Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is a component of natural gas and is used in domestic cooking and heating. (a) Balance the following equation representing the combustion of propane in air: $$ \mathrm{C}_{3} \mathrm{H}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} $$ (b) How many grams of carbon dioxide can be produced by burning 3.65 moles of propane? Assume that oxygen is the excess reagent in this reaction.

Understanding how to balance chemical equations is essential for studying chemical reactions. A balanced chemical equation has the same number of atoms of each element on both sides of the reaction. This complies with the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

For our propane combustion example, the initial unbalanced equation is given as \( C_3H_8 + O_2 \rightarrow CO_2 + H_2O \). To balance it, start by counting the number of atoms of each element on both sides. The goal is to ensure that the number of atoms for each element is equal on the reactant and product sides. This often requires adding coefficients, which are whole numbers placed before molecules. For example, adding a coefficient of 5 to \( O_2 \) and adjusting the products to 3 \( CO_2 \) and 4 \( H_2O \) balances the oxygen and hydrogen atoms, resulting in the balanced equation \( C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \).

Stoichiometry is the study of quantitative relationships between the amounts of reactants and products in a chemical reaction. It's based on the balanced chemical equation and involves mole ratios. The mole is a unit for amount of substance in chemistry. One mole is defined as 6.022 x 10^23 particles of a substance.

In our example, the stoichiometry of the reaction tells us that 1 mole of propane \( C_3H_8 \) reacts to produce 3 moles of \( CO_2 \). This molar ratio is derived from the coefficients in the balanced chemical equation. When given an amount of a reactant, stoichiometry allows us to compute the amount of products formed. For instance, if we start with 3.65 moles of propane, the stoichiometry shows we can expect to produce three times that amount in moles of \( CO_2 \), which would be 10.95 moles of \( CO_2 \).

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It's calculated by adding the atomic masses of all the atoms in a molecule, as provided on the periodic table. Calculating molar mass is essential for converting between moles and grams in chemical reactions.

For carbon dioxide \( CO_2 \), the molar mass is calculated by adding the mass of one carbon atom (about 12.01 g/mol) to the mass of two oxygen atoms (each about 16.00 g/mol), resulting in a molar mass of approximately 44.01 g/mol. Therefore, if we have calculated that burning propane produces 10.95 moles of \( CO_2 \), we can find the mass by multiplying the number of moles by the molar mass: \[10.95 \text{ moles } \times 44.01 \text{ g/mol } = 482.4135 \text{ grams }\] of \( CO_2 \).