Enthalpy

Definition and Concept

Thermodynamic Quantity

Enthalpy (H): total heat content of a system at constant pressure. Expresses energy stored as internal energy plus pressure-volume work.

Formal Definition

H = U + PV, where U = internal energy, P = pressure, V = volume. State function dependent on state variables.

Physical Meaning

Represents energy available for heat exchange during processes at constant pressure. Simplifies heat transfer calculations.

Thermodynamic Properties

State Function

Path independent: depends only on initial and final states, not on process path.

Extensive Property

Proportional to system size or amount of substance.

Relation to Internal Energy

Includes work done by expansion/compression at constant pressure.

Enthalpy Change (ΔH)

Definition

ΔH = H_products − H_reactants. Represents heat absorbed or released at constant pressure.

Sign Conventions

ΔH < 0: exothermic (heat released). ΔH > 0: endothermic (heat absorbed).

Relation to Heat Transfer

At constant pressure, ΔH equals heat exchanged: q_p = ΔH.

Measurement and Units

Units

SI unit: joule (J). Commonly kilojoule (kJ) in chemistry.

Calorimetry

Indirect measurement via calorimeters: measure temperature change to calculate heat exchange.

Experimental Setup

Constant pressure calorimeters: coffee cup calorimeter, bomb calorimeter (constant volume, then convert).

Types of Enthalpy Changes

Enthalpy of Reaction (ΔH_rxn)

Heat change during a chemical reaction.

Enthalpy of Formation (ΔH_f)

Heat change when 1 mole of compound forms from elements in standard states.

Enthalpy of Combustion (ΔH_c)

Heat released when 1 mole of substance combusts completely in oxygen.

Enthalpy of Vaporization/Fusion/Sublimation

Heat required for phase transitions at constant pressure.

Enthalpy and State Functions

Path Independence

ΔH does not depend on reaction pathway, only initial/final states.

Implications for Calculations

Enables use of Hess's Law to determine ΔH for complex reactions.

Mathematical Expression

ΔH = ∑ΔH_steps; sum of enthalpy changes for sequential steps equals total change.

Calorimetry

Principle

Heat exchange measured by temperature changes in a known mass with known heat capacity.

Heat Capacity

q = mcΔT; q = heat absorbed/released, m = mass, c = specific heat capacity, ΔT = temperature change.

Types

Coffee cup calorimeter: constant pressure. Bomb calorimeter: constant volume, conversion needed.

Hess's Law

Statement

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

Utility

Allows calculation of ΔH for reactions difficult to measure directly.

Example

CH4 + 2O2 → CO2 + 2H2OΔH_total = ΔH1 + ΔH2 (via intermediate reactions)

Enthalpy and Phase Changes

Enthalpy of Fusion (ΔH_fus)

Heat required to convert 1 mole of solid to liquid at melting point.

Enthalpy of Vaporization (ΔH_vap)

Heat required to convert 1 mole of liquid to vapor at boiling point.

Enthalpy of Sublimation (ΔH_sub)

Heat required to convert 1 mole of solid directly to vapor.

Standard Enthalpy Changes

Standard State Definition

Pure substance at 1 atm pressure and specified temperature (usually 25°C).

Standard Enthalpy of Formation (ΔH°_f)

Enthalpy change for forming 1 mole of compound from elements in standard states.

Standard Enthalpy of Reaction (ΔH°_rxn)

Sum of standard enthalpies of formation of products minus reactants.

ΔH°_rxn = ∑ n_p ΔH°_f(products) − ∑ n_r ΔH°_f(reactants)

Applications in Chemistry

Reaction Energetics

Predicts exothermic/endothermic nature, feasibility of reactions.

Thermodynamic Calculations

Used in Gibbs free energy calculations: ΔG = ΔH − TΔS.

Industrial Processes

Design of reactors, energy management, safety assessments.

Limitations and Considerations

Pressure Dependence

Strictly defined at constant pressure; variable pressure complicates interpretation.

Temperature Dependence

ΔH varies with temperature; standard values referenced at 25°C.

Non-ideal Systems

Assumes ideal behavior; deviations in real systems may occur.

References

• Atkins, P.; de Paula, J. Physical Chemistry, 10th Ed., Oxford University Press, 2014, pp. 120-160.
• Laidler, K.J.; Meiser, J.H.; Sanctuary, B.C. Physical Chemistry, 4th Ed., Houghton Mifflin, 2003, pp. 200-245.
• Chang, R. Chemistry, 12th Ed., McGraw-Hill, 2010, pp. 310-350.
• McQuarrie, D.A.; Simon, J.D. Physical Chemistry: A Molecular Approach, University Science Books, 1997, pp. 260-300.
• Silberberg, M.S. Chemistry: The Molecular Nature of Matter and Change, 7th Ed., McGraw-Hill, 2012, pp. 400-450.