Problem 36 - Chemistry The Central Science

Question

Suppose that the gas-phase reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow\) \(2 \mathrm{NO}_{2}(g)\) were carried out in a constant-volume container at constant temperature. Would the measured heat change represent \(\Delta H\) or \(\Delta E ?\) If there is a difference, which quantity is larger for this reaction? Explain.

Step-by-Step Solution

Answer

In this gas-phase reaction at constant volume and constant temperature, the measured heat change represents both ΔH (change in enthalpy) and ΔE (change in internal energy) since there is no difference between the two quantities. This is because the change in volume (ΔV) is 0, making the relationship between ΔH and ΔE as follows: ΔH = ΔE. Therefore, both ΔH and ΔE represent the same heat change for this reaction, and there is no need to compare them to determine which one is larger.

Step 1: Understanding ΔH and ΔE

ΔH (change in enthalpy) and ΔE (change in internal energy) are two important thermodynamic properties that can describe the energy changes in a chemical reaction. The relationship between the two can be given by the equation: ΔH = ΔE + PΔV, where P is the constant pressure and ΔV is the change in volume.

Step 2: Analyzing the reaction at constant volume and temperature

Since we are told that the reaction takes place in a constant-volume container, there is no change in the volume of the system (ΔV = 0). The reaction is also happening at a constant temperature. Now, using the relationship between ΔH and ΔE, we will determine which quantity is represented by the measured heat change.

Step 3: Determining the measured heat change

Given that ΔV = 0, we can rewrite the equation for the relationship between ΔH and ΔE as: ΔH = ΔE This means that at constant volume and constant temperature, there is no difference between the change in enthalpy (ΔH) and the change in internal energy (ΔE). Therefore, the measured heat change represents both ΔH and ΔE in this case.

Step 4: Comparing ΔH and ΔE

Since ΔH and ΔE are the same for this particular reaction, there is no need to compare them to determine which one is larger. They are equal in magnitude and represent the same heat change for the given reaction at constant volume and temperature.

Key Concepts

Enthalpy

Enthalpy, often represented as \(\Delta H\), is a key concept in thermodynamics used to measure the total heat content of a system during a reaction at constant pressure. It accounts for the internal energy of the system as well as the work done by the system due to volume change.

When a reaction occurs, energy can be absorbed or released, leading to changes in enthalpy. This change is significant when calculating how heat is transferred in open systems where pressure may change, like in reactions occurring in an open container.

However, when volume change is null, such as in our scenario with a constant volume container, the enthalpy and internal energy changes are the same. Therefore, the distinction between these terms becomes less relevant under these specific conditions. Under such circumstances, measuring the heat change provides you with only one value that represents both enthalpy and internal energy changes.

Internal Energy

Internal energy, denoted as \(\Delta E\), is the total energy contained within a thermodynamic system. It encompasses the kinetic and potential energy of the molecules in the system.

In chemical reactions, changes in internal energy can occur due to various factors, including changes in volume, temperature, or phase. However, if a reaction takes place at constant volume, like in the discussion of our given reaction in the exercise, the change in internal energy can be directly correlated to the heat of the reaction.

It is important to note that at constant volume, there is no work done by or on the system (because work is related to volume changes). Thus, all the heat absorbed or released is accounted for by the change in internal energy alone. This concept simplifies calculations and is critical in understanding thermodynamic changes in specific settings like sealed containers.

Constant Volume Reaction

A constant volume reaction refers to a process occurring within a system where the volume does not change. This is typically achieved by conducting the reaction in a sealed, rigid container.

The significance of maintaining a constant volume is that it simplifies the thermodynamic analysis: the pressure-volume work term (\(P\Delta V\)) becomes zero. Consequently, under these conditions, the heat exchange for the reaction is equal to the change in internal energy, \(\Delta E\), since no work is done by or against atmospheric pressure.

This makes constant volume settings ideal for calculating internal energy changes directly from measured heat. In the example reaction of forming \(\text{NO}_2\) from \(\text{NO}\) and \(\text{O}_2\), the calculation of energy changes becomes straightforward, enabling a clear understanding of the heat changes involved without the complication of volume work.