Revision: Chemical Thermodynamics JEE Main 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 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”.

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

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. \[\ce{N2H4_{(g)} + H2_{(g)} -> 2NH3_{(g)}, \Delta_rH^0_2 = -187.6 kJ}\]
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\[\ce{\phantom{.....}3H2_{(g)} + N2_{(g)} -> 2NH3_{(g)}}\], 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 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.

• 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.

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°)