Question

In a hypothetical reaction \(\mathrm{X} \rightarrow \mathrm{Y}\), the activation energy for the forward and backward reaction is 15 and \(9 \mathrm{~kJ}\) mol \(^{-1}\) respectively. The potential energy of \(X\) is \(10 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\), Identify the correct statement(s). (a) The threshold energy of the reaction is \(25 \mathrm{~kJ}\). (b) The potential energy \(\mathrm{fY}\) is \(16 \mathrm{~kJ}\) (c) Heat of reaction is \(6 \mathrm{~kJ}\). (d) The reaction is endothermic.

Short answer

The correct statements are (a), (b), (c), and (d).

Step-by-step solution

Understand the Concepts

Activation energy is the energy needed to convert reactants into products. The heat of reaction (ΔH) is the difference in potential energy between products and reactants.

Calculate the Threshold Energy

Threshold energy = Potential energy of reactants + Activation energy (forward). Given, potential energy of X = 10 kJ/mol and activation energy for forward reaction = 15 kJ/mol. Thus, Threshold energy = 10 kJ/mol + 15 kJ/mol = 25 kJ/mol.

Calculate Potential Energy of Y

To find the potential energy of Y, subtract the activation energy of the backward reaction from the threshold energy. Potential energy of Y = Threshold energy - Activation energy (backward). Given, activation energy for backward reaction = 9 kJ/mol, Potential energy of Y = 25 kJ/mol - 9 kJ/mol = 16 kJ/mol.

Determine the Heat of Reaction

The heat of reaction (ΔH) is the difference in potential energy between products and reactants. ΔH = Potential energy of Y - Potential energy of X. ΔH = 16 kJ/mol - 10 kJ/mol = 6 kJ/mol.

Determine the Reaction Endo/Exothermicity

A reaction is endothermic if ΔH is positive. Since we calculated ΔH = 6 kJ/mol, which is positive, the reaction is endothermic.

Key concepts

Activation Energy

Activation energy is the minimum energy that reactants must possess to transform into products during a chemical reaction. Think of it as the hill that reactants need to climb over for a reaction to occur.
Without sufficient activation energy, the reactants cannot overcome the barrier to react.

• For the forward reaction in our example, the activation energy is 15 kJ/mol.
• For the backward reaction, it is 9 kJ/mol.

This energy is essential because it determines how quickly or slowly a reaction will proceed. Lower activation energy means reactions can occur more easily, while higher activation energy makes reactions occur slowly unless sufficient energy is provided.

Heat of Reaction

The heat of reaction, often denoted as ΔH, represents the overall energy change during a chemical reaction. It is the difference in potential energy between the products and the reactants.
In our exercise:

• Potential energy of X (reactant) is 10 kJ/mol.
• Potential energy of Y (product) is 16 kJ/mol.

The calculation of ΔH is straightforward:\[ΔH = ext{Potential Energy of Y} - ext{Potential Energy of X} \]\[ΔH = 16 ext{ kJ/mol} - 10 ext{ kJ/mol} = 6 ext{ kJ/mol}\]A positive ΔH indicates that the products have higher potential energy than the reactants, implying that energy is absorbed during the reaction.

Potential Energy

Potential energy in the context of a chemical reaction refers to the stored energy within chemical bonds of the substances involved. This energy is a critical factor when determining how much energy is required or released during a reaction.
We calculated:

• The potential energy of reactant X as 10 kJ/mol.
• The potential energy of product Y as 16 kJ/mol.

These values help us understand the energy landscape of a reaction, showing where energy is required or released. The comparison of potential energies between reactants and products helps determine both the heat of reaction and whether the reaction is endothermic or exothermic.

Endothermic Reaction

An endothermic reaction is one where energy is absorbed from the surroundings into the system. This type of reaction requires more energy to break bonds in the reactants than is released when new bonds form in the products.
In our scenario, the calculation showed a positive heat of reaction (ΔH = 6 kJ/mol), which tells us that energy is absorbed.
This energy absorption increases the potential energy of the system, making it an endothermic process. Some real-life examples of endothermic reactions include photosynthesis and the melting of ice. Recognizing endothermic reactions is important because they often require a continuous input of energy to proceed.