Homework Help is Here – Start Your Trial Now!
Science
Physics
5) A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules are at STP. Which statements are true about these molecules? (There could be more than one correct choice.) A) Both gases have the same average momentum per molecule. B) Both gases have the same average molecular speeds. C) Both gases have the same average kinetic energy per molecule. D) Both gases have the same number of molecules.

5) A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules are at STP. Which statements are true about these molecules? (There could be more than one correct choice.) A) Both gases have the same average momentum per molecule. B) Both gases have the same average molecular speeds. C) Both gases have the same average kinetic energy per molecule. D) Both gases have the same number of molecules.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
icon
Concept explainers
Question
100%
### Problem 5: Analysis of Diatomic Gases at Standard Temperature and Pressure (STP) **Context**: Consider a mole of diatomic oxygen molecules (O₂) and a mole of diatomic nitrogen molecules (N₂) both at standard temperature and pressure (STP). **Question**: Which statements below are true about these molecules? (Note: There could be more than one correct choice.) **Statements**: A) Both gases have the same average momentum per molecule. B) Both gases have the same average molecular speeds. C) Both gases have the same average kinetic energy per molecule. D) Both gases have the same number of molecules. **Considerations for Answering**: - At STP, both gases are under the same temperature and pressure conditions. - One mole of any ideal gas contains Avogadro's number of molecules, which is approximately \(6.022 \times 10^{23}\) molecules. **Detailed Analysis**: - **Average Momentum**: The momentum of a molecule is a product of its mass and velocity. Since oxygen and nitrogen molecules have different masses, their average momentum per molecule would differ even if their velocities were the same. - **Average Molecular Speeds**: According to the kinetic theory of gases, the average speed of a gas molecule depends on the mass of the molecule. Since O₂ and N₂ have different molecular masses, their average speeds will be different. - **Average Kinetic Energy**: Kinetic energy for gas molecules at a given temperature is given by \(\frac{3}{2} k_B T\), where \(k_B\) is Boltzmann's constant and T is the temperature. This is independent of the mass of the molecule, meaning O₂ and N₂ molecules at the same temperature have the same average kinetic energy. - **Number of Molecules**: By definition, one mole of any substance contains the same number of molecules, Avogadro’s number. Therefore, a mole of O₂ and a mole of N₂ will contain the same number of molecules. **Conclusion**: From the given statements: - **Statement C (True)**: Both gases have the same average kinetic energy per molecule. - **Statement D (True)**: Both gases have the same number of molecules. Thus, the correct answers are **C** and **D**.
Transcribed Image Text:### Problem 5: Analysis of Diatomic Gases at Standard Temperature and Pressure (STP) **Context**: Consider a mole of diatomic oxygen molecules (O₂) and a mole of diatomic nitrogen molecules (N₂) both at standard temperature and pressure (STP). **Question**: Which statements below are true about these molecules? (Note: There could be more than one correct choice.) **Statements**: A) Both gases have the same average momentum per molecule. B) Both gases have the same average molecular speeds. C) Both gases have the same average kinetic energy per molecule. D) Both gases have the same number of molecules. **Considerations for Answering**: - At STP, both gases are under the same temperature and pressure conditions. - One mole of any ideal gas contains Avogadro's number of molecules, which is approximately \(6.022 \times 10^{23}\) molecules. **Detailed Analysis**: - **Average Momentum**: The momentum of a molecule is a product of its mass and velocity. Since oxygen and nitrogen molecules have different masses, their average momentum per molecule would differ even if their velocities were the same. - **Average Molecular Speeds**: According to the kinetic theory of gases, the average speed of a gas molecule depends on the mass of the molecule. Since O₂ and N₂ have different molecular masses, their average speeds will be different. - **Average Kinetic Energy**: Kinetic energy for gas molecules at a given temperature is given by \(\frac{3}{2} k_B T\), where \(k_B\) is Boltzmann's constant and T is the temperature. This is independent of the mass of the molecule, meaning O₂ and N₂ molecules at the same temperature have the same average kinetic energy. - **Number of Molecules**: By definition, one mole of any substance contains the same number of molecules, Avogadro’s number. Therefore, a mole of O₂ and a mole of N₂ will contain the same number of molecules. **Conclusion**: From the given statements: - **Statement C (True)**: Both gases have the same average kinetic energy per molecule. - **Statement D (True)**: Both gases have the same number of molecules. Thus, the correct answers are **C** and **D**.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Kinetic theory of gas
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS