Revision: Std XII >> Chemical Thermodynamics MAH-MHT CET (PCM/PCB) Chemical Thermodynamics

The study of heat and other forms of energy entering or leaving the system due to physical or chemical transformations is called thermodynamics.

A property which is independent of the amount of matter in a system is called an intensive property.
e.g., pressure, temperature.

A property that depends on the state of a system and is independent of the path taken to reach that state is called a state function.

A property that depends on the amount of matter present in a system is called an extensive property.
Example: mass, volume.

A closed system is one that is able to interchange energy but not matter with its surroundings.

A process in which there is no exchange of heat between the system and surroundings is an adiabatic process, or Q = 0.

In isobaric process the pressure remains constant during the transformation.

A quasi-static process is an infinitely slow process in which the system changes its variables (P, V, T) so slowly such that it remains in thermal, mechanical, and chemical equilibrium with its surroundings throughout.

One calorie is defined as the amount of heat energy needed to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere.

The internal energy of a thermodynamic system is the sum of kinetic and potential energies of all the molecules of the system with respect to the center of mass of the system.

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

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.

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.

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

H = U + PV

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

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

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

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

The enthalpy change accompanying the dissociation of one mole of gaseous substance into atoms is called enthalpy of atomization.

The enthalpy change that accompanies the solidification of one mole of a liquid into a solid at constant temperature and pressure is called the enthalpy of freezing.

Enthalpy of vaporization is the enthalpy change accompanying the vaporization of one mole of liquid without changing its temperature at constant pressure.

Enthalpy of sublimation is the enthalpy change for the conversion of one mole of solid directly into vapour at constant temperature and pressure.

The standard enthalpy of formation of a compound is the enthalpy change that accompanies a reaction in which one mole of pure compound in its standard state is formed from its elements in their standard states.

The standard enthalpy of combustion of a substance is the standard enthalpy change accompanying a reaction in which one mole of the substance in its standard state is completely oxidised.

The enthalpy change required to break a particular covalent bond in one mole of the gaseous molecule to produce gaseous atoms and/or radicals is called bond enthalpy.

Enthalpy of ionization is the enthalpy change accompanying the removal of an electron from one mole of a gaseous atom.

The maximum amount of energy available to a system during a process that can be converted into useful work is called the Gibbs free energy. 

It is given as, ΔG = ΔH – TΔS

where,

• ΔG = change in Gibbs energy
• ΔH = change in enthalpy
• ΔS = change in entroру.

Entropy (S) is defined more precisely as a thermodynamic state function that measures the degree of randomness or disorder of the particles in a system.

Second law of thermodynamics: In a spontaneous process, the overall entropy of the system and its surroundings grows.

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.

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 entropy of the universe keeps increasing and tends to reach a maximum.

Total entropy change:
ΔS_universe = ΔS_system + ΔS_surroundings > 0

• ΔS_total > 0 → Process is spontaneous
• ΔS_total < 0 → Process is non-spontaneous
• ΔS_total = 0 → System is at equilibrium

Basic Terms:

• System: The specific part of the universe selected for study in thermodynamics
• Surroundings: Everything outside the system
• Boundary: Surface separating system & surroundings

Types of System:

• Open: Matter + Energy exchange (Δm ≠ 0, ΔE ≠ 0)
• Closed: Only Energy exchange (Δm = 0, ΔE ≠ 0)
• Isolated: No exchange (Δm = 0, ΔE = 0)

Properties:

• Extensive: Properties whose magnitude depends on the amount of matter → Mass, Volume
• Intensive: Properties independent of the amount of matter→ Temperature, Pressure

Functions:

• State Function: Depends only on state → P, V, T, U, H, G, S
• Path Function: Depends on path → Heat (q), Work (W)

Thermodynamic Processes:

• Adiabatic: Process in which no heat exchange occurs → dq = 0
• Isothermal: Process carried out at constant temperature → dT = 0
• Isobaric: Process carried out at constant pressure → dP = 0
• Isochoric: Process carried out at constant volume → dV = 0

Other Processes:

• Reversible: Process which occurs infinitely slowly and can be reversed by small changes
• Irreversible: Process which cannot be reversed completely

• Work is done during expansion or compression against external pressure and is a path function.
• Formula: W = −P_ext ΔV
• Heat is the transfer of energy between a system and its surroundings.
• Heat is also a path function (depends on the path followed).
• q > 0 when heat is absorbed by system; q < 0 when heat is released.
• Both heat and work are modes of energy transfer, not state functions.

Work in Isothermal Reversible Process

\[W_{rev}=-2.303nRT\log_{10}\frac{V_2}{V_1}\]

Or equivalently using Boyle's law (at constant T):

\[W_{rev}=-2.303nRT\log_{10}\frac{P_1}{P_2}\]

Where: n = number of moles; R = gas constant; T = absolute temperature (K); V₁, V₂ = initial and final volumes; P₁, P₂ = initial and final pressures.

Work in Isothermal Irreversible Process:

• Expansion: ΔV > 0 → W_expansion is positive (work done by system → negative sign)

• Contraction: ΔV < 0 → W_contraction is positive

Work in Free Expansion-

When a gas expands into a vacuum (P_ext = 0): W = 0

No work is done, regardless of whether the process is reversible or irreversible.

For maximum work, the external pressure must be infinitesimally smaller than the internal pressure of the gas (near-reversible conditions).

The maximum work is obtained only from a thermodynamically reversible change.

Every system is associated with a definite amount of energy stored in it, called its internal energy (U). It is the sum of all forms of kinetic and potential energies of the particles in the system.

• Internal energy is a state function — its change depends only on initial and final states.
• It is an extensive property.

Internal energy changes when:

• Heat flows into or out of the system
• Work is done on or by the system
• Matter enters or leaves the system

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

• Thermochemistry deals with heat energy changes during chemical reactions
• Enthalpy change (ΔH) = difference between products and reactants → ΔH = H_p − H_r
• Exothermic reactions: ΔH < 0, heat is released to the surroundings
• Endothermic reactions: ΔH > 0, heat is absorbed by the system
• Standard enthalpy (ΔH°) measured at 298 K and 1 bar pressure
• Enthalpy of formation (Δ_fH°): formation of 1 mole; for elements = 0
• Enthalpy of combustion (Δ_cH°): always negative (heat released)
• Bond enthalpy: energy required to break bonds in the gaseous state
• Reaction enthalpy using bond energy:
  Δ_rH° = ΣBE(reactants) − ΣBE(products)
• Hess’s Law: total ΔH is the same for any path → ΔH = sum of individual steps

• Spontaneous processes are those that occur naturally without any external force. They proceed in one direction and cannot be reversed unless an external influence is applied.
• Entropy is a measure of disorder or randomness in a system. Greater disorder means higher entropy.
• Entropy and spontaneity: In a spontaneous process, the entropy of the system tends to increase.