Problem 42 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction of one mole of 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) \(\Delta U<0, w<0\) (c) \(\Delta U>0, w=0\) (d) \(\Delta U>0, w>0\)

Step-by-Step Solution

Answer

(a) \(\Delta U<0, w=0\) because it's exothermic in a constant volume calorimeter.

Step 1: Analyze the Reaction Setup

The reaction takes place in a bomb calorimeter, which is a constant volume setup. This means there is no work done by expansion or compression (since work done by gases during expansion/compression is given by the equation \( w = - P \Delta V \)) at constant volume.

Step 2: Identify the Type of Reaction

The reaction of Zn with \( \mathrm{H}_2 \mathrm{SO}_4 \) is exothermic, as it releases energy in the form of heat when zinc reacts with sulfuric acid, producing hydrogen gas and zinc sulfate.

Step 3: Understand Enthalpy and Internal Energy Changes

In an exothermic reaction, the internal energy change \( \Delta U \) is negative because the system releases energy to the surroundings. Since it takes place at constant volume in a bomb calorimeter, the change in internal energy is equivalent to the heat change, \( q_v = \Delta U \).

Step 4: Determine Work Done

As identified in step 1, in a bomb calorimeter, which maintains constant volume, the work done \( w = 0 \) because \( \Delta V = 0 \). Therefore, the reaction does not involve work done by expansion or compression.

Key Concepts

Bomb Calorimeter

The bomb calorimeter is a special instrument used to measure the heat of a chemical reaction occurring at constant volume. It is crucial for understanding thermochemistry, as it helps scientists determine the energy changes during a reaction. This device consists of a strong container called a 'bomb,' where the reactants are placed. Once the reaction occurs, the heat generated or absorbed is measured by the surrounding water bath or another medium. The essential characteristic of the bomb calorimeter is that it maintains a constant volume. This means the pressure might change during the reaction, but the container does not expand or contract.

• Constant volume: Ensures no work is done through volume change, meaning work (\( w \)) is zero.
• Applications: Commonly used for combustion reactions to accurately measure heat release since the container can withstand high pressures.

Knowing that no work is done due to constant volume is key to solving many thermochemical problems involving bomb calorimeters, like the reaction between zinc and sulfuric acid.

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy by light or heat. It occurs when the energy needed to break the bonds in the reactants is less than the energy released when new bonds are formed in the products.In the case of zinc reacting with sulfuric acid, this reaction is exothermic. Here zinc displaces hydrogen from the acid, forming zinc sulfate and hydrogen gas, which results in the release of heat.

• Characteristics of exothermic reactions:
  - Release energy
  - Temperature of the surroundings increases
  - Often accompanies combustion and oxidation reactions
• Examples: Combustion of fuels, formation of rust, and cellular respiration in living organisms.

Understanding this concept clarifies why the internal energy change (\( \Delta U \)) is negative, signifying an exothermic process in a bomb calorimeter.

Internal Energy

Internal energy is a fundamental concept in thermochemistry. It is the total energy contained within a system, and it comprises both the kinetic energy from particle movement and the potential energy from chemical bonds. During a chemical reaction, changes in internal energy (\( \Delta U \)) occur, representing whether energy is absorbed or released.For the reaction of zinc with sulfuric acid in a bomb calorimeter, understanding how internal energy changes help explain the process:

• Negative \( \Delta U \): Indicates the system loses energy, aligning with exothermic reactions which release heat.
• Energy Equation at Constant Volume: In a bomb calorimeter, \( \Delta U = q_v \), reflecting the entire change in internal energy is due to heat since no work is done from volume change.

Grasping these concepts allows students to predict and interpret energy changes accurately in chemical reactions.