Problem 44
Question
The enthalpy changes of the following reactions can be measured: $$\begin{aligned}\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow & 2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \\\& \Delta H^{\circ}=-1411.1 \mathrm{kJ}\end{aligned}$$ $$\begin{aligned}\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) & \\\\\Delta H^{\circ}=-1367.5 \mathrm{kJ}\end{aligned}$$ (a) Use these values and Hess's law to determine the enthalpy change for the reaction $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$$ (b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.
Step-by-Step Solution
Verified Answer
Enthalpy change (a): \( \Delta H^{\circ} = -41.1 \text{kJ} \). Energy diagram: Ethanol lower than ethene + water.
1Step 1: Write the Given Reactions
We are provided with two reactions:1. \( \mathrm{C}_{2} \mathrm{H}_{4}( ext{g}) + 3 \mathrm{O}_{2}( ext{g}) \longrightarrow 2 \mathrm{CO}_{2}( ext{g}) + 2 \mathrm{H}_{2} \mathrm{O}( ext{l}) \) with \( \Delta H^{\circ} = -1411.1 \text{ kJ} \).2. \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}( ext{l}) + 3 \mathrm{O}_{2}( ext{g}) \longrightarrow 2 \mathrm{CO}_{2}( ext{g}) + 3 \mathrm{H}_{2} \mathrm{O}( ext{l}) \) with \( \Delta H^{\circ} = -1367.5 \text{ kJ} \).
Key Concepts
Enthalpy ChangeExothermic ReactionsEnergy Level Diagram
Enthalpy Change
In chemistry, enthalpy change is a vital concept as it represents the heat absorbed or released in a chemical reaction at constant pressure. It is often represented by the symbol \( \Delta H \). Let's take a closer look at how these changes work. When we observe a chemical reaction, the substances involved experience changes in energy due to bonds being broken and formed. This energy change can either be absorbed from or released to the surroundings.
Consider the given reactions in our exercise: the combustion of ethylene \( (\text{C}_2\text{H}_4) \) and ethanol \( (\text{C}_2\text{H}_5\text{OH}) \). For ethylene, the enthalpy change \( \Delta H = -1411.1 \text{ kJ} \), and for ethanol \( \Delta H = -1367.5 \text{ kJ} \). Both of these reactions release energy, indicated by the negative sign.
To find the enthalpy change for the reaction \( \text{C}_2\text{H}_4 + \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_5\text{OH} \), we use Hess's Law. This law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step of the reaction process, regardless of the path taken. By reorganizing and combining the given reactions, we calculate the desired \( \Delta H \) value for the reaction.
Consider the given reactions in our exercise: the combustion of ethylene \( (\text{C}_2\text{H}_4) \) and ethanol \( (\text{C}_2\text{H}_5\text{OH}) \). For ethylene, the enthalpy change \( \Delta H = -1411.1 \text{ kJ} \), and for ethanol \( \Delta H = -1367.5 \text{ kJ} \). Both of these reactions release energy, indicated by the negative sign.
To find the enthalpy change for the reaction \( \text{C}_2\text{H}_4 + \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_5\text{OH} \), we use Hess's Law. This law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step of the reaction process, regardless of the path taken. By reorganizing and combining the given reactions, we calculate the desired \( \Delta H \) value for the reaction.
Exothermic Reactions
Exothermic reactions are characterized by the release of energy, usually in the form of heat, to the surroundings. Such reactions have negative enthalpy changes \( \Delta H \), as seen in both reactions provided in the exercise. Here’s why this occurs: When bonds are formed in the products, more energy is released compared to the energy consumed in breaking the bonds of reactants.
In the case of our reactions, the combustion of both ethylene and ethanol in the presence of oxygen is exothermic. This reflects common combustion processes, which are typically exothermic because they release substantial amounts of heat energy.
Understanding exothermic reactions helps us grasp why certain substances, like fuels, are useful for heating and power. As they burn, they release stored energy which can be harnessed for various applications. In our problem, identifying the energy released in these reactions aids in calculating enthalpy changes to understand the full scope of energy exchanges involved.
In the case of our reactions, the combustion of both ethylene and ethanol in the presence of oxygen is exothermic. This reflects common combustion processes, which are typically exothermic because they release substantial amounts of heat energy.
Understanding exothermic reactions helps us grasp why certain substances, like fuels, are useful for heating and power. As they burn, they release stored energy which can be harnessed for various applications. In our problem, identifying the energy released in these reactions aids in calculating enthalpy changes to understand the full scope of energy exchanges involved.
Energy Level Diagram
An energy level diagram is a visual tool representing the relative energies of reactants and products in a chemical reaction. It is especially useful in illustrating exothermic and endothermic reactions, by showing the direction and magnitude of energy change.
For exothermic reactions like those in our exercise, the energy level diagram will show the reactants at a higher energy level compared to the products. During the reaction, energy is released, and the final energy level (of the products) is lower. This difference reflects the enthalpy change, with the vertical distance between the reactants and products denoting the magnitude of energy released.
In creating an energy level diagram for our reactions, start by plotting the initial energy levels of ethylene \( (\text{C}_2\text{H}_4) \), water \( (\text{H}_2\text{O}) \), and oxygen \( (\text{O}_2) \). After the reaction, demonstrate how the energy decreases to form carbon dioxide \( (\text{CO}_2) \) and water, reflecting the negative \( \Delta H \) values and confirming the exothermic nature. Such diagrams provide a clearer insight into how energy is conserved and transferred in chemical reactions.
For exothermic reactions like those in our exercise, the energy level diagram will show the reactants at a higher energy level compared to the products. During the reaction, energy is released, and the final energy level (of the products) is lower. This difference reflects the enthalpy change, with the vertical distance between the reactants and products denoting the magnitude of energy released.
In creating an energy level diagram for our reactions, start by plotting the initial energy levels of ethylene \( (\text{C}_2\text{H}_4) \), water \( (\text{H}_2\text{O}) \), and oxygen \( (\text{O}_2) \). After the reaction, demonstrate how the energy decreases to form carbon dioxide \( (\text{CO}_2) \) and water, reflecting the negative \( \Delta H \) values and confirming the exothermic nature. Such diagrams provide a clearer insight into how energy is conserved and transferred in chemical reactions.
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