The net enthalpy change of a reaction is the amount of energy required to break all the bonds in reactant mole

NCERT Exemplar · Q42

Q. The net enthalpy change of a reaction is the amount of energy required to break all the bonds in reactant molecules minus amount of energy required to form all the bonds in the product molecules. What will be the enthalpy change for the following reaction. H2(g) + Br2(g) \to 2HBr(g) Given that Bond energy of H2, Br2 and HBr is 435 kJ mol^-1, 192 kJ mol^-1 and 368 kJ mol^-1 respectively.

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Concept understanding — Bond Enthalpy

Bond Enthalpy: The Energy Cost of Breaking a Bond

Think of a chemical bond as a spring holding two atoms together. To pull the atoms apart, you have to do work — you have to put energy in. That energy, per mole of bonds broken, is the bond enthalpy. The stronger the bond, the more energy you need to supply, and the larger the bond enthalpy.

The intuition is simple: breaking bonds costs energy; forming bonds releases energy. A reaction is exothermic if the energy released in forming new bonds is greater than the energy consumed in breaking old ones.

The Precise Definition

Bond enthalpy (symbol: $\Delta H_{\text{bond}}$ or $B.E.$ ) is defined under a specific set of conditions:

The average enthalpy change when one mole of a particular covalent bond is broken, with all species in the gaseous state.

Three key points are packed into that sentence:

One mole of bonds — we measure the energy for Avogadro's number of bonds, not just one.
Gaseous state — the atoms or molecules must be in the gas phase. This removes complications from intermolecular forces (like hydrogen bonding in liquid water) and lets us isolate the bond energy itself.
Average — in a molecule like water ( $H_2O$ ), the two O–H bonds are not identical in energy. The first O–H bond in $H_2O$ requires about 502 kJ/mol to break, but the second (in the remaining OH radical) requires about 427 kJ/mol. So we report the average bond enthalpy for O–H: roughly 464 kJ/mol.

Important

Bond enthalpy is always positive — it is the energy absorbed to break a bond. Bond formation releases the same amount of energy (negative enthalpy change).

How It's Used: Estimating Reaction Enthalpies

You can estimate the enthalpy change of a reaction ( $\Delta H_{\text{rxn}}$ ) using bond enthalpies:

\Delta H_{\text{rxn}} = \sum \text{(bond enthalpies of bonds broken)} - \sum \text{(bond enthalpies of bonds formed)}

The logic: you put energy in to break bonds (positive), and you get energy out when bonds form (negative). So:

\Delta H_{\text{rxn}} = \text{Energy in} - \text{Energy out}

Watch out

This method gives an estimate, not an exact value. Bond enthalpies are averages taken from many different molecules, so they don't account for the exact molecular environment. For precise work, use standard enthalpies of formation.

Example: Combustion of Methane

Consider: $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)$

Bonds broken (energy in):

4 C–H bonds: $4 \times 413 = 1652$ kJ/mol
2 O=O bonds: $2 \times 498 = 996$ kJ/mol
Total in: $1652 + 996 = 2648$ kJ/mol

Bonds formed (energy out):

2 C=O bonds: $2 \times 799 = 1598$ kJ/mol
4 O–H bonds: $4 \times 464 = 1856$ kJ/mol
Total out: $1598 + 1856 = 3454$ kJ/mol

\Delta H_{\text{rxn}} = 2648 - 3454 = -806 \text{ kJ/mol}

The negative sign tells you the reaction is exothermic — more energy is released in forming bonds than was consumed in breaking them. …

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Enthalpy change equals energy needed to break reactant bonds minus energy released when product bonds form. For H₂ + Br₂ → 2HBr, breaking H–H and Br–Br costs 627 kJ, forming two H–Br bonds releases 736 kJ, giving ΔH = −109 kJ mol⁻¹.

Why bond energies determine enthalpy change

A chemical reaction is fundamentally a rearrangement of atoms: old bonds break, new bonds form. Breaking a bond always requires energy (endothermic), while forming a bond always releases energy (exothermic). The net enthalpy change is simply the balance between these two processes.

When reactant bonds break, the system absorbs energy from the surroundings. When product bonds form, the system gives energy back. If more energy is released in bond formation than was consumed in bond breaking, the reaction is exothermic (ΔH < 0). If bond breaking costs more than bond formation returns, the reaction is endothermic (ΔH > 0).

\Delta H_{\text{reaction}} = \sum (\text{Bond energies of reactants}) - \sum (\text{Bond energies of products})

Notice the sign convention: bond energies are always quoted as positive numbers (the energy needed to break one mole of bonds), so we add them for breaking and subtract them for forming.

Step-by-step calculation

1. Identify all bonds in the reactants

In $\ce{H2(g) + Br2(g)}$ :

One H–H bond in H₂
One Br–Br bond in Br₂

2. Calculate total energy required to break reactant bonds

E_{\text{break}} = 1 \times 435\,\text{kJ mol}^{-1} + 1 \times 192\,\text{kJ mol}^{-1} = 627\,\text{kJ mol}^{-1}

This energy must be supplied to pull the molecules apart into individual atoms.

3. Identify all bonds in the products

In $\ce{2HBr(g)}$ :

Two H–Br bonds (one in each HBr molecule)

4. Calculate total energy released when product bonds form

$E_{\text{form}} = 2 \times 368\,\text{kJ mol}^{-1} = 736\,\text{kJ mol}^{-1}$ …

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Why bond energies determine enthalpy change

Step-by-step calculation

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