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 \(-91 \, \mathrm{kJ/mol}\).

Step-by-step solution

Identify the given values

For this exercise, we are given the activation energy for the forward reaction (125 kJ/mol), the change in energy of the reaction (-216 kJ/mol), and we are asked to find the activation energy for the reverse reaction.

Use the formula

To find the activation energy for the reverse reaction, we should use the formula that relates the activation energy of the forward and reverse reactions and the change in energy of the reaction: Activation energy of reverse reaction (Ea_reverse) = Activation energy of forward reaction (Ea_forward) + Change in energy of reaction (∆E) Plug in the given values into the formula: Ea_reverse = Ea_forward + ∆E Ea_reverse = \(125 \, \mathrm{kJ/mol} - 216 \, \mathrm{kJ/mol}\)

Calculate the activation energy for the reverse reaction

To find the activation energy for the reverse reaction, simply perform the subtraction in the equation: Ea_reverse = \(-91 \, \mathrm{kJ/mol}\) The activation energy for the reverse reaction is -91 kJ/mol. This negative value indicates that the activation energy barrier for the reverse reaction is actually lower than that of the forward reaction, making the reverse reaction more favorable to occur under certain conditions.

Key concepts

Reaction Thermodynamics

In chemical reactions, thermodynamics helps us understand how energy is transformed. It focuses on whether a reaction is energy-releasing or energy-absorbing. When discussing reaction thermodynamics, we often refer to the change in energy of a reaction, symbolized as \( \Delta E \). This value shows us how much energy is absorbed or released as reactants turn into products.

For example, in the reaction \( \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \), we are given a \( \Delta E \) of \(-216 \mathrm{kJ/mol} \). This negative value means the reaction releases energy; it's exothermic. Particularly, 216 kJ are released for every mole of reaction that occurs.

Understanding \( \Delta E \) is crucial because it tells us about the energy landscape of the reaction. It serves as a guide to predict whether a reaction will proceed energetically, as reactions that release energy (like this one) are typically more spontaneous.

Chemical Kinetics

Chemical kinetics revolves around the rate at which a chemical reaction occurs and the factors influencing this rate. It's all about understanding how quickly reactants are transformed into products.

A key factor impacting reaction rate is activation energy \( (E_a) \). Activation energy is the minimum energy that colliding molecules need to start a reaction. It acts like an energy hill that must be climbed.

• A lower activation energy means reactants can more easily form products, making the reaction faster.
• A higher activation energy means the reaction is slower because it's harder for molecules to achieve the necessary energy to react.

For the reaction \( \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \), the activation energy is 125 kJ/mol. This quantifies the energy barrier that must be overcome for the reaction to proceed. The reaction's rate will depend significantly on this parameter.

By understanding chemical kinetics, scientists can better control reactions, optimizing conditions to make them faster or slower depending on the desired outcome.

Energy Change of Reaction

The energy change of a reaction, indicated by \( \Delta E \), tells us the difference in energy between reactants and products. It is a key component in both reaction thermodynamics and chemical kinetics.

For any given reaction, such as \( \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \rightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \), knowing \( \Delta E \) helps us understand the thermodynamic favorability. This particular reaction has a \( \Delta E \) of \(-216 \mathrm{kJ/mol} \), indicating an energy release.

• When \( \Delta E \) is negative, the reaction tends to release energy, possibly making it spontaneous.
• When \( \Delta E \) is positive, energy is absorbed, suggesting the reaction might need an input of energy to occur.

The energy change also plays a role in the activation energy for the reverse reaction. In our example, we calculated the activation energy for the reverse process as \(-91 \mathrm{kJ/mol} \), meaning that the reverse reaction has a lower energy barrier to overcome. This can sometimes make the reverse reaction more feasible under differing conditions. Understanding the energy change of a reaction thus allows us to predict the energy demands and overall feasibility of chemical processes.