A compact car gets 37.5 miles per gallon on the highway. If gasoline contains 84.2\% carbon by mass and has a density of \(0.8205 \mathrm{g} / \mathrm{mL}\), determine the mass of carbon dioxide produced during a 500 -mile trip \((3.785\) liters per gallon).

Combustion analysis is an essential laboratory procedure used to identify the elemental composition of a substance, especially hydrocarbons, by burning the substance and analyzing the resulting products. In the context of the problem provided, combustion analysis would be applied to gasoline, which is primarily composed of hydrocarbons. During combustion, these hydrocarbons react with oxygen to produce carbon dioxide and water. By understanding the composition of the gasoline, we can predict the mass of carbon dioxide produced from a given volume of gasoline consumed during a trip.For accurate analysis, the percentage of carbon in the fuel must be known, which in this scenario is 84.2%. This percentage is a crucial piece of information because it allows us to calculate the mass of carbon that will be converted into carbon dioxide upon combustion.

The molar mass of a substance is the mass of one mole of that substance. It's a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base units for molar mass are grams per mole (g/mol). In our exercise, the molar mass is used to convert the mass of carbon found in the gasoline into moles, which is a necessary step in relating the mass of gasoline used to the mass of carbon dioxide produced. The molar mass of carbon is approximately 12.01 g/mol, which is essential to determine the moles of carbon that will further lead to calculation of moles of CO2 upon its combustion.

Chemical stoichiometry is the calculation of reactants and products in chemical reactions. It's based on the law of conservation of mass, where the total mass of the reactants equals the total mass of the products in a chemical reaction. Stoichiometry translates quantitative relationships between the substances as they participate in various chemical reactions. In the case of gasoline combustion, stoichiometry allows us to predict the amount of products (carbon dioxide and water) from the known quantity of reactants (gasoline and oxygen). The stoichiometric relationship between carbon and carbon dioxide in a combustion reaction is 1:1, meaning one mole of carbon yields one mole of carbon dioxide.

Gasoline combustion is the process by which gasoline, a hydrocarbon fuel, reacts with oxygen to release energy, carbon dioxide, and water. This process powers the engine of a car. Car engines are designed to optimize the combustion of gasoline to get the maximum energy yield. The combustion reaction follows the chemical equation: C_xH_y + O₂ → CO₂ + H₂O. By understanding the percentage of carbon in the gasoline and the density of gasoline, we can estimate the mass of gasoline used during a trip, calculate the mass of carbon in that gasoline, and hence find out the mass of CO₂ produced in a typical 500-mile journey. For instance, the fuel efficiency provided (37.5 miles per gallon) lets us calculate the total gallons of gasoline used, which is the starting point for subsequent calculations.

Carbon dioxide emissions are a significant concern as they contribute to greenhouse gas effects and climate change. The emission from vehicles, such as a compact car on a 500-mile trip, can be quantified using the principles of stoichiometry and chemistry. After determining the mass of gasoline, the associated mass of carbon, and the molar mass of both carbon and carbon dioxide, we can calculate the exact mass of CO₂ released. This information is crucial for environmental impact assessments and for developing strategies to reduce carbon footprints. It allows us to understand the correlation between the use of fossil fuels, in this case, gasoline, and the amount of carbon emissions contributing to global warming.