The following equation shows the conversion of aluminum oxide (from the ore bauxite) to aluminum: 2 Al2O3(s) → 4 Al(s) + 3 O2(g) ∆H = +801 kcal/mol (+3350 kJ/mol) c. How many kilocalories are required to produce 10.0 g of aluminum? How many kilojoules?

Ch.7 Chemical Reactions: Energy, Rate and Equilibrium

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

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McMurry 8th Edition

Ch.7 Chemical Reactions: Energy, Rate and Equilibrium

문제 4c

7장, 문제 4c

The following equation shows the conversion of aluminum oxide (from the ore bauxite) to aluminum:
2 Al₂O₃(s) → 4 Al(s) + 3 O₂(g) ∆H = +801 kcal/mol (+3350 kJ/mol)
c. How many kilocalories are required to produce 10.0 g of aluminum? How many kilojoules?

검증된 단계별 안내

Step 1: Calculate the molar mass of aluminum (Al) using the periodic table. The atomic mass of aluminum is approximately 26.98 g/mol.

Step 2: Convert the given mass of aluminum (10.0 g) to moles using the formula: moles = mass / molar mass. Substitute the values: moles = 10.0 g / 26.98 g/mol.

Step 3: Use the stoichiometry of the reaction to determine the relationship between moles of aluminum and the enthalpy change (∆H). From the balanced equation, 4 moles of Al correspond to +801 kcal. Set up a proportion to find the energy required for the calculated moles of aluminum.

Step 4: Convert the energy from kilocalories to kilojoules using the conversion factor: 1 kcal = 4.184 kJ. Multiply the energy in kilocalories by 4.184 to find the energy in kilojoules.

Step 5: Report the energy required in both kilocalories and kilojoules, ensuring the units are clearly labeled.

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주요 개념

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Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this case, stoichiometry will help determine how much aluminum can be produced from a given mass of aluminum oxide.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. For aluminum, the molar mass is approximately 27 g/mol, which will be used to find out how many moles correspond to 10.0 g of aluminum.

Enthalpy Change (∆H)

Enthalpy change (∆H) represents the heat absorbed or released during a chemical reaction at constant pressure. In this equation, the positive value indicates that the reaction is endothermic, meaning it requires energy input. Understanding ∆H is crucial for calculating the total energy required to produce a specific amount of aluminum from aluminum oxide, as it directly relates to the amount of heat needed per mole of aluminum produced.