The combustion of gasoline produces carbon dioxide and water. Assume gasoline to be pure octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) and calculate how many kilograms of carbon dioxide are added to the atmosphere per \(1.0 \mathrm{~kg}\) of octane burned. (Hint: Begin by writing a balanced equation for the combustion reaction.)

The combustion of octane, a major component of gasoline, is a chemical reaction that requires careful balancing to adhere to the law of conservation of mass. This law states that matter cannot be created or destroyed, so each element must have the same number of atoms on the reactant side (before the reaction) as on the product side (after the reaction).

In our equation, we start with octane \(\mathrm{C}_{8}\mathrm{H}_{18}\) and oxygen \(\mathrm{O}_2\) as reactants, which combine to form carbon dioxide \(\mathrm{CO}_2\) and water \(\mathrm{H}_2\mathrm{O}\) as products. To balance this equation, we need to ensure that the number of carbon, hydrogen, and oxygen atoms are the same on both sides. The balanced equation \[2\mathrm{C}_{8}\mathrm{H}_{18} + 25\mathrm{O}_2 \rightarrow 16\mathrm{CO}_2 + 18\mathrm{H}_2\mathrm{O}\] shows that this balance has been achieved. There are 16 carbon atoms, 36 hydrogen atoms, and 50 oxygen atoms on both sides of the reaction.

Understanding molar mass is key to converting between the weight of a substance and the number of molecules or atoms it contains. The molar mass is the weight in grams of one mole of a substance, and one mole contains Avogadro's number (\(6.022 \times 10^{23}\) entities) of molecules or atoms.

Octane Molar Mass

To calculate the molar mass of octane \(\mathrm{C}_{8}\mathrm{H}_{18}\), the calculation is \[8 \times 12.01 + 18 \times 1.008 = 114.23\] g/mol. This calculation comes from adding the molar masses of eight carbon atoms and eighteen hydrogen atoms, which are approximately 12.01 g/mol and 1.008 g/mol, respectively.

Carbon Dioxide Molar Mass

Similarly, for carbon dioxide \(\mathrm{CO}_2\), the molar mass calculation is \(12.01 + 2 \times 16.00 = 44.01\) g/mol. Here, we add the molar mass of one carbon atom to that of two oxygen atoms to get the total molar mass for carbon dioxide.

Stoichiometry is the aspect of chemistry that involves calculating the proportions of reactants and products in chemical reactions.

In our case, stoichiometry allows us to link the mass of octane burned to the mass of carbon dioxide produced. Using the balanced chemical equation, we know the ratio of octane to carbon dioxide is 2:16. This means that from every two moles of octane, sixteen moles of carbon dioxide are produced. With this ratio, we can determine that from \(8.752\) moles of octane, we would get \(70.016\) moles of carbon dioxide. Thus, stoichiometry serves as the bridge between the balanced equation and the quantitative outcome of the reaction.

The environmental impact of gasoline combustion is a significant concern, as this process releases pollutants, including carbon dioxide, a major greenhouse gas contributing to climate change.

During the combustion process, octane combines with oxygen to yield carbon dioxide and water vapor. Specifically, the combustion of \(1.0\) kg of octane results in about \(3.08145\) kg of carbon dioxide emission. Considering the vast amount of gasoline burned daily worldwide, this compound's release at such a scale significantly affects the atmospheric concentration of CO2, driving up the greenhouse effect and global warming. Moreover, other compounds, such as nitrogen oxides and particulates released during combustion, also contribute to air pollution and can have direct health impacts. It is clear that understanding the chemistry behind gasoline combustion is crucial for addressing its environmental footprint.