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Chemistry · Ch 4 — Chemical Bonding and Molecular Structure

Bond Enthalpy

4.3.3

Bond Enthalpy

Bond Enthalpy: The Energy Cost of Breaking a Bond

Chemical bonds hold atoms together, and breaking them requires energy. Bond enthalpy is the quantitative measure of that energy cost. It is defined as the amount of energy required to break one mole of bonds of a particular type between two atoms, with all substances in the gaseous state.

The unit of bond enthalpy is kJ mol−1\text{kJ mol}^{-1}.

For a diatomic molecule like hydrogen, the bond enthalpy is straightforward:

H2(g)→H(g)+H(g);ΔaH⊖=435.8 kJ mol−1\text{H}_2(g) \rightarrow \text{H}(g) + \text{H}(g); \quad \Delta_a H^\ominus = 435.8\ \text{kJ mol}^{-1}

This means that to break one mole of H–H bonds in gaseous hydrogen, 435.8 kJ of energy must be supplied.

The same idea applies to molecules with multiple bonds. For oxygen (a double bond) and nitrogen (a triple bond):

O2 (O=O)(g)→O(g)+O(g);ΔaH⊖=498 kJ mol−1\text{O}_2\ (\text{O}=\text{O})(g) \rightarrow \text{O}(g) + \text{O}(g); \quad \Delta_a H^\ominus = 498\ \text{kJ mol}^{-1}

N2 (N≡N)(g)→N(g)+N(g);ΔaH⊖=946.0 kJ mol−1\text{N}_2\ (\text{N}\equiv\text{N})(g) \rightarrow \text{N}(g) + \text{N}(g); \quad \Delta_a H^\ominus = 946.0\ \text{kJ mol}^{-1}

Important

The larger the bond dissociation enthalpy, the stronger the bond. A triple bond (N≡N, 946 kJ mol⁻¹) is much harder to break than a single bond (H–H, 435.8 kJ mol⁻¹).

For a heteronuclear diatomic molecule like HCl:

HCl(g)→H(g)+Cl(g);ΔaH⊖=431.0 kJ mol−1\text{HCl}(g) \rightarrow \text{H}(g) + \text{Cl}(g); \quad \Delta_a H^\ominus = 431.0\ \text{kJ mol}^{-1}

The Complication: Polyatomic Molecules

For molecules with more than two atoms, the situation is not as simple. The energy required to break each bond of the same type is not necessarily equal. Consider water, H2O\text{H}_2\text{O}.

The first O–H bond breaks with an enthalpy change of:

H2O(g)→H(g)+OH(g);ΔaH1⊖=502 kJ mol−1\text{H}_2\text{O}(g) \rightarrow \text{H}(g) + \text{OH}(g); \quad \Delta_a H_1^\ominus = 502\ \text{kJ mol}^{-1}

The second O–H bond, now in the OH radical, breaks with a different enthalpy:

OH(g)→H(g)+O(g);ΔaH2⊖=427 kJ mol−1\text{OH}(g) \rightarrow \text{H}(g) + \text{O}(g); \quad \Delta_a H_2^\ominus = 427\ \text{kJ mol}^{-1}

The difference of 502−427=75 kJ mol−1502 - 427 = 75\ \text{kJ mol}^{-1} shows that the chemical environment of the second O–H bond has changed after the first bond was broken. The OH radical is a different species from the water molecule, so the bond strength is different.

Watch out

Do not assume that all bonds of the same type (e.g., all O–H bonds) have the same bond enthalpy. The value depends on the rest of the molecule.

This is why the bond enthalpy for an O–H bond in ethanol (C2H5OH\text{C}_2\text{H}_5\text{OH}) differs from that in water. The chemical environment is different.

Mean or Average Bond Enthalpy

Because of this variation, for polyatomic molecules we use the mean or average bond enthalpy. It is calculated by dividing the total bond dissociation enthalpy by the number of bonds broken.

For the water molecule, two O–H bonds are broken. The total enthalpy required is: …

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