Enthalpy Change, ΔrH of a Reaction – Reaction Enthalpy

Full Notes

Introduction

Chemical reactions are almost always accompanied by energy changes, usually in the form of heat. The enthalpy change of reaction (Δ_rH) refers to the heat absorbed or released when a chemical reaction occurs at constant pressure.

The enthalpy change of a chemical reaction, is given by the symbol ∆_rH

To standardise measurements, these enthalpy changes are commonly reported under standard conditions (298 K, 1 atm, 1 M concentration), and are called standard reaction enthalpies, symbolised as Δ_rH^° (Standard conditions are denoted by adding the superscript ^° to the symbol ∆H)

Standard Enthalpy of Reactions (Δ_rH^°)

The standard enthalpy of reaction is the enthalpy change when all reactants and products are in their standard states.

For Example The Combustion of Methane:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
Δ_rH^° = −890.3 kJ mol⁻¹

• Negative sign: exothermic reaction
• Positive sign: endothermic reaction

The magnitude of Δ_rH depends on the physical state of reactants/products and conditions.

Enthalpy Changes during Phase Transformations

Enthalpy also changes during physical changes, particularly phase transitions. These include:

• Fusion (melting):
  Example H₂O(s) → H₂O(l); Δ_fusH = +6.0 kJ mol⁻¹ (energy absorbed to overcome lattice forces)
• Vaporisation:
  Example H₂O(l) → H₂O(g); Δ_vapH = +44.0 kJ mol⁻¹
  (energy needed to break intermolecular forces)
• Sublimation:
  Example I₂(s) → I₂(g); Δ_subH = +62.39 kJ mol⁻¹

These values are always per mole of substance and are positive (endothermic), because energy is required to overcome attractive forces.

Standard Enthalpy of Formation (Δ_fH^°)

Standard Enthalpy of Formation (Δ_fH^°) is the enthalpy change when 1 mole of a compound is formed from its elements, with all substances in their standard states.

Examples:

C(s) + O₂(g) → CO₂(g); Δ_fH^° = −393.5 kJ mol⁻¹
½H₂(g) + ½Cl₂(g) → HCl(g); Δ_fH^° = −92.3 kJ mol⁻¹

By convention, the standard enthalpy of formation of elements in their most stable form is zero.
E.g., Δ_fH^° of O₂(g) = 0, H₂(g) = 0, C(s) (graphite) = 0

Thermochemical Equations

A thermochemical equation is a balanced chemical equation that includes the enthalpy change (Δ_rH).

The enthalpy change given refers to when reactants react in the molar ratios given in the balanced equation.

For example:

H₂(g) + ½O₂(g) → H₂O(l)
Δ_rH = −285.8 kJ mol⁻¹

Key features:

• States of all substances are specified (g, l, s, aq)
• The sign and magnitude of enthalpy are mentioned
• If you reverse the reaction, sign of ΔH changes
• If you multiply the equation, multiply ΔH too

Hess’s Law of Constant Heat Summation

Hess’s Law states:

‘if a reaction takes place in several steps then its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.’ (NCERT definition)

or we can re-write that as:

“The total enthalpy change for a reaction is the same whether it occurs in one step or through multiple steps.”

This principle is based on the fact that enthalpy is a state function—it depends only on initial and final states, not the path taken.

Hess’s Law and Enthalpy Cycles:

Hess’s Law is useful when directly measuring an enthalpy change is difficult. Instead, we use enthalpy cycles to calculate it indirectly.

For example the reaction of A + B to form X + Y can be found using reactions of A + B to D + E (ΔH 1) and from X + Y + C to D + E (ΔH2).

Example (based on the NCERT textbook example, Page 143):
Calculate ΔH for:
C(graphite) + ½O₂(g) → CO(g)

Given:

C(graphite) + O₂(g) → CO₂(g); ΔH = −393.5 kJ
CO(g) + ½O₂(g) → CO₂(g); ΔH = −283.0 kJ

Reverse the second equation:
CO₂(g) → CO(g) + ½O₂(g); ΔH = +283.0 kJ

Now add:

C(graphite) + O₂(g) → CO₂(g); ΔH = −393.5 kJ
CO₂(g) → CO(g) + ½O₂(g); ΔH = +283.0 kJ

C(graphite) + ½O₂(g) → CO(g); ΔH = −110.5 kJ

Thus, Hess’s Law lets us calculate ΔH values indirectly when direct measurement isn’t possible.

Summary

• Δ_rH is the heat change at constant pressure for a reaction
• Standard reaction enthalpy uses 298 K and 1 atm
• Phase changes have characteristic enthalpy values per mole
• Δ_fH^° is for forming 1 mole from elements in standard states
• Thermochemical equations show balanced states and ΔH
• Hess’s Law uses state function property to add enthalpies