Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) burns in air: $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ Balance the equation and determine the volume of air in liters at \(35.0^{\circ} \mathrm{C}\) and \(790 \mathrm{mmHg}\) required to burn \(227 \mathrm{~g}\) of ethanol. Assume that air is 21.0 percent \(\mathrm{O}_{2}\) by volume.

Stoichiometry is the sect of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. For students grappling with balancing chemical equations, it's essential to understand that stoichiometry is not just about balancing atoms on both sides of the equation, but it's also about understanding the ratios in which substances react and form products.

Consider the burning of ethanol in the presence of oxygen to produce carbon dioxide and water. Here, the stoichiometry shows a one-to-three-to-two-to-three molar ratio, respectively. This ratio means that for each mole of ethanol, you'll need three moles of oxygen to ensure the complete conversion into two moles of carbon dioxide and three moles of water.

By understanding stoichiometry, you can comprehend the importance of reactant amounts, predict product yields, and calculate reactants or products needed for desired chemical outcomes. This background is especially valuable when scaling reactions for lab work or industrial processes.

The ideal gas law is a fundamental equation in chemistry that relates the pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas, through the equation PV=nRT. Here, R is the ideal gas constant which has several values depending on the unit system in use.

The ideal gas law allows us to interpret the behavior of gases under different conditions. In our problem with the combustion of ethanol, we determine the volume of air required using this law, taking into account the temperature and pressure conditions given. It's crucial to convert temperature to Kelvin and pressure to atmospheres to use the ideal gas law correctly.

Learning to apply the ideal gas law also serves as a foundation for understanding more complex gas behaviors and can guide you through other topics such as gas stoichiometry, partial pressures, and kinetic molecular theory.

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's directly equivalent to the substance's atomic or molecular weight taken from the periodic table. In the case of ethanol (\( \text{C}_{2}\text{H}_{5}\text{OH} \)), you need to calculate the molar mass by summing the atomic weights of each atom involved in its formula.

The molar mass serves as a bridge between the mass of a substance and the number of moles, which is paramount in stoichiometry to convert from grams to moles and vice versa. For any chemical reaction, calculating the molar mass is the initial step towards uncovering the stoichiometric relationships that define the reactants’ conversion into products. A deep familiarity with molar mass directly translates into the ability to successfully manage various quantitative aspects in chemistry experiments and real-world applications.