/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 44 The enthalpy changes of the foll... [FREE SOLUTION] | 91Ó°ÊÓ

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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.

Short Answer

Expert verified
Enthalpy change (a): \( \Delta H^{\circ} = -41.1 \text{kJ} \). Energy diagram: Ethanol lower than ethene + water.

Step by step solution

01

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 \( \Delta H^{\circ} = -1367.5 \text{ kJ} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.
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.
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.

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Most popular questions from this chapter

Suppose that an inch of rain falls over a square mile of ground. (A density of \(1.0 \mathrm{g} / \mathrm{cm}^{3}\) is assumed.) The heat of vaporization of water at \(25^{\circ} \mathrm{C}\) is \(44.0 \mathrm{kJ} / \mathrm{mol} .\) Calculate the quantity of heat transferred to the surroundings from the condensation of water vapor in forming this quantity of liquid water. (The huge number tells you how much energy is "stored" in water vapor and why we think of storms as such great forces of energy in nature. It is interesting to compare this result with the energy given off, \(4.2 \times 10^{6} \mathrm{kJ},\) when a ton of dynamite explodes.)

A 13.8 -g piece of zinc was heated to \(98.8^{\circ} \mathrm{C}\) in boiling water and then dropped into a beaker containing \(45.0 \mathrm{g}\) of water at \(25.0^{\circ} \mathrm{C} .\) When the water and metal come to thermal equilibrium, the temperature is \(27.1^{\circ} \mathrm{C} .\) What is the specific heat capacity of zinc?

Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) boils at \(78.29^{\circ} \mathrm{C} .\) What quantity of heat energy, in joules, is required to raise the temperature of 1.00 kg of ethanol from \(20.0^{\circ} \mathrm{C}\) to the boiling point and then to change the liquid to vapor at that temperature? (The specific heat capacity of liquid ethanol is \(2.44 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) and its enthalpy of vaporization is \(855 \mathrm{J} / \mathrm{g} .\) )

A 25.0 -mL sample of benzene at \(19.9^{\circ} \mathrm{C}\) was cooled to its melting point, \(5.5^{\circ} \mathrm{C},\) and then frozen. How much heat was given off in this process? The density of benzene is \(0.80 \mathrm{g} / \mathrm{mL},\) its specific heat capacity is \(1.74 \mathrm{J} / \mathrm{g} \cdot \mathrm{K},\) and its heat of fusion is \(127 \mathrm{J} / \mathrm{g}\).

Hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}(\ell),\) is an efficient oxygen scavenger. It is sometimes added to steam boilers to remove traces of oxygen that can cause corrosion in these systems. Combustion of hydrazine gives the following information: $$\begin{aligned}&\mathrm{N}_{2} \mathrm{H}_{4}(\ell)+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\\\&\Delta H_{\mathrm{rxn}}^{\circ}=-534.3 \mathrm{kJ}\end{aligned}$$ (a) Is the reaction product- or reactant-favored? (b) Use the value for \(\Delta H_{\mathrm{rxn}}^{\circ}\) with the enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) to calculate the molar enthalpy of formation of \(\mathrm{N}_{2} \mathrm{H}_{4}(\ell)\).

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