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 \(\left[\mathrm{NO}(g)+\mathrm{CO}_{2}(g) \longrightarrow\right.\) \(\left.\mathrm{NO}_{2}(g)+\mathrm{CO}(g)\right] ?\)

Short answer

The activation energy for the reverse reaction is \(-91 \mathrm{~kJ/mol}\).

Step-by-step solution

1. Write down the formula relationship between activation energies and change in reaction energy

The formula relating activation energies for the forward and reverse reactions (\(E_{a(f)}\) and \(E_{a(r)}\), respectively) and the change in energy for the reaction (\(\Delta E\)), is: \[ E_{a(r)} = E_{a(f)} + \Delta E \]

2. Plug in the given values

We are given the activation energy for the forward reaction, \(E_{a(f)} = 125 \mathrm{~kJ/mol}\), and the change in energy for the reaction, \(\Delta E = -216 \mathrm{~kJ/mol}\). Plug these values into the formula: \[ E_{a(r)} = 125 \mathrm{~kJ/mol} - 216 \mathrm{~kJ/mol} \]

3. Calculate the activation energy for the reverse reaction

Perform the subtraction to find the activation energy for the reverse reaction: \[ E_{a(r)} = -91 \mathrm{~kJ/mol} \] The activation energy for the reverse reaction is \(-91 \mathrm{~kJ/mol}\).

Key concepts

Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the rates of chemical reactions and the steps they take to proceed. It helps us understand how different factors like temperature, concentration, and catalysts affect the speed of reactions.

When you're dealing with reactions such as \( \mathrm{NO}_{2}(g)+\mathrm{CO}(g) \to \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \), kinetics plays a crucial role. The rate of this reaction depends on the activation energy, which is the minimum energy required to start the reaction.

Key influences on reaction rate include:

• Temperature: Higher temperature usually increases reaction rate by providing more energy to the reactants.
• Concentration: More reactants lead to a higher chance of collisions, resulting in faster reactions.
• Catalysts: These substances speed up a reaction without being consumed by lowering the activation energy.

The study of kinetics guides us in optimizing reactions in industrial and laboratory settings by adjusting these factors.

Endothermic and Exothermic Reactions

Chemical reactions are either endothermic or exothermic, depending on the flow of energy. Understanding these concepts helps you predict whether a reaction absorbs or releases energy.

• Endothermic Reactions: These reactions absorb energy from their surroundings. An example is photosynthesis, where plants take in sunlight.
• Exothermic Reactions: These release energy, usually in the form of heat. Combustion reactions, like burning wood, are common examples.

Looking at the exercise's reaction:
The change in energy \( \Delta E = -216 \mathrm{~kJ/mol} \) indicates it's exothermic. The energy is released to the surroundings.
The opposite, or reverse reaction, absorbs energy, making it endothermic.
These energy changes help determine the direction and feasibility of reactions in natural and controlled environments.

Reaction Energy Change

Reaction energy change \( (\Delta E) \) is vital for understanding how energy is transformed during a chemical reaction. It helps predict whether the reaction will be spontaneous.

The given reaction has a \( \Delta E = -216 \mathrm{~kJ/mol} \), meaning that it releases energy as products are more stable than reactants. This change is derived from comparing the potential energy of products and reactants.

• Calculating Reaction Energy Change: Use bond energies to determine the net energy change. Add all the energies required to break bonds and subtract the energy released from forming new bonds.
• Spontaneity and Feasibility: A negative \( \Delta E \) often means the reaction happens naturally, as it releases energy. Positive \( \Delta E \) suggests energy input is needed.

Understanding \( \Delta E \) allows scientists to develop efficient production methods, like in pharmaceuticals, ensuring reactions proceed in the desired direction efficiently.