Question

For the reaction of one mole of \(\mathrm{Zn}\) dust with one mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in a bomb calorimeter, \(\Delta \mathrm{U}\) and \(\mathrm{w}\) corresponds to: (a) \(\Delta \mathrm{U}<0, \mathrm{w}=0\) (b) \(\Delta \mathrm{U}<0, \mathrm{w}<0\) (c) \(\Delta \mathrm{U}>0, \mathrm{w}=0\) (d) \(\Delta U>0, w>0\)

Short answer

(a) \(\Delta \mathrm{U}<0, \mathrm{w}=0\)

Step-by-step solution

Understand the Reaction Context

The problem involves a reaction between zinc (Zn) and sulfuric acid (\(\mathrm{H}_{2} \mathrm{SO}_{4}\)) happening inside a bomb calorimeter. In a bomb calorimeter, the reaction occurs at constant volume, which means no work is done through expansion or compression of the gas phase.

Recall the Relationship between ΔU and Work (w)

For a system at constant volume, such as a bomb calorimeter, the change in internal energy (\(\Delta \mathrm{U}\)) is equal to the heat added to the system, as no work is done (\(w = 0\)). Therefore, \(\Delta \mathrm{U}\) is affected only by the heat exchange.

Relate the Sign of ΔU to the Type of Reaction

The reaction of zinc with sulfuric acid is exothermic, releasing heat. For exothermic reactions, \(\Delta \mathrm{U}\) is negative because the system loses energy as heat is released to the surroundings.

Determine the Correct Option

Since \(\Delta \mathrm{U} < 0\) and \(w = 0\) (constant volume with no work done), the correct choice is (a).

Key concepts

Bomb Calorimeter

A bomb calorimeter is a special type of device used to measure the energy change, specifically the heat that is released or absorbed during a chemical reaction. It consists of a strong, sealed container—the bomb—that holds the reaction mixture. Because this container is sealed, reactions within a bomb calorimeter occur at constant volume. Thus, the energy changes assessed in bomb calorimeters are unique because they avoid the complications that arise from volume changes.

• Structure: It includes a sturdy vessel to withstand high pressures, as it is closed tightly to prevent gas expansion or compression.
• Function: It isolates the reaction from its surroundings, ensuring that all heat exchange is focused on the reaction's heat output or absorption, providing precise energy change data.

Understanding bomb calorimeters is essential because they offer a practical approach for observing reactions in terms of energy, essential in thermochemistry.

Internal Energy Change

Internal energy change is indicated by the symbol \(B\Delta UD\), representing the total change in energy within a system. For reactions in a bomb calorimeter, which occur at constant volume, this change in internal energy is crucial.
In thermodynamics, \(B\Delta U = q + wD\) (change in internal energy = heat added to the system + work done on the system). However, in a constant volume process with a bomb calorimeter, the term for work (B\(wD\)) becomes zero because there is no change in volume: \[\Delta U = q\ (at\ constant\ volume)\]

• For exothermic reactions (heat released), \(B\Delta UD\) is typically negative as energy exits the system.
• In contrast, an endothermic reaction (heat absorbed) would have \(B\Delta UD\) positive, reflecting energy entering the system.

The key is recognizing how internal energy relates exclusively to heat during constant volume processes.

Constant Volume Process

During a constant volume process, such as one in a bomb calorimeter, the volume of the system does not change. This unique setting simplifies energy considerations because no expansion or compression work is performed.

• No Work: With volume held constant, work (B\(wD\)) due to pressure-volume changes is zero, simplifying calculations of energy change.
• Focus on Heat: With B\(wD\) being zero, \(B\Delta UD\) is solely determined by heat transfer (B\(qD\)). Thus, understanding the heat involved in the reaction directly informs us of internal energy changes.

This environment allows chemists to focus mainly on the heat absorbed or released, crucial for accurate analysis of exothermic or endothermic reactions.

Exothermic Reaction

An exothermic reaction is defined by its release of heat to its surroundings. In the context of thermochemistry and particularly in a bomb calorimeter, these reactions are significant because they directly lower the internal energy of the system.

• Heat Release: Energy is released in the form of heat, which means the products of the reaction hold less energy than the reactants did.
• Energy Flow: The system loses energy, leading to a negative \(B\Delta UD\), as seen in the reaction of zinc with sulfuric acid.
• Real-world Examples: Combustion reactions, like that of hydrocarbons, are classic exothermic processes.

Recognizing an exothermic reaction involves observing the system's energy loss, which helps in understanding energy changes during reactions within thermochemical studies.