2 carry out calculations using cycles and relevant energy terms, including:

(a) determining enthalpy changes that cannot be found by direct experime

Applying Hess's Law is a powerful method in thermochemistry that allows us to calculate the overall enthalpy change of a reaction using known enthalpy changes of other reactions. This principle is based on the concept that enthalpy is a state function, meaning it depends only on the initial and final states of a system and not on the path taken.

To construct a simple energy cycle using Hess's Law, we start with a target reaction for which we want to determine the enthalpy change. This target reaction may not have direct experimental data, but we can use known enthalpy changes of other reactions to derive the desired enthalpy change.

The key idea is to break down the target reaction into a series of intermediate reactions, known as the "thermochemical equations," for which we have the corresponding enthalpy changes. By carefully selecting and manipulating these equations, we can cancel out common reactants and products to obtain the desired target reaction.

For example, suppose we want to determine the enthalpy change for the combustion of methane (CH4). However, we don't have direct experimental data for this specific reaction. We can construct an energy cycle using known enthalpy changes of reactions involving the combustion of other compounds, such as hydrogen (H2) and carbon monoxide (CO).

First, we identify the known reactions that can be used to build the energy cycle. In this case, we can use the combustion reactions of H2 and CO, for which we have the corresponding enthalpy changes. These reactions become the intermediate steps in the energy cycle.

Next, we manipulate the intermediate reactions and their enthalpy changes to cancel out common species and align the stoichiometry with the target reaction. This can involve reversing reactions, multiplying them by coefficients, or combining multiple reactions to achieve the desired cancellation.

By summing up the enthalpy changes of the manipulated intermediate reactions, taking into account the stoichiometric coefficients, we obtain the overall enthalpy change for the target reaction. This value represents the enthalpy change that would be measured if the reaction were directly carried out under standard conditions.

It's important to note that the validity of applying Hess's Law relies on the assumption that enthalpy changes are additive. This assumption holds as long as the reactions occur under the same conditions and there is no change in temperature or pressure during the process.

By applying Hess's Law and constructing simple energy cycles, we can determine the enthalpy changes of reactions that are difficult or impractical to measure directly. This approach provides a powerful tool for calculating enthalpy changes and understanding the energy transformations in chemical reactions.

In summary, applying Hess's Law involves constructing energy cycles using known enthalpy changes of intermediate reactions to determine the enthalpy change of a target reaction. By manipulating and combining these reactions, we can cancel out common species and obtain the desired enthalpy change. This method allows us to calculate enthalpy changes for reactions that lack direct experimental data and enhances our understanding of energy transformations in chemical systems.