Enthalpy

Definition and Concept

Basic Idea

Enthalpy (H): thermodynamic state function. Represents total heat content of a system at constant pressure. Combines internal energy (U) and product of pressure (P) and volume (V).

Historical Context

Concept introduced by Heike Kamerlingh Onnes (1909). Developed to simplify heat transfer calculations at constant pressure. Widely used in chemistry and engineering.

Physical Interpretation

Heat absorbed or released in processes at constant pressure equals enthalpy change (ΔH). Provides direct insight into reaction energetics and phase changes.

Mathematical Formulation

Definition Equation

H = U + PV

Differential Form

dH = dU + PdV + VdP

First Law Relation

From first law: dU = δQ - PdV (for reversible processes). Substitute in dH:

dH = δQ + VdP

At constant pressure (dP=0), dH = δQ (heat exchanged).

Thermodynamic Properties

State Function

Depends only on current state, independent of path. Enables use in Hess's law and other state function-based calculations.

Extensive Property

Proportional to system size or amount of substance. Doubling quantity doubles enthalpy.

Units and Dimensions

SI unit: joule (J). Also expressed in calories (cal), kilowatt-hours (kWh) in applied contexts.

Enthalpy Change (ΔH)

Definition

ΔH = H_final - H_initial. Represents heat absorbed or released at constant pressure.

Sign Conventions

ΔH < 0: exothermic process (releases heat). ΔH > 0: endothermic process (absorbs heat).

Calculation Methods

Direct measurement via calorimetry. Indirect calculation via Hess's law or standard enthalpies of formation.

Measurement Methods

Calorimetry

Directly measures heat exchange at constant pressure. Types: coffee-cup, bomb, differential scanning calorimetry (DSC).

Indirect Methods

Use Hess's law with known standard enthalpies. Apply thermodynamic cycles for complex reactions.

Experimental Considerations

Accuracy depends on insulation, pressure constancy, and calibration. Corrections applied for non-idealities.

Applications

Chemical Thermodynamics

Determines reaction energetics, spontaneity, and equilibrium positions.

Phase Transitions

Calculates enthalpy of fusion, vaporization, sublimation. Essential in material science and meteorology.

Engineering

Design of engines, turbines, HVAC systems. Evaluates energy efficiency and heat exchange processes.

Relation to Other Thermodynamic Potentials

Internal Energy (U)

H = U + PV links enthalpy to internal energy plus work done by system expansion.

Gibbs Free Energy (G)

G = H - TS. Combines enthalpy with entropy and temperature to predict spontaneity under constant pressure and temperature.

Helmholtz Free Energy (A)

Less directly related; defined as A = U - TS. Enthalpy incorporates pressure-volume work absent in A.

State Function Characteristics

Path Independence

Enthalpy depends solely on system state variables: pressure, temperature, composition.

Implications

Enables summation of enthalpy changes over multiple steps regardless of reaction path.

Thermodynamic Consistency

Allows use in Maxwell relations and other thermodynamic identities involving state variables.

Hess's Law and Enthalpy

Statement

Total enthalpy change for a process is sum of enthalpy changes of intermediate steps.

Practical Use

Calculate difficult-to-measure ΔH by combining known reactions with tabulated enthalpy changes.

Example

Calculate combustion enthalpy of compound via formation enthalpies of reactants and products.

Standard Enthalpy Values

Standard State Definition

Pure substances at 1 bar pressure, defined temperature (usually 25°C or 298.15 K).

Standard Enthalpy of Formation (ΔHf°)

Change in enthalpy when one mole of compound forms from elements in standard states.

Tabulated Data

Used as reference for calculating reaction enthalpies and thermodynamic properties.

Enthalpy in Chemical Reactions

Reaction Enthalpy

Heat absorbed or released during chemical transformation at constant pressure.

Exothermic vs Endothermic

Exothermic: ΔH negative, heat released. Endothermic: ΔH positive, heat absorbed.

Calculation from Standard Enthalpies

ΔH_reaction = Σ ΔHf° (products) - Σ ΔHf° (reactants)

Thermodynamic Cycles

Purpose

Calculate enthalpy changes for complex reactions or phase changes indirectly.

Born-Haber Cycle

Determines lattice enthalpy of ionic solids via formation enthalpies and ionization energies.

Other Cycles

Hess cycles, refrigeration cycles, Rankine cycle use enthalpy for energy balance calculations.

References

• Atkins, P., & de Paula, J., Physical Chemistry, 10th Ed., Oxford University Press, 2014, pp. 120-150.
• Smith, J.M., Van Ness, H.C., Abbott, M.M., Introduction to Chemical Engineering Thermodynamics, 7th Ed., McGraw-Hill, 2005, pp. 200-245.
• Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, 2nd Ed., Wiley, 1985, pp. 80-110.
• Laidler, K.J., Meiser, J.H., Physical Chemistry, 3rd Ed., Benjamin/Cummings, 1982, pp. 310-340.
• Levine, I.N., Physical Chemistry, 6th Ed., McGraw-Hill, 2009, pp. 500-530.