How can energy cycles be used to determine unknown enthalpies?

Energy cycles can be used to determine unknown enthalpies by applying Hess's Law of constant heat summation.

Hess's Law states that the total enthalpy change for a chemical reaction is independent of the route by which the chemical reaction takes place. It is only dependent on the initial and final states. This principle allows us to determine unknown enthalpies by creating an energy cycle, which is a diagram representing the different routes a reaction can take.

In an energy cycle, the enthalpy change of a reaction can be calculated by adding up the enthalpy changes of the individual steps that make up the reaction. This is possible because enthalpy is a state function, meaning its value depends only on the state of the system and not on the path taken to reach that state.

To use an energy cycle to determine an unknown enthalpy, you would first need to identify a series of reactions that, when added together, give the overall reaction of interest. These reactions should have known enthalpy changes. You would then add or subtract these known enthalpy changes to find the enthalpy change of the overall reaction.

For example, if you wanted to find the enthalpy change for the reaction A + B → C, but only knew the enthalpy changes for the reactions A → D and D + B → C, you could use an energy cycle. You would add the enthalpy change for A → D to the enthalpy change for D + B → C to find the enthalpy change for A + B → C.

In summary, energy cycles are a powerful tool in thermochemistry that allow us to determine unknown enthalpies. By applying Hess's Law and the principle that enthalpy is a state function, we can calculate the enthalpy change for a reaction even if we don't know the enthalpy changes for all the individual steps of the reaction.