Write a balanced equation for the combus- tion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) with oxygen to obtain carbon dioxide and water. What is the mole ratio of oxygen to octane?

A chemical reaction is a process where substances, referred to as reactants, transform into different substances, known as products. This transformation occurs through the breaking and forming of chemical bonds. An essential aspect of a chemical reaction is that it must adhere to the law of conservation of mass, which dictates that the total mass of the reactants must equal the total mass of the products.

Understanding this concept is crucial when studying the combustion of octane, where octane and oxygen are the reactants that react to form carbon dioxide and water, the products. The process releases energy, which is characteristic of combustion reactions. To use this theory, we must write down the initial, unbalanced reaction and then systematically adjust the coefficients of each reactant and product until the equation is balanced, ensuring no atoms are lost in the process.

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations that relate the amounts of substances involved in a reaction.

In the context of balancing the equation for the combustion of octane, stoichiometry is used to find the right coefficients that will balance the equation. It requires a meticulous process of balancing each element on both sides of the chemical equation. For instance, the oxygen molecules in the reactants must be equal in number to the oxygen atoms in the carbon dioxide and water molecules in the products. By using stoichiometry, we can also calculate the amounts of substances needed for a reaction or produced by a reaction in terms of moles, mass, or volume.

The mole ratio is an expression of the relative amounts of moles of reactants and products in a balanced chemical equation. It is derived from the coefficients in a balanced equation, which indicate the proportions of each substance involved in the reaction.

For the combustion of octane, the balanced equation shows that for every 2 moles of octane (C8H18), 25 moles of oxygen (O2) are required. Thus, the mole ratio of oxygen to octane is 25:2. This mole ratio is essential for scientists and engineers, for instance, when designing engines, as it ensures the correct amounts of reactants for efficient combustion, avoiding excess or deficiency of any reactant. As an important stoichiometric concept, the mole ratio is a critical factor determining the quantitative outcome of chemical processes.