Write the balanced chemical equation for the reaction between pentane, \(\mathrm{C}_{5} \mathrm{H}_{12}\), and oxygen gas that produces carbon dioxide and water.

A combustion reaction is a type of chemical reaction where a substance combines with oxygen to produce heat and light, typically in the form of a flame. Most commonly, this reaction involves a hydrocarbon—a compound made up of carbon and hydrogen—reacting with oxygen gas to form carbon dioxide (CO₂) and water (H₂O).

In our exercise, we look at pentane (C₅H₁₂), which is a hydrocarbon, undergoing combustion. The simplified version of this reaction is represented as a hydrocarbon plus oxygen yields carbon dioxide and water. The real-world applications of combustion reactions include driving car engines, producing energy in power plants, cooking, and heating. It's essential that these reactions are balanced to conform with the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction.

Chemical stoichiometry concerns the quantitative relationship between reactants and products in a chemical reaction. It is based on the balanced chemical equation that provides a ratio between the number of moles of each substance involved. For instance, in the balanced equation of the combustion of pentane, stoichiometry tells us that one mole of pentane reacts with eight moles of oxygen to produce five moles of carbon dioxide and six moles of water.

This concept is vital in fields like chemistry and engineering, where precise measurements are required to ensure that reactions proceed efficiently. Chemical stoichiometry is not only about getting the right amount of product; it's also about minimizing waste and understanding reaction yields. It forms the basis of calculations like determining how much reactant you need to make a certain amount of product, which is crucial for large-scale industrial processes.

In our particular example involving the combustion of pentane, balancing hydrogen atoms are crucial. As indicated, pentane has 12 hydrogen atoms, whereas each water molecule has only 2 hydrogen atoms. To balance the hydrogen atoms on both sides of the equation, we require 6 water molecules, as the calculation \( 2 \times 6 = 12 \) illustrates.

When balancing equations, ensure you adjust the coefficients and not the subscripts of the molecules, as changing subscripts alters the substances' identities. Balancing requires patience and practice. Sometimes, balancing other atoms in the equation might throw off the balance achieved with hydrogen, requiring iterations of adjustments. This step-by-step process to tackle each atom separately helps simplify complex balancing tasks and is a key skill in problem-solving within chemistry.

Balancing oxygen atoms often serves as the final step in balancing combustion reactions due to the diatomic nature of oxygen gas (O₂). Oxygen can be tricky as it appears in multiple products - in this case, in both CO₂ and H₂O. In our exercise, the combined products have a total of 16 oxygen atoms. Therefore, we divide this by the number of oxygen atoms in an O₂ molecule to find the coefficient needed for oxygen gas on the reactant side, which results in eight O₂ molecules.

This demonstrates the conservation of mass, as the total number of oxygen atoms must be equal on both sides of the equation. It reiterates the importance of systematically balancing chemical equations to ensure that all atoms are accounted for, reflecting a true depiction of the chemical reaction taking place, which is essential for precise scientific and practical applications.