Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 17: Problem 101

Consider the reaction: $$ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) $$ At \(25^{\circ} \mathrm{C}, \Delta H^{\circ}=-92.50 \mathrm{~kJ}\). Which of the following statements is(are) true? a. This is an endothermic reaction. b. \(\Delta S^{\circ}\) for this reaction is negative. c. If the temperature is increased, the ratio \(\frac{\mathrm{PCl}_{5}}{\mathrm{PCl}_{3}}\) will increase. d. \(\Delta G^{\circ}\) for this reaction has to be negative at all temperatures. e. When \(\Delta G^{\circ}\) for this reaction is negative, then \(K_{\mathrm{p}}\) is greater than \(1.00\).

Short Answer

Expert verified
Only statement e is true: When $\Delta G^{\circ}$ for this reaction is negative, then $K_{\mathrm{p}}$ is greater than $1.00$.

Step by step solution

01

Statement a

We are given that \(\Delta H^{\circ} = -92.50 \ \text{kJ}\). Since it is negative, this reaction is exothermic, not endothermic. So, statement a is false.
02

Statement b

To assess the sign of \(\Delta S^{\circ}\), we need to look at the reaction. Since the number of moles of reactants is equal to the number of moles of the product, it is not possible to definitively state that the entropy change \(\Delta S^{\circ}\) for this reaction is negative. Hence, statement b is not necessarily true.
03

Statement c

For this statement, we have to consider the effect of temperature on the equilibrium of the reaction using the Van't Hoff equation: $$\frac{d \ln K}{dT} = \frac{\Delta H^{\circ}}{RT^2}$$ Since the reaction is exothermic (\(\Delta H^{\circ}<0\)), increasing the temperature will shift the equilibrium towards the reactants (\(\mathrm{PCl_{3}}\) and \(\mathrm{Cl_{2}}\)). Consequently, the ratio \(\frac{\mathrm{PCl}_{5}}{\mathrm{PCl}_{3}}\) will decrease, not increase. So, statement c is false.
04

Statement d

The following relationship governs the standard Gibbs free energy change, \(\Delta G^{\circ}\): $$\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}$$ The statement claims that \(\Delta G^{\circ}\) is negative at all temperatures. However, without knowing the sign and magnitude of \(\Delta S^{\circ}\), we cannot conclusively determine the sign of \(\Delta G^{\circ}\) at all temperatures. Thus, statement d is not necessarily true.
05

Statement e

The relationship between \(\Delta G^{\circ}\) and the equilibrium constant \(K_\text{p}\) is: $$\Delta G^{\circ} = -RT \ln K_\text{p}$$ When \(\Delta G^{\circ}<0\), the ln term must be positive, which implies that \(K_\text{p}>1\). So, when \(\Delta G^{\circ}\) for this reaction is negative, \(K_{\mathrm{p}}\) is greater than \(1.00\). Thus, statement e is true. Summing up, only statement e is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Using data from Appendix 4, calculate \(\Delta H^{\circ}, \Delta G^{\circ}\), and \(K(\) at \(298 \mathrm{~K}\) ) for the production of ozone from oxygen: $$ 3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g) $$ At \(30 \mathrm{~km}\) above the surface of the earth, the temperature is about \(230 . \mathrm{K}\) and the partial pressure of oxygen is about \(1.0 \times 10^{-3}\) atm. Estimate the partial pressure of ozone in equilibrium with oxygen at \(30 \mathrm{~km}\) above the earth's surface. Is it reasonable to assume that the equilibrium between oxygen and ozone is maintained under these conditions? Explain.

Predict the sign of \(\Delta S^{\circ}\) and then calculate \(\Delta S^{\circ}\) for each of the following reactions. a. \(\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) b. \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{HCl}(g) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q)\)

At \(100 .{ }^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}, \Delta H^{\circ}=40.6 \mathrm{~kJ} / \mathrm{mol}\) for the vaporiza- tion of water. Estimate \(\Delta G^{\circ}\) for the vaporization of water at \(90 .{ }^{\circ} \mathrm{C}\) and \(110 .{ }^{\circ} \mathrm{C}\). Assume \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) at \(100 .{ }^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) do not depend on temperature.

Consider the following system at equilibrium at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) \quad \Delta G^{\circ}=-92.50 \mathrm{~kJ} $$ What will happen to the ratio of partial pressure of \(\mathrm{PCl}_{5}\) to partial pressure of \(\mathrm{PCl}_{3}\) if the temperature is raised? Explain completely.

The equilibrium constant for a certain reaction decreases from \(8.84\) to \(3.25 \times 10^{-2}\) when the temperature increases from \(25^{\circ} \mathrm{C}\) to \(75^{\circ} \mathrm{C}\). Estimate the temperature where \(K=1.00\) for this reaction. Estimate the value of \(\Delta S^{\circ}\) for this reaction. (Hint: Manipulate the equation in Exercise \(79 .\) )
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

Read Explanation

Making Measurements

Read Explanation

Inorganic Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free