Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q12Q (page 507)

Many chemical reactions proceed at rates that depend on the temperature. Discuss this from the point of view of the Boltzmann distribution.

Short Answer

Expert verified

The fractions of molecules with lower energies decreasing while the fraction of molecules with higher energies increasing. The total area of Boltzmann distribution remains constant.

Step by step solution

01

Understanding the Boltzmann distribution

The Boltzmann distribution gives the distribution of molecular speeds (or molecular energies) of gas sample at a given temperature.

02

Discuss about many chemical reactions proceed at rates that depends on the temperature from the point of view of the Boltzmann distribution.

The Boltzmann distribution curve that represents the rate of chemical reaction that depends on the temperature is given below.

As temperature increases, the curve shifts towards right and flattens out. The peak of the curves becomes shorter. The total area under the curves, however, remains the same. Also, the fraction of molecules with low energies decreases while the fraction of molecules with high energies increases.

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 interatomic spring stiffness for tungsten is determined from Young’s modulus measurements to be 90 N. The mass of one mole of tungsten is 0185 kg . If we model a block of tungsten as a collection of atomic “oscillators” (masses on springs), note that since each oscillator is attached to two “springs,” and each “spring” is half the length of the interatomic bond, the effective interatomic spring stiffness for one of these oscillators is 4 times the calculated value given above.Use these precise values for the constants: h̶=1.05×10-34 J.s(Planck’s constant divided by 2π), Avogadro’s number = 6.0221×1023 molecule/mole, kB=1.3807×10-23 J/K(the Boltzmann constant). (a) What is one quantum of energy for one of these atomic oscillators? (b) Figure 12.56 contains the number of ways to arrange a given number of quanta of energy in a particular block of tungsten. Fill in the blanks to complete the table, including calculating the temperature of the block. The energy E is measured from the ground state. Nothing goes in the shaded boxes. Be sure to give the temperature to the nearest 0.1 kelvin. (c) There are about 60 atoms in this object. What is the heat capacity on a per-atom basis? (Note that at high temperatures the heat capacity on a per-atom basis approaches the classical limit of 3kB = 4.2×10−23 J/K/atom.)

At sufficiently high temperatures, the thermal speeds of gas molecules may be high enough that collisions may ionize a molecule (that is, remove an outer electron). An ionized gas in which each molecule has lost an electron is called a “plasma.” Determine approximately the temperature at which air becomes a plasma.

Explain qualitatively the basis for the Boltzmann distribution. Never mind the details of the math for the moment. Focus on the trade-offs involved with giving energy to a single oscillator vs. giving that energy to a large object.

Buckminsterfullerene, C60, is a large molecule consisting of 60 carbon atoms connected to form a hollow sphere. The diameter of a C60 molecule is about 7×10-10 m. It has been hypothesized that C60 molecules might be found in clouds of interstellar dust, which often contain interesting chemical compounds. The temperature of an interstellar dust cloud may be very low; around 3 K. Suppose you are planning to try to detect the presence of C60 in such a cold dust cloud by detecting photons emitted when molecules undergo transitions from one rotational energy state to another. Approximately, what is the highest-numbered rotational level from which you would expect to observe emissions? Rotational levels are l= 0, 1, 2, 3, …

In Chapter 4 you determined the stiffness of the interatomic “spring” (chemical bond) between atoms in a block of lead to be 5 N/m, based on the value of Young’s modulus for lead. Since in our model each atom is connected to two springs, each half the length of the interatomic bond, the effective “interatomic spring stiffness” for an oscillator is

4 × 5 N/m = 20 N/m. The mass of one mole of lead is 207 g (0.207 kg). What is the energy, in joules, of one quantum of energy for an atomic oscillator in a block of lead?
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Dynamics

Read Explanation

Linear Momentum

Read Explanation

Kinematics Physics

Read Explanation

Electricity

Read Explanation

Medical Physics

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