JEE Main 2025 Jan 28 Shift 1, Chemistry Q25: Hess’s Law and Bond Energy

Construct a Hess cycle that turns ${\text{H}}_2(g)+\frac{1}{2}{\text{O}}_2(g)$ into ${\text{H}}_2\text{O}(g)$ via gas-phase atoms.

Atomise the reactants (note H${}_2$ is fully atomised, producing 2 H atoms):

${\text{H}}_2(g)+\frac{1}{2}{\text{O}}_2(g)\to 2\text{H}(g)+\text{O}(g)$,
$\Delta H_1=2(220)+250=690$ kJ mol${}^{-1}$.

Then form two O-H bonds:

$2\text{H}(g)+\text{O}(g)\to {\text{H}}_2\text{O}(g)$,
$\Delta H_2=-2({\text{B.E.}}_{\text{O-H}})$.

Total: $\Delta H_f^{\ominus }({\text{H}}_2\text{O},g)=\Delta H_1+\Delta H_2$

$-242=690-2({\text{B.E.}}_{\text{O-H}})$

$2({\text{B.E.}}_{\text{O-H}})=690+242=932$

${\text{B.E.}}_{\text{O-H}}=466$ kJ mol${}^{-1}$.

$\therefore$ Average O-H bond enthalpy = $466$ kJ mol${}^{-1}$.