Consider the following reaction: 2 CH₃OH(g) → 2 CH₄(g) + O₂(g) ΔH = +252.8 kJ (d) How many kilojoules of heat are released when 38.5 g of CH₄(g) reacts completely with O₂(g) to form CH₃OH(g) at constant pressure?

Verified step by step guidance

1. First, determine the molar mass of CH₄ (methane) by adding the atomic masses of carbon (C) and hydrogen (H). The molar mass of C is approximately 12.01 g/mol and H is approximately 1.01 g/mol. Since CH₄ has one carbon and four hydrogens, its molar mass is 12.01 g/mol + (4 imes 1.01 g/mol) = 16.05 g/mol.
2. Next, calculate the number of moles of CH₄ by dividing the given mass of CH₄ by its molar mass. Use the formula: Number of moles = Mass (g) / Molar mass (g/mol).
3. According to the stoichiometry of the reverse reaction, 2 moles of CH₄ produce 2 moles of CH₃OH and release 252.8 kJ of heat. Therefore, calculate the heat released per mole of CH₄ by dividing the total heat change by the number of moles of CH₄ involved in the reaction.
4. Multiply the number of moles of CH₄ calculated in step 2 by the heat released per mole of CH₄ (from step 3) to find the total heat released when 38.5 g of CH₄ reacts.
5. Since the reaction is exothermic (releases heat), ensure the sign of the heat released is negative, indicating that energy is being released by the system.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of substance consumed or produced in a reaction. In this case, we need to use the stoichiometric coefficients from the balanced equation to relate the moles of CH4 produced to the moles of CH3OH formed.

Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a measure of the heat content of a system at constant pressure. A positive ΔH indicates that the reaction is endothermic, meaning it absorbs heat. In this question, the ΔH value of +252.8 kJ indicates that this amount of energy is required to convert CH3OH into CH4 and O2, which will help us calculate the heat released when CH4 reacts to form CH3OH.

Molar Mass and Heat Calculations

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. To find out how much heat is released when a certain mass of CH4 reacts, we first convert grams of CH4 to moles using its molar mass. Then, we can use the stoichiometry of the reaction and the enthalpy change to calculate the total heat released during the reaction.