What happens to the chemical energy that is extracted from molecules by cellular activities but that is not used for cellular work?

That chemical energy which is not used for cellular work is used to contribute to the entropy of the system.

Explanation:

The chemical energy is stored in the form of sugar in plants and as fats or lipids is used to store energy in animals. The entropy of the system in plant cell is used to produce carbohydrates by combining the water and carbon dioxide.

Humans and animals convert energy obtained from food as fat for the long-term storage of the energy.