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O Macmillan Learning Find the rms speed of the molecules of a sample of N, (diatomic nitrogen) gas at a temperature of 31.5° C. Drms= m/s

O Macmillan Learning Find the rms speed of the molecules of a sample of N, (diatomic nitrogen) gas at a temperature of 31.5° C. Drms= m/s

Chemistry
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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What is the speed?
The text on the image reads: "The rms speed of the molecules of a gas at 149 °C is 205 m/s. Calculate the mass \( m \) of a single molecule in the gas." Below this text, there is a box for users to input or calculate the value of \( m \). There are no graphs or diagrams in the image.
Transcribed Image Text:The text on the image reads: "The rms speed of the molecules of a gas at 149 °C is 205 m/s. Calculate the mass \( m \) of a single molecule in the gas." Below this text, there is a box for users to input or calculate the value of \( m \). There are no graphs or diagrams in the image.
**Question:** Find the rms speed of the molecules of a sample of \( N_2 \) (diatomic nitrogen) gas at a temperature of \( 31.5^\circ C \). **Answer:** \[ v_{\text{rms}} = \] --- **Explanation:** This question asks you to calculate the root mean square (rms) speed of nitrogen gas molecules at a specified temperature. The rms speed is a measure of the average speed of gas particles, which is crucial for understanding gas behavior in thermodynamics. To calculate \( v_{\text{rms}} \), use the formula: \[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \] Where: - \( k \) is the Boltzmann constant (\(1.38 \times 10^{-23} \, \text{J/K}\)), - \( T \) is the absolute temperature in Kelvin, - \( m \) is the mass of one molecule of the gas. Remember to convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For the nitrogen molecule, you may need to calculate the mass using its molar mass and Avogadro's number.
Transcribed Image Text:**Question:** Find the rms speed of the molecules of a sample of \( N_2 \) (diatomic nitrogen) gas at a temperature of \( 31.5^\circ C \). **Answer:** \[ v_{\text{rms}} = \] --- **Explanation:** This question asks you to calculate the root mean square (rms) speed of nitrogen gas molecules at a specified temperature. The rms speed is a measure of the average speed of gas particles, which is crucial for understanding gas behavior in thermodynamics. To calculate \( v_{\text{rms}} \), use the formula: \[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \] Where: - \( k \) is the Boltzmann constant (\(1.38 \times 10^{-23} \, \text{J/K}\)), - \( T \) is the absolute temperature in Kelvin, - \( m \) is the mass of one molecule of the gas. Remember to convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For the nitrogen molecule, you may need to calculate the mass using its molar mass and Avogadro's number.
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