Step 1: Begin by understanding the process of cellular respiration. Cellular respiration is a metabolic pathway that converts glucose ($\mathrm{C_6H_{12}O_6}$) into usable energy (ATP) for the cell. This process requires oxygen ($\mathrm{O_2}$) and produces carbon dioxide ($\mathrm{CO_2}$), water ($\mathrm{H_2O}$), and energy.
Step 2: Recall the general chemical equation for cellular respiration. The correct equation is: $\mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2} \rightarrow 6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} + \text{energy}$. This equation represents the breakdown of glucose in the presence of oxygen to produce carbon dioxide, water, and energy.
Step 3: Analyze the options provided in the problem. Compare each option to the correct chemical equation for cellular respiration. Look for the reactants (glucose and oxygen) and the products (carbon dioxide, water, and energy).
Step 4: Eliminate incorrect options. For example, the first option incorrectly lists $\mathrm{CO_2}$ as a reactant instead of $\mathrm{O_2}$. The third option represents photosynthesis, not cellular respiration, as it shows the production of glucose and oxygen. The fourth option incorrectly lists $\mathrm{H_2O}$ as a reactant instead of $\mathrm{O_2}$.
Step 5: Identify the correct answer. The second option matches the chemical equation for cellular respiration: $\mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2} \rightarrow 6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} + \text{energy}$. This is the correct representation of the process.