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) \(\Delta U<0, w=0\) (b) \(\Delta U<0, w<0\) (c) \(\Delta U>0, w=0\) (d) \(\Delta U>0, w>0\)

Short answer

(a) \( \Delta U<0, w=0 \)

Step-by-step solution

Understand Bomb Calorimeter

In a bomb calorimeter, reactions take place at constant volume. This means there is no work done by expansion or compression (since work \( w = -P\Delta V \) and \( \Delta V = 0 \)), thus \( w = 0 \).

Analyze Energy Change (\( \Delta U \))

The reaction between \( \mathrm{Zn} \) and \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is exothermic, meaning it releases heat. For exothermic reactions, the internal energy change \( \Delta U \) is negative because energy is released from the system to the surroundings.

Evaluate the Options

Given that \( \Delta U < 0 \) and \( w = 0 \), we compare these findings with the given options: (a) \( \Delta U<0, w=0 \) (b) \( \Delta U<0, w<0 \) (c) \( \Delta U>0, w=0 \) (d) \( \Delta U>0, w>0 \). The correct answer is option (a) because it matches our analysis.

Key concepts

Bomb Calorimeter

A bomb calorimeter is an essential tool in thermochemistry for measuring the heat of combustion of a substance. It's called a "bomb" calorimeter because the reaction takes place in a strong, sealed container — essentially a "bomb" — that can withstand high pressure. In this set-up, the reaction occurs at a constant volume, which is crucial for understanding certain properties of the reaction.

• Constant Volume: In a bomb calorimeter, the volume remains unchanged during the reaction. This means that any work done would be related to volume change, which is zero in this case.
• Work Equation: Since work (\(w\) = -\(P\Delta V\)) depends on a change in volume (\(\Delta V\)), and here \(\Delta V = 0\), it follows that \(w = 0\).
• Heat Measurement: The main objective is to measure the heat involved in the reaction. The heat absorbed or released gives insight into the energy changes within the system.

This ability to measure the energy change without the complexities of pressure-volume work makes the bomb calorimeter a powerful tool for studying exothermic and endothermic reactions.

Exothermic Reaction

An exothermic reaction is a type of chemical reaction that releases energy in the form of heat. These reactions are often seen in combustion processes and certain types of chemical bonding, where more energy is given off than is taken in.

• Energy Release: During an exothermic reaction, the energy released when bonds form in the reaction products is greater than the energy required to break the bonds in the reactants.
• Temperature Effect: The release of energy typically results in an increase in temperature of the surroundings, which can often be felt or measured.
• Internal Energy Change (\(\Delta U\)): For exothermic reactions, the internal energy change is negative, since the system loses energy to the surroundings. This is why the value of \(\Delta U\) in these reactions is less than zero.

Exothermic reactions are crucial in many real-world applications, such as energy generation in power plants and metabolic processes in living organisms.

Internal Energy Change

Internal energy change, represented by \(\Delta U\), plays a key role in thermochemistry as it reflects the total change in a system's energy during a chemical process. It embodies all forms of energy, including kinetic and potential energies, of the particles within the system.

• Energy Conservation: According to the first law of thermodynamics, the energy of an isolated system is constant, but it can change form. Hence, \(\Delta U\) gives us insights into how energy is either absorbed or released in a reaction.
• System and Surroundings: In chemical reactions, systems release or absorb energy from their surroundings. If \(\Delta U\) is negative, the system has released energy, typical of exothermic reactions. Conversely, if \(\Delta U\) is positive, energy is absorbed, indicating an endothermic process.
• Non-Work Changes: In scenarios like reactions in a bomb calorimeter, where there’s no volume change, \(\Delta U\) captures energy changes without involving work, simplifying the analysis.

Understanding internal energy change helps in predicting spontaneity and feasibility of reactions, making it a cornerstone concept in physical chemistry and engineering fields.