Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I)oxide decomposes into silver metal and oxygen gas when heated; (c) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air; (d) methyl tert- butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

Understanding stoichiometry is essential for balancing chemical equations and predicting the quantities of substances consumed and produced in a chemical reaction. It involves the calculation of the relative quantities of reactants and products, often measured in moles, taking into account the conservation of mass and the coefficients provided in a balanced equation.

For example, in the reaction where titanium metal reacts with oxygen, stoichiometry is used to determine that one mole of titanium reacts with half a mole of oxygen to produce one mole of titanium dioxide. Stoichiometry not only ensures that the chemical equation adheres to the law of conservation of mass but also enables us to predict how much product can be formed from a given amount of reactant.

Decomposition reactions involve a single compound breaking down into two or more simpler substances, usually when energy, such as heat, is supplied. For instance, the decomposition of silver(I) oxide into silver metal and oxygen gas is a typical example often used in laboratory demonstrations.

This process requires careful balancing of the chemical equation to ensure that the atoms on the left side of the equation equal the atoms on the right side. In the silver(I) oxide example, the balanced equation shows that two formula units of silver(I) oxide decompose to produce four atoms of silver and one molecule of oxygen gas, signifying that the reaction preserves the mass and number of atoms involved.

Combustion reactions are rapid chemical reactions that typically involve oxygen from the air and produce heat and light. A familiar example of a combustion reaction is the burning of fuels like propane. When combustion reactions occur, reactants like hydrocarbons and oxygen are converted into products like carbon dioxide and water.

Propanol burning in air is a specific case of a combustion reaction. The balanced chemical equation carefully accounts for all the carbon, hydrogen, and oxygen atoms, ensuring that the chemical equation is physically plausible. Stoichiometry plays a crucial role in determining the coefficient of oxygen necessary to completely burn propanol, resulting in the proper quantities of carbon dioxide and water.

The balancing of chemical equations is a skill that involves equalizing the number of atoms of each element present in the reactants and products. This is a fundamental practice in chemistry because it reflects the conservation of matter and provides the correct proportions of substances involved in the chemical reaction.

Consider the case of methyl tert-butyl ether burning in air. The balanced chemical equation ensures that each carbon, hydrogen, and oxygen atom is accounted for on both sides of the equation. The process generally involves adjusting the stoichiometric coefficients before the compounds, and it is often helpful to balance certain elements last, such as hydrogen and oxygen, due to their frequent occurrence in multiple compounds within the equation.