Hess's Law: Why Heat of Reaction Does Not Care About the Path

Can you find the enthalpy change of a reaction that cannot be carried out directly in the lab? Yes, by using Hess's law of constant heat summation, stated in 1840 by Germain Henri Hess, a Swiss-born chemist working in Russia. The law says that the total heat change in a chemical reaction is the same whether it takes place in one step or in several steps. It is a statement of the conservation of energy, written before the first law of thermodynamics was properly formulated. For students it is one of the most useful tools in thermochemistry, appearing in Boards, JAM, NET and GATE every year.

The Scientific Problem Before the Discovery

In the 1830s heat was thought by many to be a fluid called "caloric". Lavoisier and Laplace had measured heats of combustion with an ice calorimeter, but the results were not organised. Many reactions cannot be measured directly. For example, when carbon burns in a limited supply of oxygen, it gives a mixture of CO and CO₂, so the heat for C → CO cannot be found with a calorimeter. Another case is the formation of methane from carbon and hydrogen, which does not go directly.

Chemists needed a general principle to relate the heats of different reactions. Hess provided that principle by careful experiments on the heat released when substances combined in different ways.

The Discovery: Hess's Experiments

Hess studied the heat evolved when sulfuric acid was mixed with water in different proportions and when it was neutralised by bases such as ammonia. He found that the total heat released when acid was combined with ammonia was the same, whether the acid was first diluted in stages or neutralised in one step. From such work, he concluded in 1840 that the heat produced in a reaction depends only on the initial and final states.

Hess's statement (in modern words): "The enthalpy change of a reaction is the same, whether it takes place in one step or in a series of steps." This is because enthalpy (H) is a state function.

A classic example is the formation of CO₂ from carbon:

Path 1 (direct):   C(s) + O2(g) → CO2(g)         ΔH1 = −393.5 kJ

Path 2 (two steps):
  C(s) + ½O2(g) → CO(g)                          ΔH2 = −110.5 kJ
  CO(g) + ½O2(g) → CO2(g)                        ΔH3 = −283.0 kJ
  Sum:  C(s) + O2(g) → CO2(g)                    ΔH = −393.5 kJ

Here ΔH1 = ΔH2 + ΔH3. We can find the unmeasurable ΔH2 from ΔH1 and ΔH3: −393.5 − (−283.0) = −110.5 kJ.

Rules for using Hess's law:

1. If a reaction is reversed, change the sign of ΔH.
2. If a reaction is multiplied by a number, multiply ΔH by the same number.
3. Add the equations and cancel species that appear on both sides; add the ΔH values.

The Chemistry Behind It

Enthalpy is H = U + PV. Because U, P and V are state functions, H is a state function too. ΔH depends only on the initial and final states, not on the path. This is the thermodynamic meaning of Hess's law.

• Enthalpy of formation: From Hess's law, ΔH°(reaction) = Σ ΔH°f (products) − Σ ΔH°f (reactants).
• Enthalpy of combustion: ΔH°(reaction) = Σ ΔH°c (reactants) − Σ ΔH°c (products). Note the order is reversed.
• Bond enthalpies: ΔH(reaction) ≈ Σ (bonds broken) − Σ (bonds formed), an approximate use of the law.
• Born-Haber cycle: Lattice enthalpy of an ionic solid cannot be measured directly. It is found by applying Hess's law to a cycle of sublimation, ionisation, dissociation, electron gain and formation steps. For NaCl: ΔH°f = ΔH(sub, Na) + ½ΔH(diss, Cl₂) + IE(Na) + EA(Cl) + lattice enthalpy.

Example problem: Find ΔH for the formation of methane, C(s) + 2H₂(g) → CH₄(g), given the combustion enthalpies: C = −393.5, H₂ = −285.8, CH₄ = −890.3 kJ/mol.

ΔHf(CH4) = [ΔHc(C) + 2 ΔHc(H2)] − ΔHc(CH4)
         = [−393.5 + 2(−285.8)] − (−890.3)
         = −965.1 + 890.3 = −74.8 kJ/mol

Applications Today

• Fuel calorific values: Hess's law is used to calculate heat values of fuels like LPG, coal and biogas, important for India's energy planning.
• Industrial heat balance: Plants making ammonia, sulfuric acid and cement calculate energy requirements using enthalpy cycles.
• Lattice energies: Born-Haber cycles explain stability of ionic solids such as NaCl, MgO and CaF₂.
• Food energy: Calorific values of carbohydrates, fats and proteins are linked to heats of combustion.
• Rocket and explosive chemistry: Heats of formation predict the energy released by propellants.

Exam Corner

• Hess's law is based on enthalpy being a state function and follows from the first law of thermodynamics.
• ΔH°r = Σ ΔH°f(products) − Σ ΔH°f(reactants).
• Reverse a reaction: sign of ΔH changes; multiply the equation: ΔH multiplies.
• Used for ΔH of reactions which cannot be measured directly (C → CO), lattice enthalpy and electron gain enthalpy.
• ΔH°f of an element in its standard state is zero.

Common Misconceptions

• "Heat is a state function." Heat q is path dependent; enthalpy change at constant pressure is path independent.
• "Hess's law works only for formation reactions." It works for any set of reactions that add up.
• "Hess's law gives the rate of reaction." It says nothing about speed or whether a path is feasible; it concerns energy only.

FAQ

What is Hess's law?

The enthalpy change of a reaction is the same whether it occurs in one step or many steps, because enthalpy is a state function.

Who discovered it and when?

Germain Henri Hess, in 1840, in St Petersburg, Russia.

What is the use of Hess's law?

It calculates enthalpy changes that cannot be measured directly, such as lattice enthalpy and the enthalpy of C → CO.

Is Hess's law related to the first law of thermodynamics?

Yes. It is a consequence of the conservation of energy and was an early, experimental form of it.

Published by ABC Chemistry — IIT-JAM | CSIR-NET | GATE Chemistry Coaching. Visit abcchemistry.com