Question

The reaction \(\mathrm{H}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2}+\mathrm{H}\) has been studied for many years. Sketch a potential-energy-versusreaction-progress diagram for this reaction.

Short answer

The potential energy versus reaction progress diagram of this reaction would have reactants (H+H2) and products (H2+H) at the same energy level, indicating that there is no net energy change (ΔE = 0). The activation energy is represented by a peak between the two.

Step-by-step solution

Identify Reactants and Products

Here, we have two reactants: a single hydrogen atom (H) and a hydrogen molecule (H2). The products of the reaction are another molecule of hydrogen (H2) and a single hydrogen atom (H). Since this is a balanced chemical reaction, reactants and products are the same.

Draw Potential-Energy-Versus-Reaction-Progress Axis

Draw a graph with two axes. The vertical axis is for potential energy (E) and the horizontal is for reaction progress.

Plot Reactants and Products

On the graph, mark the position of the reactants (H+H2) on the left side and the products (H2+H) on the right side.

Indicate Activation Energy and Energy Changes

The activation energy is the minimum amount of energy the reactants need to start the reaction. This is represented by a peak in the graph, located between the reactants and products. The energy change between reactants and products is typically represented by ΔE. In this reaction, since the reactants and products are the same, ΔE can be considered as zero; hence the reactants and products will be at the same energy level.

Key concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that deals with the speed or rate at which a chemical reaction occurs, and the factors that affect this rate. Understanding kinetics helps us control processes, from the combustion of fuels to the metabolism of food in our bodies. The rate of a reaction is usually expressed in terms of concentration change of reactants or products over time. In our example reaction, \(\mathrm{H} + \mathrm{H}_2 \longrightarrow \mathrm{H}_2 + \mathrm{H}\), the rate would depend on the frequency and energy of collisions between the hydrogen atom and molecule.

Factors such as temperature, concentration of reactants, surface area, and catalysts can significantly impact the reaction rate. For instance, increasing the temperature typically increases the reaction rate as it raises the energy of the molecules involved, leading to more frequent and higher-energy collisions. In educational materials, it's crucial to highlight that kinetics is not only about how fast the reaction takes place but also the steps it takes to get to the final products, often visualized in potential energy diagrams.

Activation Energy

The term 'activation energy' refers to the minimum energy that reacting particles must possess for a reaction to occur. It is a crucial concept for students to grasp because it dictates whether a reaction will happen spontaneously or requires an input of energy. In the potential-energy-versus-reaction-progress diagram for our given reaction \(\mathrm{H} + \mathrm{H}_2 \longrightarrow \mathrm{H}_2 + \mathrm{H}\), the activation energy is visualized as a peak on the graph.

This peak represents the energy barrier that the reactants have to overcome to transform into products. Even if the products are at the same energy level as the reactants, as in this reaction where \(\Delta E\) is zero, there is still a need for this activation energy. It can be supplied by heat, light, or a catalyst—a substance that lowers the activation energy, making it easier for a reaction to occur without being consumed in the process.

Chemical Equilibrium

Chemical equilibrium is a state in a reversible reaction where the rates of the forward and reverse reactions are equal, leading to no overall change in the amounts of reactants and products. It's a dynamic balance, not a static one, meaning that the reactants and products are continuously converting into one another, but their concentrations remain constant.

For the example reaction \(\mathrm{H} + \mathrm{H}_2 \longleftrightarrow \mathrm{H}_2 + \mathrm{H}\), which is reversible, it could reach equilibrium. At equilibrium, the potential energy levels of the reactants and products are the same, indicating that the system has no tendency to change. It's important for students to understand that while the conditions of equilibrium may vary depending on the reaction specifics, the concept of a balance between the forward and reverse reactions remains a cornerstone of chemical reactions.

Reaction Coordinate

The reaction coordinate is a term used to describe the progress of a chemical reaction from reactants to products, often visualized as the horizontal axis in a potential-energy-versus-reaction-progress diagram. It can be thought of as an abstract representation of the sequence of molecular transformations that occur from the start of a reaction to its end.

In our example reaction's diagram, the reaction coordinate illustrates the pathway the reaction follows, moving from \(\mathrm{H} + \mathrm{H}_2\) on the left side across to \(\mathrm{H}_2 + \mathrm{H}\) on the right side. The highest point on this pathway represents the activation energy, while the diagram shows the energy of the reactants and products remains the same, reinforcing the concept that they are in a state of equilibrium when the reaction is reversible. It’s important for students to recognize the reaction coordinate as a tool for visualizing the reaction process, not a physical distance the molecules travel.