Calculate \(\Delta_{\mathrm{f}} H^{\circ}\) for aqueous chloride ion from the following data: \(\frac{1}{2} \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{HCl}(\mathrm{g}), \quad \Delta_{\mathrm{f}} H^{\mathrm{o}}\) \(=-92.4 \mathrm{~kJ}\) \(\mathrm{HCl}(\mathrm{g})+n \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})\) \(\Delta H^{\circ}=-74.8 \mathrm{~kJ}\) \(\Delta_{\mathrm{f}} H^{\circ}\left(\mathrm{H}^{+}\right.\), aq. \()=0.0 \mathrm{~kJ}\) (a) \(0.0\) (b) \(+83.6 \mathrm{~kJ}\) (c) \(+167.2 \mathrm{~kJ}\) (d) \(-167.2 \mathrm{~kJ}\)

In chemistry, Hess's Law is a principle that relates to the total enthalpy change in a chemical reaction. It states that the total enthalpy change, regardless of the number of steps or intermediate stages of the reaction, is the same as if the reaction were to happen in a single step. This is because enthalpy is a state function, which means its value is determined only by the current state of the system and not by the path the system took to reach that state.

Now, let's take a real-world analogy to simplify this concept: imagine building a house. The total cost to build it will be the same whether you pay for it in one lump sum or in smaller payments over time. Similarly, when it comes to chemical reactions, the total heat change (like the total cost of the house) doesn't care about the