When 0.850 g of Mg was burned in oxygen in a constant-volume...

When $0.850 \mathrm{g}$ of $\mathrm{Mg}$ was burned in oxygen in a constant-volume calorimeter, 25.4 kJ of energy as heat was evolved. The calorimeter was in an insulated container with $750 .$ g of water at an initial temperature of $18.6^{\circ} \mathrm{C}$. The heat capacity of the bomb in the calorimeter is $820 . \mathrm{J} / \mathrm{K}.$ (a) Calculate $\Delta U$ for the oxidation of $\mathrm{Mg}$ (in kJ/mol Mg). (b) What will be the final temperature of the water and the bomb calorimeter in this experiment?

When $0.850 \mathrm{g}$ of $\mathrm{Mg}$ was burned in oxygen in a constant-volume calorimeter, 25.4 kJ of energy as heat was evolved. The calorimeter was in an insulated container with $750 .$ g of water at an initial temperature of $18.6^{\circ} \mathrm{C}$. The heat capacity of the bomb in the calorimeter is $820 . \mathrm{J} / \mathrm{K}.$
(a) Calculate $\Delta U$ for the oxidation of $\mathrm{Mg}$ (in kJ/mol Mg).
(b) What will be the final temperature of the water and the bomb calorimeter in this experiment?

Key Concepts

Conservation of Energy in Calorimetry

This fundamental principle states that the energy released or absorbed by a reaction must equal the energy absorbed or lost by the surrounding system—in this case, the water and the calorimeter. This balance is used to calculate changes such as temperature rises or internal energy changes.

Calorimeter and Specific Heat Capacity

Understanding the combined heat capacity of the calorimeter and the water it contains is crucial. The calorimeter's heat capacity (a measure of how much heat is needed to raise its temperature) along with the water’s specific heat capacity enables precise calculation of the temperature change resulting from the reaction.

Molar Energy Conversion

Converting the energy change from a given mass of reactant to a per-mole basis is essential for comparing reaction energetics. This involves using the molar mass of the reactant to determine the number of moles, thereby allowing the energy change to be expressed in kJ per mole.

Constant Volume Calorimetry

This is a technique used to measure the energy change of a reaction where the reaction occurs at a fixed volume. In a bomb calorimeter, because the volume remains constant, no work is done by expansion; thus, the heat evolved directly represents the change in internal energy (?U) of the system.

Internal Energy (?U) Determination

In a constant-volume process, the energy measured as heat corresponds to the change in the system's internal energy. This is particularly important when determining the thermochemistry of a reaction, as it provides insight into the energy released or absorbed at a molecular level.

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