxygen at standard conditions. It is always negative (exothermic).
Standard enthalpy of combustion ( _c H^ ) is the enthalpy change when 1 mole of a substance is completely burned in excess O_2 under standard conditions. 'Complete' means C → CO₂, H → H₂O, S → SO₂.
_c H^ is always negative (exothermic) — burning releases heat
Must specify the physical state of water produced: H_2O(l) gives a more negative _c H^ than H_2O(g)
_c H^ values are used to calculate calorific values of fuels (kJ/g)
Calorific value = | _c H^ | molar mass
Quick recall
Can you define the enthalpy of combustion of carbon?
C(graphite) + O_2(g) arrow CO_2(g) ; _c H^ = -393.5 kJ/mol. Note: This is ALSO the enthalpy of formation of CO₂! When the combustion product is formed from its elements, _c H^ = _f H^ .
Bond Dissociation & Mean Bond Enthalpy
Bond dissociation enthalpy is the energy needed to break one mole of a specific bond in a specific molecule in the gas phase. Mean bond enthalpy is the average over multiple molecules. ΔrH° ≈ Σ(bonds broken) − Σ(bonds formed).
Breaking bonds ALWAYS requires energy (endothermic). Forming bonds ALWAYS releases energy (exothermic). The bond dissociation enthalpy is the energy to break one specific bond in one specific molecule in the gas phase (homolytic fission into neutral atoms/fragments).
_r H^ (bond enthalpies of bonds broken) - (bond enthalpies of bonds formed)
Bond dissociation enthalpy is ALWAYS positive (endothermic — energy input needed)
This formula gives approximate _r H^ because mean bond enthalpies are averages
Works best for gaseous reactions — does not account for intermolecular forces in liquids/solids
Stronger bond → higher bond enthalpy → more stable molecule
Triple bond > Double bond > Single bond (for the same pair of atoms): e.g., N N (941 kJ) > N = N (418 kJ) > N - N (163 kJ)
Other Enthalpy Types
NCERT defines several more standard enthalpy changes. Each has a precise definition and sign convention that NEET tests directly.
Beyond formation, combustion, and bond enthalpy, NCERT defines several more enthalpy changes. Each is defined per mole with specific conditions.
Atomization ( _a H^ ): Energy to convert 1 mol of a substance into gaseous atoms. Always positive. For metals: Na(s) arrow Na(g) . For molecules: H_2(g) arrow 2H(g) , _a H^ = 435.8 kJ/mol (per mole of H₂)
Sublimation ( _ sub H^ ): Solid → gas directly. Always positive. Example: H_2O(s) arrow H_2O(g)
Ionization enthalpy ( _i H ): Energy to remove 1 mol of electrons from 1 mol of gaseous atoms. Always positive. Na(g) arrow Na^+(g) + e^-
Electron gain enthalpy ( _ eg H ): Enthalpy change when 1 mol of gaseous atoms gains 1 mol of electrons. Usually negative (energy released) for halogens, but positive for noble gases and group 2
Lattice enthalpy ( _ lattice H^ ): Energy to completely separate 1 mol of ionic solid into gaseous ions. Always positive (endothermic). Higher for small, highly charged ions
Solution enthalpy ( _ sol H ): Enthalpy change when 1 mol dissolves in a specified amount of solvent. Can be positive or negative
Hydration enthalpy ( _ hyd H ): Enthalpy change when 1 mol of gaseous ions is hydrated. Always negative (exothermic)
Hess's Law & Born-Haber Cycle
Hess's law states that the total enthalpy change for a reaction is the same regardless of the route taken (because H is a state function). This allows calculating unknown ΔH values by combining known reactions. The Born-Haber cycle applies Hess's law to calculate lattice enthalpy of ionic compounds by breaking the formation into measurable steps.
_r H = H_1 + H_2 + H_3 + (regardless of path)
Hess's Law
Since enthalpy is a state function, the total ΔH for a reaction is the same whether it occurs in one step or multiple steps. This lets us combine known reactions to find unknown ΔH values.
Hess's Law of Constant Heat Summation (1840): The total enthalpy change for a reaction is independent of the pathway — it depends only on the initial and final states. This works because H is a state function.
Practical power: Many reactions can't be carried out in a calorimeter (too slow, side reactions, dangerous). But if you can break the reaction into steps whose H values ARE measurable, Hess's law lets you add them up.
If a reaction is reversed, the sign of H is reversed ( H arrow - H )
If a reaction is multiplied by a factor n , H is also multiplied by n
Hess's law is a direct consequence of enthalpy being a state function
Two main applications: (1) combining known reactions algebraically, (2) using _f H^ values via the products-minus-reactants formula
Enthalpy Diagrams
Enthalpy-level diagrams show reactants and products at different enthalpy levels. The direct path and the multi-step path both connect the same start and end points, confirming Hess's law visually.
