Problem 55 - Introductory Chemistry Atoms First

Question

For a particular reaction, the reactants are at \(30 \mathrm{~kJ}\), the products are at \(60 \mathrm{~kJ}\), and the transition state is at \(100 \mathrm{~kJ} .\) Sketch a reactionenergy profile showing both \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}}\). Also, calculate the value of \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}}\), and state whether this reaction is endothermic or exothermic.

Step-by-Step Solution

Answer

The reaction energy profile will have the reactants at \(30 \mathrm{~kJ}\), the products at \(60 \mathrm{~kJ}\), and the transition state at \(100 \mathrm{~kJ}\). The change in reaction energy (\(\Delta E_{\mathrm{rxn}}\)) is \(60 \mathrm{~kJ} - 30 \mathrm{~kJ} = 30 \mathrm{~kJ}\), and the activation energy (\(E_{\mathrm{a}}\)) is \(100 \mathrm{~kJ} - 30 \mathrm{~kJ} = 70 \mathrm{~kJ}\). Since \(\Delta E_{\mathrm{rxn}}\) is positive, the reaction is endothermic.

Step 1: Plot the Reactants and Products

Plot the points for the reactants at \(30 \mathrm{~kJ}\) and the products at \(60 \mathrm{~kJ}\) on the vertical axis (y-axis) of the reaction energy profile.

Step 2: Plot the Transition State

Plot the point for the transition state at \(100 \mathrm{~kJ}\), which occurs between the reactants and the products along the horizontal axis (x-axis).

Step 3: Determine \(\Delta E_{\mathrm{rxn}}\)

To determine the change in reaction energy (\(\Delta E_{\mathrm{rxn}}\)), subtract the initial energy of the reactants from the energy of the products: \(\Delta E_{\mathrm{rxn}} = E_{\mathrm{products}} - E_{\mathrm{reactants}} = 60 \mathrm{~kJ} - 30 \mathrm{~kJ} = 30 \mathrm{~kJ}\).

Step 4: Determine \(E_{\mathrm{a}}\) (Activation Energy)

To determine the activation energy (\(E_{\mathrm{a}}\)), subtract the initial energy of the reactants from the energy of the transition state: \(E_{\mathrm{a}} = E_{\mathrm{transition~state}} - E_{\mathrm{reactants}} = 100 \mathrm{~kJ} - 30 \mathrm{~kJ} = 70 \mathrm{~kJ}\).

Step 5: Determine if the Reaction is Endothermic or Exothermic

Since the \(\Delta E_{\mathrm{rxn}}\) is positive, the reaction requires energy to proceed and is therefore endothermic.

Step 6: Sketch the Reaction Energy Profile

Draw a curve connecting the reactants to the transition state and then to the products. Label the energy levels of the reactants, products, and transition state, as well as the values of \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}}\) according to the calculations in the previous steps.

Key Concepts

Endothermic and Exothermic Reactions

Chemical reactions are either endothermic or exothermic based on whether they absorb or release energy, respectively.

Endothermic reactions require an input of energy to proceed. The energy absorbed from the surroundings is often in the form of heat. This results in a temperature decrease around the reaction site because the reaction is using up thermal energy. In an endothermic reaction, the energy level of the products is higher than that of the reactants, indicative of the energy absorbed during the process.

Exothermic reactions, on the other hand, release energy into the surrounding environment. Here, the energy level of the products is lower than that of the reactants because the reaction has liberated energy. If you were to touch a container where an exothermic reaction is taking place, it would feel warm or even hot to the touch due to the release of energy as heat.

In the exercise provided, the reaction is labeled as endothermic since the energy level of the products (60 kJ) is higher than the energy level of the reactants (30 kJ), indicating that energy was absorbed.

Activation Energy (Ea)

The concept of activation energy (Ea) is crucial in understanding how chemical reactions occur.

Activation energy is the minimum energy required to initiate a chemical reaction. This energy kick-starts the process by breaking the bonds of the reactants, leading to the formation of new products. Think of activation energy as the initial push needed to start a boulder rolling down a hill. Without that push, the boulder (or in our case, the reaction) would remain static.

In the reaction energy profile, the peak between the reactants and products represents the transition state, which corresponds to the highest energy level the reactants must reach to transform into products. The difference in energy between the reactants and this peak is the activation energy.For instance, in the given exercise, the activation energy (Ea) is calculated as the difference between the energy of the transition state (100 kJ) and the reactants (30 kJ), resulting in an Ea value of 70 kJ.

Change in Reaction Energy (ΔErxn)

The change in reaction energy (ΔErxn) is a direct measure of the difference in energy between the products and the reactants of a reaction.

In a graphical representation, such as a reaction energy profile, ΔErxn is illustrated as the vertical difference between the energy levels of the products and the reactants. If the products lie at a higher energy level than the reactants, the reaction has absorbed energy (ΔErxn is positive), indicating it is endothermic. Conversely, if the products are at a lower energy level, the reaction has released energy (ΔErxn is negative), implying it's exothermic.

From the exercise, calculating ΔErxn involves taking the energy of the products (60 kJ) and subtracting the energy of the reactants (30 kJ), yielding a ΔErxn of 30 kJ. Since this value is positive, the reaction has absorbed energy and it can be concluded that the reaction is endothermic.