Suppose that the gas-phase reaction 2 NO(g) + O2(g) → 2 NO2(g) were carried out in a constant-volume container at constant temperature. (a) Would the measured heat change represent _x001F_H or _x001F_E? (b) If there is a difference, which quantity is larger for this reaction? (c) Explain your answer to part (b).

Verified step by step guidance

Step 1: Understand the difference between enthalpy change (ΔH) and internal energy change (ΔE). ΔH is the heat change at constant pressure, while ΔE is the heat change at constant volume.

Step 2: Recognize that the problem states the reaction occurs in a constant-volume container, which means the measured heat change represents ΔE, the change in internal energy.

Step 3: Recall the relationship between ΔH and ΔE: ΔH = ΔE + ΔnRT, where Δn is the change in moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

Step 4: Calculate Δn for the reaction: 2 NO(g) + O2(g) → 2 NO2(g). The change in moles of gas, Δn, is (moles of products) - (moles of reactants) = 2 - (2 + 1) = -1.

Step 5: Since Δn is negative, ΔH = ΔE + ΔnRT will be less than ΔE, meaning ΔE is larger than ΔH for this reaction.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy (_x001F_H)

Enthalpy is a thermodynamic quantity that represents the total heat content of a system at constant pressure. It accounts for the internal energy of the system plus the product of its pressure and volume. In reactions occurring at constant volume, the change in enthalpy can be related to heat transfer, but it is not directly measured since pressure is not constant.

Internal Energy (_x001F_E)

Internal energy is the total energy contained within a system, including kinetic and potential energies of the particles. For reactions occurring in a constant-volume container, the change in internal energy is equal to the heat exchanged, as no work is done on or by the system. This makes internal energy a crucial factor in understanding heat changes in gas-phase reactions.

Work and Heat in Reactions

In chemical reactions, the distinction between heat and work is essential. At constant volume, no work is done by the system (since volume does not change), meaning that the heat change observed corresponds directly to the change in internal energy. Therefore, for the reaction in question, the change in internal energy (_x001F_E) will be greater than the change in enthalpy (_x001F_H) because _x001F_H includes the work term that is zero in this scenario.

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