Q.Given that $C(g) + O_2(g) \rightarrow CO_2(g)$, $\Delta H^0 = -a$ kJ; $2CO(g) + O_2(g) \rightarrow 2CO_2(g)$, $\Delta H^0 = -b$ kJ. Calculate the $\Delta H^0$ for the reaction $C(g) + \tfrac{1}{2}O_2(g) \rightarrow CO(g)$

Because $\Delta U$ and $\Delta H$ are both state functions, a reaction's heat change depends only on its initial and final states -- never on the path or number of steps taken between them. Hess's law: the enthalpy change of a reaction, at constant volume or constant pressure, is the same whether it happens in one step or several, provided the initial and final states match. Its main value is computing enthalpies that are hard or impossible to measure directly, by building the target reaction as a sum of measurable ones (reversing a known equation flips the sign of its $\Delta H$; scaling an equation scales its $\Delta H$ by the same factor) -- graphite's combustion to pure CO cannot be measured cleanly, but graphite$\rightarrow$CO$_2$ and CO$\rightarrow$CO$_2$ both can, and combining them via Hess's law recovers graphite$\right …