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...
Related questions
Question
Which gas will have the lowest vrmsat 298 K?
A. NH3
B. CO
C. SF6
D. H2
![**Question:**
Which gas will have the lowest \( v_{\text{rms}} \) at 298 K?
**Options:**
A. \( \text{NH}_3 \)
B. CO
C. \( \text{SF}_6 \)
D. \( \text{H}_2 \)
**Explanation:**
Root mean square speed (\( v_{\text{rms}} \)) is a measure of the average speed of particles in a gas and is given by the formula:
\[
v_{\text{rms}} = \sqrt{\frac{3kT}{m}}
\]
where:
- \( k \) is the Boltzmann constant,
- \( T \) is the temperature in Kelvin,
- \( m \) is the molar mass of the gas.
At a constant temperature, gases with larger molar masses have lower \( v_{\text{rms}} \). Therefore, the gas with the highest molar mass will have the lowest \( v_{\text{rms}} \).
In this case, \( \text{SF}_6 \) has the highest molar mass among the options provided, making it the gas with the lowest \( v_{\text{rms}} \) at 298 K.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1d14486-aab8-45fa-9185-3d15b7af8b4b%2F9247f7e3-51f1-42ae-83e4-52720ab5d330%2Fcape2c_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Which gas will have the lowest \( v_{\text{rms}} \) at 298 K?
**Options:**
A. \( \text{NH}_3 \)
B. CO
C. \( \text{SF}_6 \)
D. \( \text{H}_2 \)
**Explanation:**
Root mean square speed (\( v_{\text{rms}} \)) is a measure of the average speed of particles in a gas and is given by the formula:
\[
v_{\text{rms}} = \sqrt{\frac{3kT}{m}}
\]
where:
- \( k \) is the Boltzmann constant,
- \( T \) is the temperature in Kelvin,
- \( m \) is the molar mass of the gas.
At a constant temperature, gases with larger molar masses have lower \( v_{\text{rms}} \). Therefore, the gas with the highest molar mass will have the lowest \( v_{\text{rms}} \).
In this case, \( \text{SF}_6 \) has the highest molar mass among the options provided, making it the gas with the lowest \( v_{\text{rms}} \) at 298 K.
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