An enthalpy diagram (or enthalpy-level diagram) places reactants and products on a vertical enthalpy axis. An exothermic reaction has products below reactants ( H < 0 , energy released). An endothermic reaction has products above reactants ( H > 0 , energy absorbed).
Downward arrow = exothermic ( H < 0 ) — system releases energy
Upward arrow = endothermic ( H > 0 ) — system absorbs energy
Multiple arrows (multi-step path) from the same start to the same end = Hess's law
The sum of all step arrows equals the single direct arrow — visually obvious from the diagram
Born-Haber Cycle
The Born-Haber cycle breaks the formation of an ionic compound (like NaCl) into measurable thermochemical steps: sublimation, ionization, dissociation, electron gain, and lattice formation. It's the standard method to determine lattice enthalpy experimentally.
The Born-Haber cycle applies Hess's law to the formation of ionic compounds. Instead of directly forming NaCl from Na(s) and Cl₂(g), we break it into five individual steps whose enthalpies are independently measurable.
Entropy (S) is a measure of the randomness or disorder of a system. ΔS = q_rev/T for a reversible process. The Second Law states that for any spontaneous process, the total entropy of the universe increases (ΔS_universe > 0). The Third Law states that the entropy of a perfectly crystalline substance at 0 K is zero.
S = q_ rev T
Entropy
Entropy (S) quantifies the degree of randomness or disorder in a system. A gas has more entropy than a liquid, which has more than a solid. Entropy is a state function measured in J/K/mol.
Entropy ( S ) is a thermodynamic quantity that measures the randomness or disorder in a system. High entropy = high disorder. A gas with molecules flying everywhere has far more entropy than a crystal where atoms sit in fixed positions.
S = q_ rev T
This defines entropy change: heat absorbed in a reversible process divided by temperature. Units: J K ^ -1 mol ^ -1 . Note: q must be for the reversible path, even if the actual process is irreversible.
S is a state function — S depends only on initial and final states
S is an extensive property — doubles when amount doubles
Entropy increases: solid → liquid → gas (more freedom of motion at each step)
Entropy increases when: temperature rises, volume increases, mixing occurs, number of moles of gas increases
Units of S : J K ^ -1 mol ^ -1 (NOT kJ — common unit mismatch trap)
Second Law of Thermodynamics
The second law says that for any spontaneous process, the total entropy of the universe (system + surroundings) increases. At equilibrium, ΔS_universe = 0. No process can decrease the total entropy of the universe.
The Second Law has many equivalent statements. The most useful for chemistry:
For a non-spontaneous process: S_ universe < 0 (it won't happen on its own)
A system's entropy CAN decrease (e.g., freezing water) — as long as the surroundings' entropy increases by MORE
S_ surroundings = - H_ system T (heat released by system is absorbed by surroundings)
Third Law of Thermodynamics
The entropy of a perfectly crystalline substance at absolute zero (0 K) is exactly zero. This provides the reference point for measuring absolute entropies.
The Third Law states: The entropy of a perfectly crystalline substance at absolute zero (0 K) is zero. At 0 K, a perfect crystal has only one possible microstate (every atom in its perfect lattice position), so the disorder is minimum = zero.
S = 0 at T = 0 K (perfect crystal)
This applies only to perfectly crystalline substances — any disorder (defects, impurities) means S > 0 even at 0 K
The third law provides the reference point for absolute entropy values (standard molar entropy, S^ )
Unlike H where only differences matter, we can know the absolute value of S at any temperature
At any T > 0 K: S > 0 (thermal motion creates disorder)
Gibbs Free Energy
Gibbs free energy G = H − TS combines enthalpy and entropy into a single criterion for spontaneity at constant T and P. A process is spontaneous when ΔG < 0, at equilibrium when ΔG = 0, and non-spontaneous when ΔG > 0. Standard Gibbs energy of formation and the relation ΔG° = −RT ln K connect thermodynamics to equilibrium.
G = H - T S
Gibbs Free Energy
G = H − TS is defined so that at constant T and P, the sign of ΔG alone determines whether a process is spontaneous. No need to separately calculate ΔS_universe.
Checking spontaneity via S_ universe > 0 requires calculating entropy changes of both system AND surroundings. Gibbs saw a shortcut: define a new function that combines both into one system-only calculation.
G = H - TS
G = H - T S (at constant T and P)
The connection to the second law: at constant T and P , G_ system = -T S_ universe . So G < 0 is exactly equivalent to S_ universe > 0 .
