= Sequential bond-dissociation energies
{title2=$D_1,D_2,\ldots$}
Equivalent <chemical bonds> in an intact <molecule> need not have equal successive <bond-dissociation enthalpies>. Once one <chemical bond> is removed, the next reactant has a different electronic <quantum state> and may relax to a different <molecular geometry>. The successive steps compare different species. This distinction also explains why a tabulated average <chemical bond> strength is not necessarily the cost of the first cleavage.<Chemistry 2e by Paul Flowers and others/7.5 Strengths of Ionic and Covalent Bonds>[“Bond Strength: Covalent Bonds”, methane paragraph: equivalent initial bonds and unequal sequential breaking costs]{ref}
For an invented species $AB_2$, stipulate the following gas-phase steps, with all <enthalpies> at the same <temperature> and the same <standard states>:
$$
\begin{aligned}
AB_2(g)&\longrightarrow AB(g)+B(g),&D_1&=300\,\mathrm{kJ\,mol^{-1}},\\
AB(g)&\longrightarrow A(g)+B(g),&D_2&=400\,\mathrm{kJ\,mol^{-1}}.
\end{aligned}
$$
The symbols stand for hypothetical species with consistently chosen electronic states. They are not values for <water> or another measured <molecule>. By <Hess's law>, the total <enthalpy of atomization> for $AB_2(g)\to A(g)+2B(g)$ is $700\,\mathrm{kJ\,mol^{-1}}$; the <arithmetic mean> per broken <chemical bond> is $350\,\mathrm{kJ\,mol^{-1}}$. Neither individual step equals that mean. Nor must the second step be cheaper: here it is deliberately more expensive. An exact sequence sums exactly; substituting averages taken from other <molecules> generally gives only an estimate.
\Image[/bond-energy-conventions-and-sequential-cleavage.png]
{title=Two stipulated examples: changing the <energy> convention for one dissociation, and changing the reactant during sequential cleavage}
{id=image-bond-energy-conventions-and-sequential-cleavage}
{description=Left: $N_{\rm A}D_e$, $N_{\rm A}D_0$, and the model <bond-dissociation enthalpy> at $300\,\mathrm K$. Right: cumulative <enthalpy> levels $0,300,700\,\mathrm{kJ\,mol^{-1}}$ for two successive steps, with costs $300$ and $400$ and mean $350$. The panels are separate hypothetical systems; neither contains molecular measurements.}
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