1) State the number of degrees of freedom of a gas composed of one of the following a. Ne (neon atom) b. N2 (nitrogen molecule)

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
icon
Related questions
icon
Concept explainers
Question
Answer question one please.
1) State the number of degrees of freedom of a gas composed of one of the following
Ne (neon atom)
b. N2 (nitrogen molecule)
a.
2) A diatomic molecule which consists of two atoms can have translational, rotational, and vibrational
degrees of freedom because the molecule can translate, rotate, and vibrate. However, it is known
that just because a molecule is capable of rotating or vibrating does not mean that there is enough
energy available to do so. The temperature has to be high enough to enable different types of
motion. In that case, we say that the degree of freedom is active if the temperature is high enough
or inactive if it is not. How many degrees of freedom are active in a hydrogen molecule, H2, at 500
K?
3) Write an expression for the internal energy U of a gas of N particles (that is, atoms or molecules) at
temperature T in terms of N and T and any required constants, when the gas consists of
a. Ne (neon atoms)
b. N2 (nitrogen molecules), assuming all degrees of freedom are active.
4) Calculate the internal energy U of a liter of helium at room temperature and atmospheric pressure.
Then repeat the calculation for a liter of air.
5) The equipartition theorem allows us to write U = aNkT, where the constant a is the number of
(active) degrees of freedom per molecule and k is Boltzmann's constant. Write an expression for
the change in internal energy AU.
6) What does the expression for AU from the previous problem say about AU if the temperature is
constant?
a
22
hp
Transcribed Image Text:1) State the number of degrees of freedom of a gas composed of one of the following Ne (neon atom) b. N2 (nitrogen molecule) a. 2) A diatomic molecule which consists of two atoms can have translational, rotational, and vibrational degrees of freedom because the molecule can translate, rotate, and vibrate. However, it is known that just because a molecule is capable of rotating or vibrating does not mean that there is enough energy available to do so. The temperature has to be high enough to enable different types of motion. In that case, we say that the degree of freedom is active if the temperature is high enough or inactive if it is not. How many degrees of freedom are active in a hydrogen molecule, H2, at 500 K? 3) Write an expression for the internal energy U of a gas of N particles (that is, atoms or molecules) at temperature T in terms of N and T and any required constants, when the gas consists of a. Ne (neon atoms) b. N2 (nitrogen molecules), assuming all degrees of freedom are active. 4) Calculate the internal energy U of a liter of helium at room temperature and atmospheric pressure. Then repeat the calculation for a liter of air. 5) The equipartition theorem allows us to write U = aNkT, where the constant a is the number of (active) degrees of freedom per molecule and k is Boltzmann's constant. Write an expression for the change in internal energy AU. 6) What does the expression for AU from the previous problem say about AU if the temperature is constant? a 22 hp
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Ideal and Real Gases
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY