Question

The standard heat of combustion of \(\mathrm{Al}\) is \(-837.8 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\) at \(25^{\circ} \mathrm{C}\). If \(\mathrm{Al}\) reacts with \(\mathrm{O}_{2}\) at \(25^{\circ} \mathrm{C}\), which of the following releases \(250 \mathrm{kcal}\) of heat? (a) The reaction of \(0.312 \mathrm{~mol}\) of \(\mathrm{Al}\) (b) The formation of \(0.624 \mathrm{~mol}\) of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) (c) The reaction of \(0.712 \mathrm{~mol}\) of \(\mathrm{Al}\) (d) The formation of \(0.615 \mathrm{~mol}\) of \(\mathrm{A} \mathrm{l}_{2} \mathrm{O}_{3}\)

Short answer

Option (b) releases the closest to 250 kcal (1046 kJ).

Step-by-step solution

Convert kcal to kJ

First, convert the amount of heat released from kilocalories (kcal) to kilojoules (kJ). Use the conversion factor: 1 kcal = 4.184 kJ.\[250 \text{ kcal} \times 4.184 \frac{\text{kJ}}{\text{kcal}} = 1046 \text{ kJ}\]

Understand Heat of Combustion

The standard heat of combustion for aluminum is given as \(-837.8 \text{ kJ/mol}\). This means that burning 1 mole of aluminum releases 837.8 kJ of heat. We are looking for the reaction that releases 1046 kJ of heat.

Calculate Heat Released for Each Option

Check each option to determine if it releases 1046 kJ when aluminum reacts with oxygen.(a) \(0.312 \text{ mol} \times -837.8 \text{ kJ/mol} = -261.2 \text{ kJ}\) (b) Formation of aluminum oxide: Since each \( \text{Al}_2 \text{O}_3\) needs 2 moles of \( \text{Al} \), convert \( \text{mol Al}_2 \text{O}_3 \) to \( \text{mol Al} \): \(0.624 \text{ mol} \times 2 \text{ mol Al/mol Al}_2\text{O}_3 = 1.248 \text{ mol Al}\) \(1.248 \text{ mol} \times -837.8 \text{ kJ/mol} = -1045 \text{ kJ}\) (c) \(0.712 \text{ mol} \times -837.8 \text{ kJ/mol} = -596.6 \text{ kJ}\) (d) Using the same conversion as (b), \ \(0.615 \text{ mol} \times 2 \text{ mol Al/mol Al}_2\text{O}_3 = 1.230 \text{ mol Al}\) \ \(1.230 \text{ mol} \times -837.8 \text{ kJ/mol} = -1030 \text{ kJ}\)

Compare Calculated Values with 1046 kJ

Compare each calculated energy release with 1046 kJ to determine which reaction is closest to this energy output.- Option (b) releases \(1045 \text{ kJ}\), which is closest to \(1046 \text{ kJ}\).- Options (a), (c), and (d) release significantly less heat.

Key concepts

Heat of Combustion

In thermochemistry, the heat of combustion refers to the energy released as heat when a compound undergoes complete combustion with oxygen under standard conditions. For aluminum (\(\mathrm{Al}\)), the standard heat of combustion is \(-837.8\text{ kJ/mol}\).
This means burning one mole of aluminum releases 837.8 kJ of energy. Combustion reactions like this are crucial in powering various processes, providing significant energy conversion from chemical to thermal form.

• The negative sign indicates that the process is exothermic, meaning it releases heat to the surroundings.
• This value serves as a crucial parameter in calculating energy changes during reactions involving aluminum, such as engine systems or metallurgical operations.

Understanding this concept helps engineers and scientists design systems that effectively use or manage the energy released during combustion.

Aluminum Reaction

The reaction of aluminum (\(\mathrm{Al}\)) with oxygen (\(\mathrm{O}_2\)) is a type of oxidation reaction that forms aluminum oxide (\(\mathrm{Al}_2\mathrm{O}_3}\)).
This reaction is expressed as:\[4\,\mathrm{Al} + 3\, \mathrm{O}_2 \rightarrow 2\, \mathrm{Al}_2\mathrm{O}_3\]During this reaction, aluminum acts as the reducing agent, donating electrons to oxygen and thus forming the product, aluminum oxide.

• The stoichiometry of the reaction indicates that 4 moles of \(\mathrm{Al}\) react with 3 moles of \(\mathrm{O}_2\)
• This reaction is highly exothermic, contributing to the significant release of energy noted in its heat of combustion.

This transformation is also practical in contexts where controlled heat release and stability are desired, such as in materials production and thermite reactions.

Energy Conversion

Energy conversion is a central aspect of thermochemistry, notably in reactions involving combustion where chemical energy transforms into thermal energy. When aluminum burns, the stored chemical energy in its bonds is released as heat. This example shows the direct conversion of chemical energy into usable thermal energy, important for applications like engines and power plants.

• Efficiency of energy conversion is a critical parameter, as some energy is lost to the surroundings as waste heat.
• Understanding the energy conversion helps in designing systems that can maximize the captured usable energy, reducing losses and increasing overall system efficiency.

The principles of energy conversion also play a role in developing technologies aimed at harnessing renewable energy sources.

Calorimetry

Calorimetry is the branch of thermochemistry that deals with measuring the heat of chemical reactions or physical changes. It involves using a calorimeter, which is an insulated device that measures the energy released or absorbed during a reaction.
Understanding calorimetry allows us to quantify the energy changes associated with the combustion of substances like aluminum.

• The main principle behind calorimetry is the conservation of energy: energy lost by the system is gained by the surroundings, and vice versa.
• Using calorimetric data, we can calculate specific heat capacities, enthalpy changes, and energy released during reactions.

Applying calorimetry to combustion reactions is vital in diverse fields, including material sciences, environmental studies, and energy production.