How is internal energy related to molecular kinetic and potential energy? How is a change in internal energy defined for a chemical reaction?

At the microscopic level, the internal energy of a substance is a combination of the molecular kinetic and potential energies. The kinetic energy of a molecule is due to its motion - how fast it's moving and in what way, whether that be translational, rotational or vibrational. For instance, the faster a gas molecule moves, the higher its kinetic energy will be.

Potential energy, on the other hand, is related to the position and interaction of molecules. It is the energy stored within the molecular bonds and structural configuration. When molecules are pulled apart or pushed closer together, potential energy changes due to the adjusting intermolecular forces.

In a nutshell, to measure the total internal energy of a substance, one must think beyond the movement of individual molecules to include the energy that resides within the bonds that connect atoms and in the forces that hold molecules together.

Chemical reactions involve breaking old bonds and forming new ones, leading to changes in molecular kinetic and potential energy. This shift is referred to as a change in internal energy. To comprehend this alteration, picture a reaction where reactants convert to products—during this process, energy is either absorbed from or released into the surroundings. Chemists define this phenomenon with the formula: \[ \Delta U = U_{products} - U_{reactants} \] where \( \Delta U \) symbolizes the change in internal energy. If \( \Delta U \) is positive, the products have higher internal energy, indicating endothermicity. Conversely, if \( \Delta U \) is negative, it implies energy release and an exothermic reaction.

An interesting fact about energy change in chemical reactions is that it is linked to temperature change. When you touch a vessel in which an exothermic reaction is taking place, it feels warmer because the internal energy of the system has decreased, releasing heat into the environment.

The first law of thermodynamics, also known as the conservation of energy principle, plays a pivotal role in understanding chemical energy changes. It states that the total energy of an isolated system is constant; energy can be transformed from one form to another but cannot be created or destroyed. In the context of a chemical reaction, this law assures that all energy changes are accounted for.

When a reaction occurs, the first law must be applied to consider both the system (the reaction itself) and the surroundings (everything outside the reaction vessel). If the system absorbs energy, that energy is drawn from the surroundings, decreasing the surroundings' energy. Conversely, if the system releases energy, it contributes to the energy of the surroundings. This law reinforces the idea that to understand the energy change due to a chemical reaction, one must look at the energy flow between the system and its environment as a whole.