Question

The activation energy for the reaction $$\mathrm{NO}_{2}(g)+\mathrm{CO}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g)$$ is \(125 \mathrm{kJ} / \mathrm{mol},\) and \(\Delta E\) for the reaction is \(-216 \mathrm{kJ} / \mathrm{mol}\). What is the activation energy for the reverse reaction \(\left[\mathrm{NO}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{CO}(g)\right] ?\)

Short answer

The activation energy for the reverse reaction is \(-91 kJ/mol\). Since the activation energy is negative, it indicates that the reverse reaction is exothermic and has a lower activation energy compared to the endothermic forward reaction.

Step-by-step solution

Write the equation relating activation energies and change in energy

The relationship between the activation energies of the forward and reverse reactions, and the change in energy for the reaction is given by the following equation: \(E_{a(reverse)} = E_{a(forward)} + \Delta E\)

Input the given values

Given the values for the activation energy of the forward reaction (\(E_{a(forward)} = 125 kJ/mol\)) and the change in energy for the reaction (\(\Delta E = -216 kJ/mol\)), plug them into the equation: \(E_{a(reverse)} = 125 kJ/mol - 216 kJ/mol\)

Calculate the activation energy for the reverse reaction

Now, we just need to perform the subtraction: \(E_{a(reverse)} = -91 kJ/mol\)

Interpret the result

The activation energy for the reverse reaction is \(-91 kJ/mol\). Since the activation energy is negative, it means that the reverse reaction is exothermic, and it has a lower activation energy compared to the forward reaction, which requires an input of energy (endothermic).

Key concepts

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, undergo a transformation to form new substances, called products. These transformations involve the breaking and forming of chemical bonds, resulting in different arrangements of atoms and a change in the chemical identity of the substances involved. For example, in the reaction \( \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \), nitrogen dioxide and carbon monoxide react to produce nitrogen monoxide and carbon dioxide.
There are several indicators that a chemical reaction has taken place, such as a change in color, temperature, the formation of a gas, or the appearance of a precipitate. The speed and outcome of a chemical reaction can be influenced by various factors, including temperature, pressure, concentration, and the presence of catalysts, which can affect the activation energy required for the reaction to proceed.
Understanding chemical reactions is fundamental in fields such as chemistry, biology, environmental science, and engineering, as they are essential to processes ranging from metabolic pathways in living organisms to industrial synthesis of materials.

Energy Change

Energy change is a critical concept when discussing chemical reactions, as it directly relates to the breaking and forming of bonds. In every chemical reaction, energy is either absorbed or released. This energy change can be quantified as \( \Delta E \), the change in energy for the reaction.
When energy is absorbed from the surroundings, the reaction is endothermic, and \( \Delta E \) is positive. Conversely, when energy is released into the surroundings, the reaction is exothermic, and \( \Delta E \) is negative. In the given exercise, \( \Delta E \) is \(-216 \mathrm{kJ/mol} \), indicating that the forward reaction releases energy, thus it is exothermic.
Knowing the energy change allows chemists to predict the energy requirements for a reaction and to understand the stability of products compared to reactants. It also helps in calculating the reverse reaction's activation energy, providing insights into the reaction's dynamics and efficiency.

Endothermic and Exothermic Reactions

Chemical reactions can be categorized based on their energy changes as endothermic or exothermic, which determine the flow of energy between the system and its surroundings.

• **Endothermic Reactions**: These reactions absorb energy from the surroundings. They require an input of energy to proceed because the products are at a higher energy level than the reactants. An example is the melting of ice, where energy in the form of heat is absorbed to change solid ice to liquid water. The activation energy of the forward reaction is often higher for endothermic reactions, as energy needs to be supplied to overcome the energy barrier and initiate the reaction.

• **Exothermic Reactions**: These reactions release energy to the surroundings. The products are at a lower energy level than the reactants, meaning energy is given off, typically in the form of heat or light. Combustion of wood is a common exothermic reaction where heat is released as the wood burns. In the exercise given, the forward reaction is exothermic, with a \( \Delta E \) of \(-216 \mathrm{kJ/mol} \), indicating it releases energy.

Understanding whether a reaction is endothermic or exothermic aids in grasping the energy dynamics. It helps predict how a reaction might progress and under what conditions it can be made more efficient or feasible for industrial applications.