Using information in Appendices B and C, calculate the minimum grams of propane, C3H8(g), that must be combusted to provide the energy necessary to convert 5.50 kg of ice at -20 °C to liquid water at 75 °C

Verified step by step guidance

1. Step 1: Calculate the total energy required to convert 5.50 kg of ice at -20 °C to liquid water at 75 °C. This process involves three steps: warming the ice to 0 °C, melting the ice, and warming the water to 75 °C. Use the specific heat capacities and heat of fusion for water from Appendix B to calculate the energy for each step and sum them up.
2. Step 2: Convert the total energy calculated in step 1 from Joules to kilojoules if necessary, as the heat of combustion of propane is usually given in kilojoules per mole.
3. Step 3: Use the heat of combustion for propane from Appendix C to calculate the number of moles of propane needed to provide the total energy calculated in step 2. Remember that the heat of combustion is the energy released per mole of propane combusted, so divide the total energy by the heat of combustion.
4. Step 4: Convert the number of moles of propane calculated in step 3 to grams using the molar mass of propane. The molar mass of propane can be calculated by adding up the molar masses of its constituent atoms (3 carbons and 8 hydrogens).
5. Step 5: The result from step 4 is the minimum grams of propane that must be combusted to provide the necessary energy. Remember that this is a theoretical minimum, and actual combustion processes may be less efficient and require more fuel.

Key Concepts

Thermodynamics of Phase Changes

Understanding the thermodynamics of phase changes is crucial for this problem. It involves calculating the energy required to change the state of a substance, such as melting ice into water and heating it. The specific heat capacity and the heat of fusion are key parameters that quantify the energy needed for these transformations.

Combustion Reactions

Combustion reactions involve the reaction of a fuel with oxygen to produce energy, typically in the form of heat. For propane (C3H8), the balanced chemical equation shows how much energy is released per mole of propane combusted. This energy release must be calculated to determine how much propane is needed to provide the required energy for the phase change and heating of water.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. In this context, it is used to convert the energy required for heating and phase changes into moles of propane needed for combustion. By applying stoichiometric principles, one can relate the energy produced from propane combustion to the energy needed for the ice-to-water conversion.