Toluene, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\), is oxidized by air under carefully controlled conditions to benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\), which is used to prepare the food preservative sodium benzoate, \(C_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{Na} .\) What is the percent yield of a reaction that converts 1.000 kg of toluene to 1.21 kg of benzoic acid? \(2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}+3 \mathrm{O}_{2} \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}+2 \mathrm{H}_{2} \mathrm{O}\)

Stoichiometry is the section of chemistry that pertains to measuring the quantitative relationships, or ratios, between the reactants and products in a chemical reaction. During stoichiometric calculations, the conservation of mass is a fundamental principle, meaning that the mass of the reactants must equal the mass of the products. Stoichiometry heavily relies on the balanced chemical equation, which provides the mole ratio of reactants to products.

For instance, to perform a stoichiometric calculation, you would start with a balanced chemical equation and use the mole ratios to calculate how much of each reactant is needed to produce a certain amount of product. This is invaluable in laboratory and industrial settings where knowing exact amounts of substances required is crucial. If the stoichiometry of a reaction shows a 1:1 ratio, it means that one mole of a substance reacts with one mole of a second substance to produce one mole of a product. In the provided exercise, stoichiometry helps users understand how many moles of toluene are theoretically required to produce a certain amount of benzoic acid.

Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by its amount of substance. It's typically expressed in units of grams per mole (g/mol), and it corresponds to the sum of the atomic masses of all atoms present in the molecule.

Calculating molar mass is essential in converting between grams and moles, an integral step in stoichiometry. To find the molar mass of a compound, as in our exercise examples of toluene and benzoic acid, you would sum up the atomic masses of each element within the compound according to its stoichiometric number in the compound's formula. For toluene, which is comprised of carbon and hydrogen, the atomic masses of these elements are obtained from the periodic table and then added according to the number of each within the molecular formula.

Theoretical yield is the amount of product expected to be produced in a chemical reaction based on the stoichiometry of the balanced equation, assuming perfect conditions where every molecule reacts exactly as described and no product is lost in the process. It is a vital concept in chemistry, as it sets the benchmark for determining the efficiency of chemical reactions through the percent yield calculation.

In practice, the theoretical yield is never reached due to side reactions, incomplete reactions, and practical losses during the process. However, it serves as an important goalpost for evaluating reaction efficiency and practicality. For chemical reactions, it is calculated using the amount of limiting reactant (the reactant that will be completely used up first in a chemical reaction) and the stoichiometric coefficients from the balanced equation. In the provided exercise, the theoretical yield is determined using the stoichiometry from the balanced equation for the conversion of toluene to benzoic acid.

A chemical reaction is a process in which one or more substances, the reactants, are converted into one or more different substances, the products. Chemical reactions are represented by chemical equations, which include symbols and formulas for the substances involved, showing the reactants on the left and the products on the right, often separated by an arrow indicating the direction of the reaction.

Chemical reactions can vary greatly, ranging from simple ones that involve a few atoms exchanging partners, to complex ones that form or break bonds within large molecules. The exact details of a reaction can include various types of changes including synthesis, decomposition, single or double displacement, and more. In our case, the reaction presented in the exercise is an oxidation reaction where toluene interacts with oxygen to produce benzoic acid and water. Understanding the details of a chemical reaction is crucial to grasp how reactants are transformed into products, which then allows for stoichiometry and percent yield calculations.