Revision: Class 11 >> Chemical Thermodynamics NEET (UG) Chemical Thermodynamics

The study of the relationships between work, temperature, heat, energy, radiation, and the physical characteristics of matter is known as thermodynamics.

A system, in thermodynamics, refers to that part of the universe in which observations are made.

The remaining part of the universe without the system is called the surroundings.

The thermodynamic state variables that depend on the size of the system (e.g., internal energy, volume) are called extensive variables.

The thermodynamic state variables that do not depend on the size of the system (e.g., pressure, temperature) are called intensive variables.

The specific values of macroscopic variables that completely describe every equilibrium state of a thermodynamic system are called thermodynamic state variables.

The total heat content of a system at constant pressure is known as enthalpу.

At constant pressure: ΔH = q_p​ (heat exchanged at constant pressure).

The enthalpy of neutralization is defined as the change in enthalpy of the system when one gram equivalent of an acid is neutralized by one gram equivalent of a base or vice versa in dilute solution.

\[\ce{H^+_{(aq)} + OH^-_{(aq)} -> H2O_{(l)}}\] = 57.32 kJ

The heat of combustion of a substance is defined as “The change in enthalpy of a system when one mole of the substance is completely burnt in excess of air or oxygen”. It is denoted by ∆H_C.

Enthalpy of a system is sum of internal energy of a system and the energy equivalent to PV work.

H = U + PV

It is the enthalpy change associated with diluting a component in a solution at constant pressure and temperature.

It is the enthalpy change during the hydration of 1 mole of anhydrous salt by the addition of a specific number of moles of water.

It is defined as the change in heat enthalpy when one mole of a substance is completely burnt in oxygen.

ΔΗ = Σ (Heat of Combustion of reactant)- Σ (Heat of Combustion of product)

It is defined as the heat evolved or decrease in enthalpy when 1 gm equivalent of an acid is neutralised by 1 gm equivalent of a base in solution.

It is the enthalpy change when one mole of it dissolves in a specified amount of solvent

The heat capacity for 1 mole of a substance, is called molar heat capacity (cm). It is defined as “The amount of heat absorbed by one mole of the substance to raise its temperature by 1 kelvin”.

A useful state variable that measures the change in heat divided by the temperature of the system, where the combined entropy of the system and its environment remains constant if the process approaches reversibility, is called entropy.

By substituting equation W = −p_ex . ΔV in the equation ΔU = q + W, we get

ΔU = q − p_ex . ΔV  ...(1)

If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.

The equation (1) becomes ΔU = q_v

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.

\[\Delta_rH^\circ=\sum\Delta_fH_{(products)}^\circ-\sum\Delta_fH_{(reactants)}^\circ\]

ΔS = \[\frac {ΔQ}{T}\]

By substituting equation W = −p_ex . ΔV in the equation ΔU = q + W, we get

ΔU = q − p_ex . ΔV  ...(1)

If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.

The equation (1) becomes ΔU = q_v

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.

Statement:
The net heat energy supplied to a system is equal to the sum of the change in internal energy of the system and the work done by the system. It is based on the law of conservation of energy.

Formula:

where Q = heat added, ΔU = change in internal energy, W = work done by the system.

The law states that, “Overall, the enthalpy change for a reaction is equal to the sum of enthalpy changes of individual steps in the reaction”.

The enthalpy change for a chemical reaction is the same regardless of the pathway taken during the reaction. Hess’s law is a direct result of the principle that enthalpy is a state function. The enthalpy change of a reaction depends only upon the initial and final states, independent of the reaction path.

To determine the overall reaction equation, the reactants and products from the different steps are combined or subtracted as algebraic entities.

Consider the synthesis of NH₃:

i. \[\ce{\phantom{...}2H2_{(g)} + N2_{(g)} -> N2H4_{(g)}, \Delta_rH^0_1 = +95.4 kJ}\]
ii. \[\ce{N2H4_{(g)} + H2_{(g)} -> 2NH3_{(g)}, \Delta_rH^0_2 = -187.6 kJ}\]
_______________________________________________
\[\ce{\phantom{.....}3H2_{(g)} + N2_{(g)} -> 2NH3_{(g)}}\], Δ_rH⁰ = −92.2 kJ

The sum of the enthalpy changes for steps (i) and (ii) is equal to the enthalpy change for the overall reaction.

Statement: If a reaction takes place in several steps, its standard reaction enthalpy is equal to the sum of the standard enthalpies of all the intermediate steps into which the overall reaction can be divided, at the same temperature.

Note: Since enthalpy is a state function, the total enthalpy change is independent of the pathway — only the initial and final states matter.

Application: 

\[\Delta_rH^\circ=\Delta_rH_1^\circ+\Delta_rH_2^\circ+\Delta_rH_3^\circ+\ldots\]

The second law of thermodynamics states that the total entropy of a system and its surroundings increases in a spontaneous process.

