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...
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![**Determining Root-Mean-Square Speed of Carbon Monoxide (CO)**
The root-mean-square (rms) speed is a measure of the average speed of particles in a gas. It can be determined using the formula:
\[ v_{\text{rms}} = \sqrt{\frac{3k_BT}{m}} \]
where:
- \( k_B \) is the Boltzmann constant (\( 1.38 \times 10^{-23} \, \text{J/K} \)),
- \( T \) is the absolute temperature in Kelvin,
- \( m \) is the mass of a gas molecule in kilograms.
### Exercise
Calculate the root-mean-square speed of carbon monoxide (CO) at a temperature of 121.7 °C.
\[ \text{The root-mean-square speed of CO at 121.7 °C is} \, \_\_\_\_\_\_\_\_ \, \text{m/s.} \]
To find the rms speed:
1. Convert the temperature from Celsius to Kelvin: \( T(K) = 121.7 + 273.15 \).
2. Substitute the values into the rms speed formula.
**Note:** Always ensure the units are consistent when using the formula, and take note of the gas constant and the molar mass of CO when converting to the appropriate units.
After the above steps, you will obtain the root-mean-square speed of carbon monoxide (CO) for the given temperature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19b0aed3-745e-4879-8577-ea35399669d0%2F5b7bee46-7bf6-42b0-9fdb-eb5e8a5b8b87%2Fftwciz4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determining Root-Mean-Square Speed of Carbon Monoxide (CO)**
The root-mean-square (rms) speed is a measure of the average speed of particles in a gas. It can be determined using the formula:
\[ v_{\text{rms}} = \sqrt{\frac{3k_BT}{m}} \]
where:
- \( k_B \) is the Boltzmann constant (\( 1.38 \times 10^{-23} \, \text{J/K} \)),
- \( T \) is the absolute temperature in Kelvin,
- \( m \) is the mass of a gas molecule in kilograms.
### Exercise
Calculate the root-mean-square speed of carbon monoxide (CO) at a temperature of 121.7 °C.
\[ \text{The root-mean-square speed of CO at 121.7 °C is} \, \_\_\_\_\_\_\_\_ \, \text{m/s.} \]
To find the rms speed:
1. Convert the temperature from Celsius to Kelvin: \( T(K) = 121.7 + 273.15 \).
2. Substitute the values into the rms speed formula.
**Note:** Always ensure the units are consistent when using the formula, and take note of the gas constant and the molar mass of CO when converting to the appropriate units.
After the above steps, you will obtain the root-mean-square speed of carbon monoxide (CO) for the given temperature.
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