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. (a) Would the measured heat change represent \(\Delta H\) or \(\Delta E\) ? (b) If there is a difference, which quantity is larger for this reaction? (c) Explain your answer to part (b).

Short answer

The measured heat change for this gas-phase reaction at constant-volume and constant-temperature conditions represents the internal energy change, ΔE. In this case, ΔE is larger than ΔH due to the reduction in the number of moles of gas during the reaction, which results in a larger internal energy change compared to the enthalpy change.

Step-by-step solution

Part (a)

Determine whether ΔH or ΔE is represented by the measured heat change. Since the reaction is carried out in a constant-volume container, there is no work being done since the volume remains constant (the work done is given by \(w = -P_{ext}\Delta V\), and ΔV = 0 in this case). Therefore, the measured heat change represents the change in internal energy, ΔE, since it accounts only for the energy change in the system and not any work done on/by the system.

Part (b)

Determine which quantity is larger, ΔH or ΔE. To find the difference between ΔH and ΔE, we can use the following equation for reactions at constant volume: \(ΔH = ΔE + ΔnRT\), where Δn is the change in the number of moles of gas between reactants and products, R is the gas constant, and T is the temperature. For the given reaction, \(2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\), the change in moles of gas is: Δn = moles of products - moles of reactants = (2 - 2 - 1) = -1. Since Δn is negative, ΔnRT will also be negative. Thus, ΔH = ΔE - |ΔnRT|. So the relationship between ΔH and ΔE for this reaction is: ΔH < ΔE. Therefore, the internal energy change, ΔE, is larger for this reaction.

Part (c)

Explain the difference between ΔH and ΔE for this reaction. The difference in ΔH and ΔE in this reaction can be attributed to the change in the number of moles of gas during the reaction. Since one mole of gas is being consumed in the process (Δn = -1), the system releases energy in the form of heat and work done due to contraction. However, since the reaction occurs at constant volume, no work is done, and the difference in ΔH and ΔE is a result of the decrease in the number of moles of gas. In this case, the decrease in the number of moles of gas results in a larger internal energy change, ΔE, compared to the enthalpy change, ΔH.

Key concepts

Enthalpy Change (ΔH)

Enthalpy change, denoted as ΔH, is a fundamental concept in thermodynamics in chemistry. It represents the heat change at constant pressure during a chemical reaction. Enthalpy itself is a state function that combines the internal energy of a system (E) with the product of its pressure (P) and volume (V), i.e., H = E + PV.

This means ΔH essentially accounts for the heat absorbed or released due to changes in the system's energy as well as the work done by the system as it expands or contracts. During reactions involving gases, especially those not at constant volume, ΔH becomes a useful indicator of the energy changes associated with reactions. Unlike ΔE (internal energy change), ΔH can include pressure-volume work, provided the reaction occurs at constant pressure.

Internal Energy Change (ΔE)

Internal energy change, denoted as ΔE, is crucial when considering reactions in the realm of thermodynamics, particularly in constant-volume settings. ΔE reflects the total energy change within a closed system. It is associated with all forms of energy including kinetic, potential, and chemical energy.

In a constant-volume reaction, no work is done on or by the system because the volume remains unchanged (work done is given by the formula: w = -P_ext ΔV, which equals zero when ΔV = 0). Therefore, any heat change observed under these conditions is directly related to ΔE. This makes ΔE easier to calculate and directly measure in reactions conducted in closed containers where volume doesn't change. This property makes internal energy change a straightforward measure of energy variation due entirely to heat.

Constant-Volume Reactions

Constant-volume reactions, such as those occurring in sealed containers or bombs, are unique in thermodynamic studies. Here, the volume of the reaction vessel does not change throughout the process, eliminating the possibility of performing work through expansion or contraction.

These reactions are particularly important when considering reactions of gases, as it provides a direct measure of the system's internal energy change ( ΔE ). In such a scenario, the reaction's heat change is indicative solely of ΔE since no work relates to volume change. This constraint simplifies calculations and measurements of energy changes for reactions. It also highlights differences in energy measurement compared to constant-pressure reactions, where work can affect energy assessments.

Mole Concept in Reactions

The mole concept is a foundational idea in chemistry and essential in interpreting thermodynamic reactions. It relates the quantitative measures of substances involved in a reaction to energy changes, helping predict the energy needing exchange.

Considering the equation for enthalpy change, ΔH = ΔE + ΔnRT, a change in the number of moles ( Δn ) of gaseous reactants versus products influences the reaction's energy dynamics. This change, Δn, represents the difference between moles of products and moles of reactants.

• If Δn is positive, more gas is produced than consumed, often increasing ΔH due to expansion work.
• If Δn is negative, like in the case of the provided reaction, the overall gas volume decreases, affecting ΔH by a negative value of ΔnRT, leading to a lower ΔH compared to ΔE under constant volume.

The mole concept is thus pivotal in understanding not just stoichiometry but also how energy transformations occur in chemical processes.