Mathematically,

ΔS_total = `Delta S_"system" + Delta S_"surroundings" gt 0`

For an equilibrium:

ΔS_total = 0

The third law of thermodynamics states that the entropy of a pure crystalline substance at absolute zero is zero. Otherwise, it can be stated that it is impossible to lower the temperature of an object to absolute zero in a finite number of steps. Mathematically,

`lim_(T->0)` S = 0 for a perfectly ordered crystalline state.

The state of a system is described by its measurable macroscopic properties, such as temperature (T), pressure (P), volume (V), and amount of substance (n).

State Variables / State Functions:

• Properties whose values depend only on the current state of the system, not on how that state was reached.
• Examples: T, P, V, U (internal energy), H (enthalpy), S (entropy), G (Gibbs energy)

Non-State Functions (Path Functions):

• Their values depend on the path followed
• Examples: Work (W), Heat (q)

Note: Enthalpy (H = U + PV) and Gibbs energy (G = H − TS) are state functions. Work (W) and heat (q) are path functions.

Reversible vs. Irreversible Processes:

First Law: Energy of system + surroundings remains constant → ΔU = q + W

ΔU: change in internal energy, q: heat, W: work done on system

Sign convention:

• Work by system (−)
• on system (+)
• Heat absorbed (+)
• released (−)

ΔU > 0: energy enters system; ΔU < 0: energy leaves system

• Isothermal: ΔU = 0 → q = −W
• Adiabatic: q = 0 → ΔU = W
• Isochoric: W = 0 → ΔU = q
• Isobaric: ΔU = q + W

• Every substance possesses a definite amount of energy.
• This energy stored within a substance is called internal energy (U).
• Internal energy is the sum of kinetic energy and potential energy of all the particles in the system.
• Change in internal energy is given by:
  ΔU = U₂ − U₁

• Enthalpy change when 1 mole of a compound is formed from its constituent elements in their standard states.
• Standard enthalpy of formation of elements in their most stable form = zero (e.g., graphite, not diamond, for carbon).
• Δ_f H^∘ can be positive or negative.

Thermochemical Equations: Balanced equations that include the physical states and the enthalpy change. Example:

Entropy (ΔS) is a thermodynamic property that measures the degree of randomness, disorder, or energy dispersal in a system. Higher entropy means greater disorder.

• For any process, the total entropy change is given by:
  ΔS_total = ΔS_system + ΔS_surroundings
• A process is spontaneous if the total entropy of the universe increases, i.e., ΔS_total > 0
• If ΔS_total < 0, the process is non-spontaneous and cannot occur on its own.
• At equilibrium, there is no net change, so ΔSₜₒₜₐₗ = 0
• Processes such as melting, vaporisation, or mixing generally increase entropy and are therefore more likely to be spontaneous.

Entropy is influenced by:

• Physical state (gas > liquid > solid)
• Number of particles
• Temperature (higher T → higher disorder)

Gibbs free energy (ΔG) is a thermodynamic quantity that determines spontaneity at constant temperature and pressure.

It is defined as: ΔG = ΔH − TΔS, 
where ΔH = enthalpy change, T = temperature, and ΔS = entropy change.

• A process is spontaneous when ΔG < 0 because free energy is released.
• If ΔG > 0, the process is non-spontaneous and requires external energy.
• At equilibrium, ΔG = 0 and no net change occurs in the system.

Temperature plays a key role when ΔH and ΔS have the same sign:

• ΔH < 0 and ΔS > 0 → always spontaneous
• ΔH > 0 and ΔS < 0 → never spontaneous
• ΔH < 0 and ΔS < 0 → spontaneous at low T
• ΔH > 0 and ΔS > 0 → spontaneous at high T

Gibbs free energy combines both enthalpy (heat changes) and entropy (disorder), making it a more practical criterion than entropy alone.

Entropy (S): A thermodynamic property that measures the degree of randomness or disorder of a system.

\[\Delta S=\frac{q_{rev}}{T}\]

Second Law: The entropy of the universe always tends to increase during any spontaneous process.

Total entropy change:

Entropy of mixing:

(ΔS for mixing is always positive, since ΔS is always fractional/positive)

Third Law: The entropy of a perfectly ordered crystalline substance at absolute zero (0 K) is zero.

Absolute Entropy (Standard Molar Entropy, S°): The entropy value of a substance at 298 K and 1 bar pressure, relative to 0 K.

• Unlike the enthalpy of formation, the absolute entropy of elements is not zero at standard conditions.
• Standard entropy of reaction: \[\Delta_{r}S^{\circ}=\sum S_{products}^{\circ}-\sum S_{reactants}^{\circ}\]

Relationship between ΔG° and equilibrium constant K:

Interpretation:

• If K > 1 → ΔG° < 0 → forward reaction favoured
• If K < 1 → ΔG° > 0 → reverse reaction favoured
• If K = 1 → ΔG° = 0 → equilibrium

At equilibrium: ΔG = 0 (not ΔG°)