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

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) \(\Delta \mathrm{U}>0, \mathrm{w}>0\)

Step-by-Step Solution

Answer

Answer: (a) ΔU < 0, w = 0 .

Step 1: Understanding the Reaction

The reaction involves zinc (Zn) reacting with sulfuric acid ( H_2SO_4 ) to generate hydrogen gas ( H_2 ). The reaction is Zn + H_2SO_4 → ZnSO_4 + H_2. This is a single replacement reaction, where zinc displaces hydrogen, releasing energy as it occurs.

Step 2: Concept of Internal Energy (ΔU)

In a bomb calorimeter, the reaction occurs at constant volume. The change in internal energy ( ΔU ) is measured. For exothermic reactions, where energy is released, ΔU decreases. Thus for this reaction, ΔU < 0 .

Step 3: Work Done in Bomb Calorimeter (w)

In a bomb calorimeter, reactions are performed at constant volume, hence no work is done by/against the surroundings. The work done ( w ) is zero as w = -PΔV and ΔV = 0 for constant volume conditions.

Step 4: Selecting the Correct Answer

Given that ΔU < 0 (exothermic reaction) and w = 0 (no work is done in bomb calorimeter), we match these with option (a): ΔU < 0, w = 0 .

Key Concepts

Bomb Calorimeter

A bomb calorimeter is a device used to measure the heat of a reaction at constant volume. Unlike other calorimeters, it does not allow the volume to change during a chemical reaction, ensuring that no mechanical work is performed. This is crucial for accurately determining the change in internal energy for reactions, particularly exothermic ones that release heat.

The setup typically involves a robust, sealed container where the reaction occurs, completely submerged in water. The temperature change in the water is monitored as the reaction proceeds, providing the data needed to calculate the energy change.

• Sealed Container: Prevents volume change.
• Highly Sensitive Thermometers: Measures slight temperature changes.
• Sturdy Construction: Handles the pressure from gaseous reactions.

Internal Energy (ΔU)

Internal energy (94U) refers to the total energy stored within a system. It includes both the kinetic and potential energy of the particles making up the system. In thermodynamics, when we talk about the change in internal energy, particularly in reactions, we're referring to how the system's energy changes from its initial state to its final state.

In the context of a bomb calorimeter, because the volume is constant, we focus solely on energy changes as heat. For an exothermic reaction, the system releases energy as heat, causing the internal energy to decrease (94U < 0). It's a direct reflection of the energy dynamics within the closed system.

• Constant Volume: Only heat transfer matters.
• Exothermic Reaction: Decreases internal energy (94U < 0).

Exothermic Reaction

An exothermic reaction is one that releases energy into its surroundings, usually in the form of heat. In simple terms, more energy is released in forming product bonds than is required to break reactant bonds. This gives off excess energy to the environment, typically raising the temperature of the surroundings.

In chemical equations, this is often indicated with negativity in enthalpy change, but more importantly here, it affects internal energy in a closed system. When a reaction occurs in a bomb calorimeter, its exothermic nature results in a reduction of the reaction’s internal energy because energy is lost as heat output.

• Heat Release: Identified by temperature rise.
• Energy Output: More is released than consumed.

Work Done (w)

In thermodynamics, work refers to the energy transferred when an object is moved by a force. It's a key component of the energy balance for chemical reactions. However, in a bomb calorimeter which operates at constant volume, there is no change in volume, which means no work is done. Mathematically, this is explained through the equation \( w = -P\Delta V \), where \( \Delta V = 0 \).

This makes it an ideal system for measuring the heat of reaction without the complication of work affecting internal energy. Therefore, for reactions executed in a bomb calorimeter, the work done (w) is always zero.

• Constant Volume: No change, no work.
• Focus on Heat: Allows precise energy measurement.

Single Replacement Reaction

A single replacement reaction involves one element being displaced out of a compound by another element. It's like a dance where one partner is swapped for another during the routine.

In the exercise, zinc ( Zn ) replaces hydrogen in sulfuric acid ( H_2SO_4 ), creating zinc sulfate ( ZnSO_4 ) and releasing hydrogen gas ( H_2 ). This reactive process not only follows a predictable pattern but is also often exothermic, releasing energy due to strong bonds formed during the reaction. It involves identifying reactive partners and understanding which elements can displace others based on reactive tendencies and activity series.

• Element Displacement: Key feature of single replacement reactions.
• Often Exothermic: Releases energy as bonds form.