G < 0 → spontaneous (process occurs on its own in the forward direction)
G = 0 → equilibrium (no net change)
G > 0 → non-spontaneous (reverse process is spontaneous)
G is a state function, extensive property, units: kJ/mol
The Gibbs energy represents the maximum useful (non-expansion) work obtainable from a process: w_ useful, max = G
Standard Gibbs Energy
Standard Gibbs energy of reaction can be calculated from ΔfG° values. The powerful relation ΔG° = −RT ln K connects thermodynamics directly to the position of equilibrium.
Just like _r H^ , we can calculate standard Gibbs energy of reaction from standard Gibbs energies of formation:
_r G^ = _f G^ (products) - _f G^ (reactants)
The most powerful connection in all of chemical thermodynamics:
_r G^ = -RT K = -2.303 RT K
If G^ < 0 → K > 0 → K > 1 → products predominate at equilibrium
If G^ > 0 → K < 0 → K < 1 → reactants predominate at equilibrium
If G^ = 0 → K = 1 → neither side predominates
G^ is at standard conditions (1 bar, specified T). The actual G at non-standard conditions: G = G^ + RT Q
At equilibrium: Q = K and G = 0 (not G^ = 0 !)
Spontaneity Conditions
The spontaneity of a reaction depends on the interplay of ΔH and ΔS via ΔG = ΔH − TΔS. Four cases arise from the signs of ΔH and ΔS: always spontaneous, never spontaneous, spontaneous only at high T, or spontaneous only at low T. The crossover temperature where ΔG = 0 is T = ΔH/ΔS.
T_ crossover = H S (where G = 0)
The Four ΔH/ΔS Combinations
The sign of ΔG depends on the signs of ΔH and ΔS, and on the temperature. There are exactly four cases, and NEET loves every one of them.
Since G = H - T S , the sign of G depends on three things: the sign of H , the sign of S , and the magnitude of T . Let's map out all four combinations.
H < 0 , S > 0
Always spontaneous at all temperatures. Both factors favour the reaction. Example: combustion of fuels
H > 0 , S < 0
Never spontaneous at any temperature. Both factors oppose the reaction. Reverse reaction is always spontaneous
H < 0 , S < 0
Spontaneous at LOW temperatures where | H| > T| S| . Enthalpy-driven. Example: freezing of water below 0°C
H > 0 , S > 0
Spontaneous at HIGH temperatures where T| S| > | H| . Entropy-driven. Example: melting of ice above 0°C
This 2×2 table is the single most important table in thermodynamics for NEET
When both signs oppose each other, there's a crossover temperature T^* = H / S where G = 0
Below T^* : enthalpy term dominates. Above T^* : entropy term dominates
At T = T^* exactly: G = 0 → system is at equilibrium (phase transition point)
Temperature Dependence of Spontaneity
For reactions where ΔH and ΔS have the same sign, there exists a crossover temperature T* = ΔH/ΔS. Below this temperature, the reaction's spontaneity flips.
When H and S have the same sign, there's a temperature where enthalpy and entropy contributions exactly cancel ( G = 0 ). This is the crossover (transition) temperature:
T^* = H S
At this temperature, the system is at equilibrium. Above or below it, one direction becomes spontaneous.
T^* = H / S — units must be consistent (both in J or both in kJ)
For H < 0, S < 0 : spontaneous when T < T^* (low temperature favours enthalpy-driven process)
For H > 0, S > 0 : spontaneous when T > T^* (high temperature favours entropy-driven process)
At T = T^* : the system is at a phase transition or equilibrium point
Quick recall
For CaCO_3(s) arrow CaO(s) + CO_2(g) : H = +178.3 kJ/mol, S = +160.4 J/K/mol. Above what temperature does this become spontaneous?
T^* = H S = 178.3 10^3 160.4 = 1112 K = 839°C. Above 839°C, limestone decomposes spontaneously. This is why cement kilns operate at ~1000°C.
Equilibrium from a Thermodynamic View
At equilibrium, ΔG = 0 (not ΔG°). The system has no net tendency to move in either direction. This connects to the equilibrium constant K through ΔG° = −RT ln K.
Chemical equilibrium is the state where the Gibbs energy of the system is at its minimum for the given T and P . At this point, G = 0 — there is no thermodynamic driving force in either direction.
At equilibrium: G = 0 , Q = K , S_ universe = 0
G^ = -RT K determines the position of equilibrium
If we start with pure reactants ( Q = 0 ): G < 0 , reaction proceeds forward
If we start with pure products ( Q = ): G > 0 , reaction proceeds backward
The reaction always moves toward the minimum of the G vs extent-of-reaction curve