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Chapter 9: Problem 34

The reaction of \(\mathrm{A}\) with \(\mathrm{B}\) to give \(\mathrm{D}\) proceeds in two steps: 1) \(\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C} \quad \Delta H^{\circ}=-20 \mathrm{~kJ}\) 2) \(\mathrm{C}+\mathrm{B} \longrightarrow \mathrm{D} \quad \Delta H^{\circ}=+50 \mathrm{~kJ}\) 3) \(\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{D} \quad \Delta H^{\circ}=?\) (a) Which Hess's Law diagram represents the reaction steps and the overall reaction? (b) What is the value of \(\Delta H^{\circ}\) for the overall reaction \(\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{D} \quad \Delta H^{\circ}=?\)

Short Answer

Expert verified
(a) Hess's Law diagram shows steps combining; (b) \( \Delta H^{\circ} = +30 \mathrm{~kJ} \).

Step by step solution

01

Understanding the Reaction Steps

We are given two reaction steps: 1) \( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} \) with \( \Delta H^{\circ} = -20 \mathrm{~kJ} \)2) \( \mathrm{C} + \mathrm{B} \rightarrow \mathrm{D} \) with \( \Delta H^{\circ} = +50 \mathrm{~kJ} \). These two steps combine to form the overall reaction: \( \mathrm{A} + 2 \mathrm{B} \rightarrow \mathrm{D} \). Our task is to find \( \Delta H^{\circ} \) for this overall reaction, using Hess's Law.
02

Applying Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step of the reaction. To find the \( \Delta H^{\circ} \) for \( \mathrm{A} + 2\mathrm{B} \rightarrow \mathrm{D} \), we add the \( \Delta H^{\circ} \) of the two steps:\[ \Delta H^{\circ} = (-20 \mathrm{~kJ}) + (50 \mathrm{~kJ}) \].
03

Calculating the Total Enthalpy Change

Perform the calculation from the previous step:\( \Delta H^{\circ} = (-20) + 50 = 30 \mathrm{~kJ} \).Thus, the enthalpy change for the overall reaction \( \mathrm{A} + 2 \mathrm{B} \rightarrow \mathrm{D} \) is \( +30 \mathrm{~kJ} \).
04

Conclusion on the Hess's Law Diagram

In the Hess's Law diagram, Step 1 and Step 2 combine to show the overall reaction. Start from \( \mathrm{A} + \mathrm{B} \) moving to \( \mathrm{C} \) (first step), then from \( \mathrm{C} \) to \( \mathrm{D} \) (second step). The direct path shown from \( \mathrm{A} + 2\mathrm{B} \) to \( \mathrm{D} \) reflects the overall reaction.

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Key Concepts

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

Enthalpy Change
Enthalpy change, denoted as \( \Delta H \), is essential in understanding chemical reactions. It represents the heat absorbed or released during a reaction at constant pressure. In our example, we look at the reaction where \( \mathrm{A} \) reacts with \( \mathrm{B} \) to eventually form \( \mathrm{D} \). Each step of this reaction has a specific enthalpy change.

Let's break it down:
  • First step: \( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} \) has an enthalpy change of \( \Delta H^{\circ} = -20 \mathrm{~kJ} \). This means the reaction releases 20 kJ of energy.
  • Second step: \( \mathrm{C} + \mathrm{B} \rightarrow \mathrm{D} \) has an enthalpy change of \( \Delta H^{\circ} = +50 \mathrm{~kJ} \), indicating this step absorbs 50 kJ of energy.
  • Overall reaction: We combine these to find the total enthalpy change for \( \mathrm{A} + 2 \mathrm{~B} \rightarrow \mathrm{D} \), which turns out to be \( +30 \mathrm{~kJ} \).
The positive sign in the overall reaction's enthalpy change signifies that the reaction is endothermic, meaning it absorbs energy.
Reaction Mechanism
A reaction mechanism provides the step-by-step sequence of elementary reactions by which overall chemical change occurs. In our scenario, the reaction between \( \mathrm{A} \) and \( \mathrm{B} \) forming \( \mathrm{D} \) is not a single event but consists of two distinct steps.

The stepwise process is important because:
  • Each step corresponds to an actual event at the molecular level, showing intermediate products like \( \mathrm{C} \).
  • The sequence and energy changes in each step control the reaction pathway and rate.
  • Sometimes intermediates like \( \mathrm{C} \) may not be visible in the overall equation, but they are crucial in understanding how reactants transform into products.
By knowing the mechanism, chemists can manipulate conditions to control the rate or outcome of the reaction. It鈥檚 akin to having detailed driving directions to reach a destination smoothly.
Overall Reaction
The overall reaction is a simplified representation of the complete transformation from reactants to products, summarizing the net result of multiple reaction steps. In our case, the overall reaction is given by combining the two steps:\[\mathrm{A} + 2 \mathrm{~B} \rightarrow \mathrm{D}\]This is achieved by applying Hess's Law, which states that the total enthalpy change of a reaction is equal to the sum of enthalpy changes of its individual steps.

Why is the overall reaction important?
  • It provides a comprehensive picture of the initial and final states without detailing the intermediate stages.
  • The overall enthalpy change (\( +30 \mathrm{~kJ} \)) gives us insight into the energy aspect of the reaction.
  • It serves as a final check to ensure that mass and energy conservation laws are satisfied.
Understanding the overall reaction helps students and chemists alike to anticipate the energy requirements and feasibility of the chemical process.

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Most popular questions from this chapter

What is the difference between heat and temperature? Between work and energy? Retween kinetic energy and potential energy?

Which of the following has the highest enthalpy content, and which the lowest at a given temperature: \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s}), \mathrm{H}_{2} \mathrm{O}(l)\), or \(\mathrm{H}_{2} \mathrm{O}(g) ?\) Explain.

The reaction \(\mathrm{S}_{8}(\mathrm{~g}) \longrightarrow 4 \mathrm{~S}_{2}(\mathrm{~g})\) has \(\Delta H^{\circ}=+237 \mathrm{k}\) ) (a) The \(\mathrm{S}_{8}\) molecule has eight sulfur atoms arranged in a ring. What is the hybridization and geometry around each sulfur atom in \(\mathrm{S}_{8}\) ? (b) The average \(\mathrm{S}-\mathrm{S}\) bond dissociation energy is \(225 \mathrm{~kJ} / \mathrm{mol}\). Using the value of \(\Delta H^{\circ}\) given above, what is the \(\mathrm{S}=\mathrm{S}\) double bond energy in \(\mathrm{S}_{2}(g)\) ? (c) Assuming that the bonding in \(\mathrm{S}_{2}\) is similar to the bonding in \(\mathrm{O}_{2}\), give a molecular orbital description of the bonding in \(\mathrm{S}_{2}\). Is \(S_{2}\) likely to be paramagnetic or diamagnetic?

Liquid butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\), the fuel used in many disposable lighters, has \(\Delta H_{\mathrm{f}}^{\circ}=-147.5 \mathrm{~kJ} / \mathrm{mol}\) and a density of \(0.579 \mathrm{~g} / \mathrm{mL}\). Write a balanced equation for the combustion of butane, and use Hess's law to calculate the enthalpy of combustion in \(\mathrm{kJ} / \mathrm{mol}, \mathrm{kJ} / \mathrm{g}\), and \(\mathrm{kJ} / \mathrm{mL}\)

Which of the following are state functions, and which are not? (a) The temperature of an ice cube (b) The volume of an aerosol can (c) The amount of time required for Paula Radcliffe to run her world-record marathon: \(2: 15: 25\)
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