Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 36

Suppose that the gas-phase reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow\) \(2 \mathrm{NO}_{2}(g)\) were carried out in a constant-volume container at constant temperature. Would the measured heat change represent \(\Delta H\) or \(\Delta E ?\) If there is a difference, which quantity is larger for this reaction? Explain.

Short Answer

Expert verified
In this gas-phase reaction at constant volume and constant temperature, the measured heat change represents both ΔH (change in enthalpy) and ΔE (change in internal energy) since there is no difference between the two quantities. This is because the change in volume (ΔV) is 0, making the relationship between ΔH and ΔE as follows: ΔH = ΔE. Therefore, both ΔH and ΔE represent the same heat change for this reaction, and there is no need to compare them to determine which one is larger.

Step by step solution

01

Understanding ΔH and ΔE

ΔH (change in enthalpy) and ΔE (change in internal energy) are two important thermodynamic properties that can describe the energy changes in a chemical reaction. The relationship between the two can be given by the equation: ΔH = ΔE + PΔV, where P is the constant pressure and ΔV is the change in volume.
02

Analyzing the reaction at constant volume and temperature

Since we are told that the reaction takes place in a constant-volume container, there is no change in the volume of the system (ΔV = 0). The reaction is also happening at a constant temperature. Now, using the relationship between ΔH and ΔE, we will determine which quantity is represented by the measured heat change.
03

Determining the measured heat change

Given that ΔV = 0, we can rewrite the equation for the relationship between ΔH and ΔE as: ΔH = ΔE This means that at constant volume and constant temperature, there is no difference between the change in enthalpy (ΔH) and the change in internal energy (ΔE). Therefore, the measured heat change represents both ΔH and ΔE in this case.
04

Comparing ΔH and ΔE

Since ΔH and ΔE are the same for this particular reaction, there is no need to compare them to determine which one is larger. They are equal in magnitude and represent the same heat change for the given reaction at constant volume and temperature.

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

The automobile fuel called E85 consists of \(85 \%\) ethanol and \(15 \%\) gasoline. \(\mathrm{E} 85\) can be used in so-called "flex-fuel" vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ), that the average heat of combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) is \(5400 \mathrm{~kJ} / \mathrm{mol}\), and that gasoline has an average density of \(0.70 \mathrm{~g} / \mathrm{mL}\). The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{mL}\). (a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of \(1.0 \mathrm{~L}\) of gasoline and of \(1.0 \mathrm{~L}\) of ethanol. (b) Assume that the density and heat of combustion of \(\mathrm{E} 85\) can be obtained by using \(85 \%\) of the values for ethanol and \(15 \%\) of the values for gasoline. How much energy could be released by the combustion of \(1.0 \mathrm{~L}\) of E85? (c) How many gallons of E85 would be needed to provide the same energy as 10 gal of gasoline? (d) If gasoline costs \(\$ 3.10\) per gallon in the United States, what is the break-even price per gallon of \(\mathrm{E} 85\) if the same amount of energy is to be delivered?

What is the connection between Hess's law and the fact that \(H\) is a state function?

(a) When a \(0.235-\mathrm{g}\) sample of benzoic acid is combusted in a bomb calorimeter (Figure 5.19 ), the temperature rises \(1.642{ }^{\circ} \mathrm{C}\). When a 0.265 -g sample of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{O}_{2} \mathrm{~N}_{4}\), is burned, the temperature rises \(1.525^{\circ} \mathrm{C}\). Using the value \(26.38 \mathrm{~kJ} / \mathrm{g}\) for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of \(0.002^{\circ} \mathrm{C}\) in each temperature reading and that the masses of samples are measured to 0.001 \(\mathrm{g}\), what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

Imagine a book that is falling from a shelf. At a particular moment during its fall, the book has a kinetic energy of \(24 \mathrm{~J}\) and a potential energy with respect to the floor of \(47 \mathrm{~J} .\) (a) How does the book's kinetic energy and its potential energy change as it continues to fall? (b) What is its total kinetic energy at the instant just before it strikes the floor? (c) If a heavier book fell from the same shelf, would it have the same kinetic energy when it strikes the floor? [Section 5.1]

(a) When a 4.25 -g sample of solid ammonium nitrate dissolves in \(60.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18), the temperature drops from \(22.0^{\circ} \mathrm{C}\) to \(16.9^{\circ} \mathrm{C}\). Calculate \(\Delta H\left(\right.\) in \(\left.\mathrm{kJ} / \mathrm{mol} \mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) for the solution process $$ \mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) $$ Assume that the specific heat of the solution is the same as that of pure water. (b) Is this process endothermic or exothermic?
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Making Measurements

Read Explanation

Chemistry Branches

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