Consider the combustion of propane: $$ \mathrm{C}_{3} \mathrm{H}_{8}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ (a) Balance the reaction. (b) Divide all coefficients by the coefficient on propane, so that you have the reaction for the combustion of 1 mol of propane. (c) \(\Delta H_{\mathrm{rxn}}\) for the combustion of one mole of propane is \(-2219 \mathrm{~kJ}\). What mass of propane would you need to burn to generate \(5.0 \mathrm{MJ}\) of heat? (d) If propane costs about \(\$ 0.67 / \mathrm{L}\) and has a density of \(2.01 \mathrm{~g} / \mathrm{cm}^{3}\), how much would it cost to generate \(5.0 \mathrm{MJ}\) of heat by burning propane?

Chemical reaction balancing is a fundamental aspect of chemistry that ensures the law of conservation of mass is respected. This law states that matter cannot be created or destroyed in a chemical reaction. Therefore, in the case of propane combustion, the number of atoms for each element must be the same on both sides of the equation. The process involves adjusting the coefficients (the numbers placed before the chemical formulas) to balance the atoms.

The balance of atoms allows us to predict the exact quantities of reactants needed and the amount of products formed. It is also crucial for calculations involving chemical reactions, like those done in the exercise to determine how much energy each mole of propane releases upon combustion. Balancing the equation makes further calculations in stoichiometry and thermochemistry possible, ensuring we can accurately depict the real-world chemical processes.

Thermochemistry is the study of heat changes that accompany chemical reactions. In the given exercise, the combustion of propane releases heat, a type of energy. The term \(\Delta H_{\mathrm{rxn}}\) represents the enthalpy change for the reaction, which is the heat absorbed or released under constant pressure. For the propane combustion reaction, \(\Delta H_{\mathrm{rxn}}\) is negative, indicating that the reaction is exothermic—it releases energy to the surroundings.

Understanding thermochemistry is crucial for various applications, such as calculating the energy content of fuels. By knowing the \(\Delta H_{\mathrm{rxn}}\) value, we can relate the quantity of a substance combusted to the amount of energy released, which is practically applicable in fields like engineering and environmental science.

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is grounded in the balanced chemical equation, through a concept known as the mole ratio. In this exercise, stoichiometry allows us to understand the quantities of propane and oxygen needed for complete combustion, as well as the amounts of carbon dioxide and water produced.

For the given problem, stoichiometry is used to find out how much mass of propane is needed to generate a certain amount of heat energy. After balancing the equation, one can use the coefficients to establish a conversion factor between moles of reactants and products. These conversion factors make it possible to relate a given mass of propane to the corresponding energy released, enabling us to solve problems involving the practical use of fuel, like in heaters or engines.

Energy conversion calculations are central to understanding how different forms of energy can be transformed from one type to another, such as chemical energy in propane to heat energy upon its combustion. These calculations are essential for determining the efficiency and cost-effectiveness of energy sources.

In the propane combustion exercise, we perform energy conversion calculations to find out how much propane is needed to produce a desired amount of heat energy, measured in mega-joules (MJ). By knowing the enthalpy change per mole of propane and the energy required, we can calculate the mass of propane needed. Moreover, by considering the cost and density of propane, we can further calculate the economic costs associated with energy production. Energy conversion calculations not only help in academic exercises but also play a crucial role in real-world applications, such as budgeting for heating costs and designing energy-efficient systems.