Question

Assume that the following reaction occurs at constant pressure: $$2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s)$$ (a) If you are given \(\Delta H\) for the reaction, what additional information do you need to determine \(\Delta E\) for the process? (b) Which quantity is larger for this reaction? (c) Explain your answer to part (b).

Short answer

To determine ΔE for the process, given ΔH, we need additional information: the change in volume (ΔV) and the pressure (P). For this reaction, ΔE is larger than ΔH due to the decrease in the volume of the system as the reaction proceeds, resulting in a higher internal energy change and a smaller enthalpy change because part of the energy released escapes the system as work.

Step-by-step solution

Part (a): Determining the additional information needed to find ΔE

Given the change in enthalpy (ΔH) for the reaction, we will need additional information to find the change in internal energy (ΔE). We can use the relationship between ΔH and ΔE: ΔH = ΔE + PΔV To find ΔE, we need to determine the change in volume (ΔV) of the system during the reaction and the constant pressure (P) at which the reaction occurs. Therefore, the additional information required to find ΔE is the change in volume (ΔV) and the pressure (P).

Part (b): Comparing ΔH and ΔE

In order to compare ΔH and ΔE for the given reaction, let's first analyze the difference in the number of moles of gas molecules involved in the reaction. The reaction is as follows: \( 2 \mathrm{Al}(s) + 3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s) \) We have 3 moles of Cl₂(g) in the reactants and no gaseous products. Therefore, the reaction results in a decrease in the number of gas molecules, which means a decrease in the volume of the system (ΔV < 0). Now let's consider the relationship between ΔH, ΔE, and ΔV: ΔH = ΔE + PΔV Since we are given that the reaction occurs at constant pressure, and we have established that ΔV is negative, the product PΔV will be negative as well. If we consider ΔH = ΔE - |PΔV|, we can see that ΔH will be smaller than ΔE for this reaction, meaning that ΔE is larger.

Part (c): Explaining the answer to part (b)

The reason ΔE is larger than ΔH for this reaction is due to the decrease in the volume of the system as the reaction proceeds. When there is a net decrease in moles of gas during the reaction, the system contracts, and work is done by the system on the surroundings. This results in a higher internal energy change (ΔE) and a smaller enthalpy change (ΔH) because part of the energy released in the reaction escapes the system as work. In summary, for the given reaction, the additional information needed to determine ΔE is the change in volume (ΔV) and the pressure (P). The quantity that is larger for this reaction is ΔE. The reason ΔE is larger than ΔH is that the system contracts during the reaction, and work is done by the system on the surroundings, resulting in a larger internal energy change.

Key concepts

Enthalpy Change

Understanding enthalpy change (ΔH) is crucial when studying thermochemistry. Enthalpy change refers to the heat absorbed or released during a chemical reaction at constant pressure. It is a thermodynamic property that provides insights into the energy exchanged between a system and its surroundings. For reactions occurring at constant pressure, the enthalpy change can be directly associated with the heat exchanged, making ΔH an essential parameter in characterizing the energetics of chemical processes.

For instance, in the given reaction between aluminum and chlorine gas to form aluminum chloride, if the reaction releases heat, it is exothermic and ΔH is negative. Conversely, if the reaction absorbs heat, it is endothermic and ΔH is positive. Thus, measuring or calculating the enthalpy change helps us determine whether a reaction is energetically favorable and provides a basis for predicting the reaction's impact on the surrounding environment.

Internal Energy Change

The concept of internal energy change (ΔE), also known as the change in internal energy, describes the total change in energy within a system. This internal energy encompasses all forms of energy within the system, including kinetic energy of the particles and potential energy due to chemical bonds and intermolecular forces.

During a chemical reaction, such as the formation of aluminum chloride from aluminum and chlorine gas, ΔE accounts for not only the heat exchange (like enthalpy) but also the work done on or by the system when there is a change in volume. The calculation of ΔE provides a more comprehensive understanding of how energy is redistributed throughout the system and its surroundings during a chemical reaction and is essential for assessing the full energy implications of chemical processes.

Relationship Between ΔH and ΔE

Exploring the relationship between ΔH and ΔE is a key aspect of thermochemistry. The two quantities are interconnected by the equation: ΔH = ΔE + PΔV, where P is the pressure and ΔV is the change in volume.

• ΔH reflects the heat at constant pressure, which can be seen as the energy change excluding any work done by the system.
• ΔE reflects the total energy change, including both heat and work.
• PΔV represents the work done on or by the system as a result of volume changes, particularly in gaseous components.

Considering the reaction under study, where aluminum reacts with chlorine gas to produce aluminum chloride, a solid, we note a decrease in the number of gas molecules - indicating a negative ΔV. This means the system does work on its surroundings as it contracts, implying that the internal energy change (ΔE) is larger than the enthalpy change (ΔH), which only accounts for heat at constant pressure.

Stoichiometry of Chemical Reactions

In the stoichiometry of chemical reactions, we examine the quantitative relationships between reactants and products in a chemical equation. Stoichiometry allows us to predict the amounts of substances consumed and formed in a reaction based on the balanced chemical equation.

In the context of the reaction provided, stoichiometry tells us that 2 moles of aluminum solid react with 3 moles of chlorine gas to produce 2 moles of aluminum chloride solid. This molar relationship is crucial for understanding the extensive properties of the reaction, such as changes in energy, because these are dependent on the amount of substance involved. By applying stoichiometry, we can calculate how much heat is produced or consumed (enthalpy change) and determine the changes in the internal energy of the system for a given amount of reactants, all of which are foundational for predictions and applications in chemistry and industry.