Question

The activation energy for some reaction $$ \mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g) $$ is \(167 \mathrm{~kJ} / \mathrm{mol}\), and \(\Delta E\) for the reaction is \(+28 \mathrm{~kJ} / \mathrm{mol}\). What is the activation energy for the decomposition of XY?

Short answer

The activation energy for the decomposition of XY (reverse reaction) is calculated using the relationship \(Ea_{reverse} = Ea - \Delta E\), where \(Ea\) represents the activation energy for the forward reaction (167 kJ/mol) and \(\Delta E\) represents the change in energy for the reaction (+28 kJ/mol). Therefore, the activation energy for the reverse reaction is \(139 \mathrm{~kJ} / \mathrm{mol}\).

Step-by-step solution

Identify the given information and the desired value

We are given the following information: 1. Activation energy for the forward reaction (Ea): 167 kJ/mol 2. Change in energy for the reaction (ΔE): + 28 kJ/mol We need to find the activation energy for the reverse reaction (Ea_reverse).

Understand the relationship between Ea, ΔE, and Ea_reverse

We know that the activation energy for the reverse reaction (Ea_reverse) is related to the forward reaction's activation energy (Ea) and the change in energy (ΔE) as follows: Ea_reverse = Ea - ΔE

Calculate the activation energy for the reverse reaction (Ea_reverse)

We can now use the given values and the relationship between Ea, ΔE, and Ea_reverse to calculate the activation energy for the reverse reaction: Ea_reverse = Ea - ΔE Ea_reverse = 167 kJ/mol - 28 kJ/mol Ea_reverse = 139 kJ/mol

Present the final answer

The activation energy for the decomposition of XY (reverse reaction) is 139 kJ/mol.

Key concepts

Chemical Kinetics

Chemical kinetics delves into the speed or rate at which chemical reactions occur and the factors influencing these rates. When studying chemical reactions like \( \mathrm{X}_{2}(g) + \mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g) \), understanding kinetics is crucial. The reaction rate can be affected by various elements, including the concentration of reactants, temperature, presence of catalysts, and the activation energy.

Activation energy, symbolized as \(E_a\), is the minimum energy required for a reaction to initiate. Higher \(E_a\) suggests that the reactants have to overcome a greater energy barrier to transform into products, leading to a slower reaction. Conversely, if the \(E_a\) is lower, reactions tend to occur faster, as it’s easier for the reactants to reach the transition state that precedes product formation.

In the presented exercise, the activation energy helps us understand how much energy is needed to start the reaction and, when comparing forward and reverse reactions, illustrates the intrinsic symmetry within chemical processes.

Endothermic Reaction

An endothermic reaction is a type of chemical process that absorbs heat from its surroundings. This intake of energy is reflected as a positive change in energy, denoted as \(\Delta E\) or \(\Delta H\) for enthalpy. In the given exercise, the reaction between \(\mathrm{X}_{2}\) and \(\mathrm{Y}_{2}\) leading to the formation of 2 \(\mathrm{XY}\) has a \(\Delta E\) of +28 kJ/mol, confirming it’s endothermic.

These reactions require a net input of energy to proceed because the bonds formed in the products are weaker than the bonds broken in the reactants, leading to an overall absorption of energy. This can be visualized on an energy profile diagram, where the products reside at a higher energy level compared to the reactants. In daily life, endothermic reactions are exemplified by processes like photosynthesis and the dissolving of salts in water, which feel cold as they draw heat in.

Energy Profile Diagram

An energy profile diagram graphically represents the energy changes that occur during a chemical reaction, illustrating how the energy of the system evolves from reactants to products. On the diagram, the y-axis typically shows the energy level, while the x-axis denotes the progression of the reaction.

For an endothermic reaction, as seen in our example with \(\Delta E = +28 \mathrm{~kJ/mol}\), the diagram would display reactants at a lower energy level than products, with a peak representing the activation energy (the highest point on the path). This peak is the transition state, a short-lived unstable arrangement of atoms that exists momentarily as reactants convert into products.

The initial rise from reactants to the peak denotes the activation energy required to initiate the reaction. After reaching the transition state, the progress towards the product might show a downward slope if the reaction were exothermic, releasing energy. However, in our exercise’s case, the slope continues upward, indicating an overall gain of energy as an endothermic process.