Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 1317

The degrees of freedom for triatomic gas \(1 \mathrm{~s}\) (At room temperature) (A) 8 (B) 6 (C) 4 (D) 2

Short Answer

Expert verified
The correct answer is (B) 6 degrees of freedom. At room temperature, a triatomic gas molecule has 3 translational degrees of freedom and for a nonlinear triatomic molecule, it has 3 rotational degrees of freedom. Vibrational degrees of freedom are not considered, as they require a high amount of energy.

Step by step solution

01

Understand Degrees of Freedom

Degrees of freedom represent the number of independent ways a system can store energy, which can be categorized into three main modes - translational, rotational, and vibrational. For a gas molecule, the total degrees of freedom are the sum of all the possible modes.
02

Translational Degrees of Freedom

In a 3D space, every molecule can move in three independent directions - along the x-axis, y-axis, and z-axis. So, a gas molecule has 3 translational degrees of freedom.
03

Rotational Degrees of Freedom

For a triatomic gas, there are two types of molecules: linear and nonlinear. A linear triatomic molecule has a single axis passing through all three atoms, which restricts its rotation to only two axes. So, it has 2 rotational degrees of freedom. On the other hand, a nonlinear triatomic molecule (such as H2O) has 3 rotational degrees of freedom.
04

Vibrational Degrees of Freedom

At room temperature, vibrational degrees of freedom are usually not activated for most gases, as they require a high amount of energy. Therefore, at room temperature, we will not consider vibrational degrees of freedom.
05

Calculate Total Degrees of freedom

Now we can sum up the degrees of freedom for each mode to find the total degrees of freedom. For a linear triatomic molecule: 3 (translational) + 2 (rotational) + 0 (vibrational) = 5 For a nonlinear triatomic molecule: 3 (translational) + 3 (rotational) + 0 (vibrational) = 6
06

Answer

Comparing our results with the given multiple-choice options, we can see that the most appropriate answer is 6 degrees of freedom, which corresponds to option (B). So the correct answer is (B) 6.

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 pressure and temperature of two different gases \(P\) and T having the volumes \(\mathrm{V}\) for each. They are mixed keeping the same volume and temperature, the pressure of the mixture will be, (A) \(\mathrm{P}\) (B) \((\mathrm{P} / 2)\) (C) \(4 \mathrm{P}\) (D) \(2 \mathrm{P}\)

For a gas, the rms speed at \(800 \mathrm{~K}\) is (A) Four times the value at \(200 \mathrm{~K}\) (B) Twice the value at \(200 \mathrm{~K}\) (C) Half the value at \(200 \mathrm{~K}\) (D) same as at \(200 \mathrm{~K}\)

The volume of a gas at \(20 \mathrm{C}\) is \(200 \mathrm{ml}\). If the temperature is reduced to \(-20^{\circ} \mathrm{C}\) at constant pressure, its volume will be. (A) \(172.6 \mathrm{~m} 1\) (B) \(17.26 \mathrm{ml}\) (C) \(19.27 \mathrm{ml}\) (D) \(192.7 \mathrm{ml}\)

Pressure of an ideal gas is increased by keeping temperature constant what is the effect on kinetic energy of molecules. (A) Decrease (B) Increase (C) No change (D) Can't be determined

The mean kinetic energy of a gas at \(300 \mathrm{~K}\) is \(100 \mathrm{~J}\). mean energy of the gas at \(450 \mathrm{~K}\) is equal to (A) \(100 \mathrm{~J}\) (B) \(150 \mathrm{~J}\) (C) \(3000 \mathrm{~J}\) (D) \(450 \mathrm{~J}\)
See all solutions

Recommended explanations on English Textbooks

Key Concepts in Language and Linguistics

Read Explanation

Discourse

Read Explanation

Phonology

Read Explanation

Rhetoric

Read Explanation

Lexis and Semantics Summary

Read Explanation

Creative Story

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