Step 1: Understand the concept of cellular respiration. Cellular respiration is a metabolic process where glucose (\(\mathrm{C_6H_{12}O_6}\)) is broken down in the presence of oxygen (\(\mathrm{O_2}\)) to produce carbon dioxide (\(\mathrm{CO_2}\)), water (\(\mathrm{H_2O}\)), and energy in the form of ATP.
Step 2: Recall the general balanced chemical equation for cellular respiration. The 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 complete oxidation of glucose.
Step 3: Compare the given options to the balanced equation for cellular respiration. The correct equation should include glucose (\(\mathrm{C_6H_{12}O_6}\)), oxygen (\(\mathrm{O_2}\)), carbon dioxide (\(\mathrm{CO_2}\)), water (\(\mathrm{H_2O}\)), and energy.
Step 4: Eliminate incorrect options. For example, \(\mathrm{C_6H_{12}O_6} + \mathrm{O_2} \rightarrow \mathrm{CO_2} + \mathrm{H_2O}\) is not balanced because it does not account for the correct stoichiometric coefficients. Similarly, \(6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} \rightarrow \mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2}\) represents photosynthesis, not cellular respiration.
Step 5: Identify the correct balanced equation for cellular respiration. The correct answer is: \(\mathrm{C_6H_{12}O_6} + 6\ \mathrm{O_2} \rightarrow 6\ \mathrm{CO_2} + 6\ \mathrm{H_2O} + \text{energy}\). This equation satisfies the law of conservation of mass and represents the process of cellular respiration.