Enthalpy

Definition and Concept

Thermodynamic State Function

Enthalpy (H): extensive thermodynamic property. Defined for systems at constant pressure. Represents total heat content. State function: depends only on current state, not path.

Physical Meaning

Quantifies heat exchanged during processes at constant pressure. Accounts for internal energy and work done by system expanding against pressure.

Historical Context

Introduced by Heike Kamerlingh Onnes (1909). Developed to simplify thermodynamic calculations involving heat transfer and work.

Mathematical Formulation

Basic Definition

Enthalpy defined as:

H = U + PV

Where: H = enthalpy, U = internal energy, P = pressure, V = volume.

Differential Form

For infinitesimal changes:

dH = dU + PdV + VdP

Relation to Heat

At constant pressure (dP = 0), heat absorbed or released (q_p) equals enthalpy change:

q_p = ΔH

Thermodynamic Properties

Extensive and State Function

Extensive: depends on amount of substance. State function: independent of path taken.

Units and Dimensions

SI unit: joule (J). Commonly kcal/mol or kJ/mol in chemistry.

Dependence on Variables

Depends on pressure, temperature, and composition. Typically expressed as H(P,T).

Enthalpy Changes in Processes

Isobaric Processes

Constant pressure. Enthalpy change equals heat exchanged:

ΔH = q_p

Phase Changes

Enthalpy changes during melting, vaporization, sublimation quantify latent heat.

Chemical Reactions

Enthalpy change reflects energy absorbed or released. Exothermic: ΔH < 0, endothermic: ΔH > 0.

Measurement Techniques

Calorimetry

Direct measurement of heat exchange. Types: constant pressure, constant volume calorimeters.

Bomb Calorimeter

Measures internal energy change at constant volume. Used to calculate ΔH indirectly.

Indirect Methods

Use Hess’s law or Kirchhoff’s equations to determine enthalpy changes from known data.

Applications of Enthalpy

Chemical Engineering

Design of reactors, heat exchangers. Energy balance calculations.

Thermodynamics of Phase Equilibria

Prediction of phase transitions, vapor pressure, boiling point.

Biochemical Systems

Protein folding, enzyme catalysis energetics, metabolic pathways.

Enthalpy and Chemical Reactions

Reaction Enthalpy (ΔH_rxn)

Amount of heat absorbed or evolved at constant pressure during reaction.

Standard Enthalpy Change

Measured under standard conditions (1 bar, 25°C). Denoted ΔH°.

Hess’s Law

Total enthalpy change independent of reaction path. Enables calculation from multiple steps.

Standard Enthalpy Values

Standard Enthalpy of Formation (ΔH_f°)

Enthalpy change to form 1 mole of compound from elements in standard states.

Standard Enthalpy of Combustion (ΔH_c°)

Heat released when 1 mole of substance combusts in oxygen under standard conditions.

Tabulated Data

Reference tables provide values for numerous compounds and elements.

Enthalpy vs Internal Energy

Definition Differences

Internal energy (U): total energy of system excluding PV work. Enthalpy (H): includes PV work term.

Physical Interpretation

U relates to microscopic energy. H relates to heat flow at constant pressure.

Mathematical Relation

H = U + PV

Useful distinction in open vs closed systems, reaction energetics.

Calorimetry and Enthalpy

Constant Pressure Calorimetry

Measures heat flow directly related to ΔH. Examples: coffee cup calorimeter.

Constant Volume Calorimetry

Measures internal energy change (ΔU). Requires correction for PV work to find ΔH.

Calculations and Corrections

Apply equations to convert measured quantities to enthalpy changes.

ΔH = ΔU + Δ(PV)

Thermodynamic Cycles

Hess’s Law Application

Calculate ΔH for complex reactions by summing steps.

Born-Haber Cycle

Determines lattice enthalpy from formation enthalpies and ionization energies.

Enthalpy in Engine Cycles

Evaluates energy efficiency and heat transfer in Carnot, Rankine cycles.

Limitations and Assumptions

Constant Pressure Approximation

ΔH = q_p only valid at constant pressure. Deviations occur under variable pressure.

Ideal Gas Assumptions

Often assumed for gases. Real gases show deviations affecting enthalpy calculations.

Neglect of Non-PV Work

Enthalpy formulation excludes electrical, magnetic, or surface work contributions.

References

• Atkins, P., de Paula, J., Physical Chemistry, 10th Ed., Oxford University Press, 2014, pp. 150-185.
• Smith, J.M., Van Ness, H.C., Abbott, M.M., Introduction to Chemical Engineering Thermodynamics, 7th Ed., McGraw-Hill, 2005, pp. 120-165.
• Laidler, K.J., Meiser, J.H., Physical Chemistry, 3rd Ed., Benjamin Cummings, 1999, pp. 210-245.
• Hepler, L.G., "Enthalpy and Thermodynamic Functions," Journal of Chemical Education, vol. 50, 1973, pp. 183-187.
• Levine, I.N., Physical Chemistry, 6th Ed., McGraw-Hill, 2009, pp. 192-225.