State Hess's law. Explain, with one example, the usefulness of this law in thermochemistry.

Named after Germain Hess, a Russian-Swiss chemist, Hess’s Law, also Fondly referred to as Hess's Law of Constant Heat Summation states that the total enthalpy change during the complete course of a chemical reaction is the same whether the reaction is made in one step or in several, provided that the final and initial conditions are the same for each case.

In thermochemistry, Hess's Law is fundamentally important as it allows the calculation of the heat of reaction for reactions which are challenging to perform experimentally. Hess's Law facilitates the measurement of the heat of reaction in stages instead of a total sum, providing a more manageable approach to calculate the heat absorption or release during the reaction.

Let's consider an example of burning methane. It's difficult to measure the enthalpy change of this reaction directly. However, this can be done in steps through reactions where enthalpy changes can be measured more easily.\[CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \triangledown H_1\]\[C(s) + O_2(g) \rightarrow CO_2(g) \quad \triangledown H_2\]\[H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l) \quad \triangledown H_3\]Here, \(\triangledown H_1\) is hard to measure, but \(\triangledown H_2\) and \(\triangledown H_3\) can be measured easily. Then applying Hess's Law, we can find \(\triangledown H_1 = \triangledown H_2 + 2\triangledown H_3\)This simplifies the process of finding the heat of reaction for complex reactions.