Question

The gas-phase reaction \(\mathrm{Cl}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{Br}(g)\) has an overall enthalpy change of \(-66 \mathrm{~kJ}\). The activation energy for the reaction is \(7 \mathrm{~kJ}\). (a) Sketch the energy profile for the reaction, and label \(E_{a}\) and \(\Delta E\). (b) What is the activation energy for the reverse reaction?

Short answer

(a) To sketch the energy profile for the reaction, draw a horizontal axis representing reaction progress and a vertical axis representing potential energy. Plot the energy levels for reactants and products, with the products' energy level lower due to the exothermic reaction. Draw an energy barrier between the reactants and products representing the activation energy (Ea) for the forward reaction (7 kJ). Label this barrier as Ea. Then, draw a downward arrow indicating the overall enthalpy change (∆E) of the reaction (-66 kJ). (b) To find the activation energy for the reverse reaction, use the equation Ea_reverse = Ea + ∆E. Plug in the values for Ea and ∆E: Ea_reverse = 7 kJ + (-66 kJ) = -59 kJ Take the absolute value to get the positive activation energy for the reverse reaction: Ea_reverse = | -59 kJ | = 59 kJ.

Step-by-step solution

Draw the axes and label them

Draw a horizontal axis representing the reaction progress and a vertical axis representing the potential energy. Label the horizontal axis as "Reaction Progress" and the vertical axis as "Potential Energy."

Plot the energy levels

Draw two energy levels representing the reactants and products on the potential energy axis. Since the overall enthalpy change is -66 kJ (exothermic reaction), the energy level of the products should be lower than that of the reactants.

Plot the activation energy and enthalpy change

Draw an energy barrier between the reactants and products, representing the activation energy (Ea) for the forward reaction. The height of the energy barrier should be 7 kJ above the energy level of the reactants. Label this energy barrier as Ea. Next, draw a downward arrow between the reactants and products, representing the overall enthalpy change (∆E) of the reaction (-66 kJ). Label this arrow as ∆E. #b) Activation energy for the reverse reaction#

Use the activation energy and enthalpy change for the forward reaction

We know the activation energy for the forward reaction (Ea) is 7 kJ and the overall enthalpy change for the reaction (∆E) is -66 kJ. We can use these values to find the activation energy for the reverse reaction (Ea_reverse).

Calculate the activation energy for the reverse reaction

The relationship between the activation energies for the forward and reverse reactions and the overall enthalpy change is given by the equation: Ea_reverse = Ea + ∆E Plug in the values for Ea and ∆E: Ea_reverse = 7 kJ + (-66 kJ) Ea_reverse = -59 kJ So the activation energy for the reverse reaction is -59 kJ. However, activation energy is always a positive value, so we need to take the absolute value: Ea_reverse = | -59 kJ | = 59 kJ The activation energy for the reverse reaction is 59 kJ.

Key concepts

Enthalpy Change

Enthalpy change, represented by the symbol \( \Delta H \), is a measure of the heat energy released or absorbed during a chemical reaction under constant pressure. It reflects the difference in heat content between products and reactants. If the \( \Delta H \) is negative, like in our gas-phase reaction \( \mathrm{Cl}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{Br}(g) \), it means that the reaction is exothermic, meaning heat is released to the surroundings.

In such reactions, the bonds formed in the product molecules are stronger than those in the reactants, resulting in a net release of energy. This is why the enthalpy level of the products is lower, by 66 kJ in this case, than that of the reactants. The magnitude of this change is important, as it determines the amount of energy that can be harnessed or needs to be supplied for a reaction to occur.

Gas-Phase Reaction

A gas-phase reaction occurs between substances in the gaseous state, as seen with chlorine and hydrogen bromide in our textbook example. These reactions are influenced by temperature, pressure, and volume, and often involve the making and breaking of bonds. In a reaction like \( \mathrm{Cl}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{Br}(g) \), the gas molecules collide with sufficient energy to overcome the activation energy barrier.

The properties of the gas-phase make these reactions ideal to study, as they conform well to ideal gas laws and kinetic molecular theory, which can help in predicting the behavior of the reactants and products during the reaction.

Energy Profile Diagram

An energy profile diagram visually represents the energy changes during a chemical reaction. It plots the potential energy of the system against the progress of the reaction. These diagrams illustrate important concepts like activation energy (\(E_a\)), enthalpy change (\(\Delta E\)), and the transition state.

For our exothermic reaction, the diagram has a peak representing the activation energy required for the reaction to proceed and a downward slope indicating the release of energy. The difference in height between the reactants and products corresponds to the enthalpy change. These diagrams not only help in understanding the energy aspects of reactions but also serve as a tool for predicting the spontaneity and the kinetics of a reaction.

Exothermic Reaction

An exothermic reaction is one that releases energy to its surroundings, usually in the form of heat. This is depicted by a negative value for the enthalpy change (\(\Delta H\)), as the energy required to break the bonds in the reactants is less than the energy released when the new bonds in the products are formed.

In the context of our exercise with the reaction \( \mathrm{Cl}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{Br}(g) \), the enthalpy change is an important factor influencing the ecosystem where the reaction happens. For instance, an exothermic reaction in an industrial setting could be harnessed for energy to power other processes, contributing to a chain of sustainable energy use.