The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. However, given the same kinetic energies, a lighter molecule will move faster than a heavier molecule, as shown in the equation for rms speed 3RT V M rms speed = where R = 8.314 J/ (mol·K) and M is molar mass in kilograms per mole. Note that a joule is the same as a kilogram-meter squared per second squared (kg-m²/s²). What is the rms speed of O, molecules at 307 K? rms speed: m/s What is the rms speed of He atoms at 307 K? rms speed: m/s
The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. However, given the same kinetic energies, a lighter molecule will move faster than a heavier molecule, as shown in the equation for rms speed 3RT V M rms speed = where R = 8.314 J/ (mol·K) and M is molar mass in kilograms per mole. Note that a joule is the same as a kilogram-meter squared per second squared (kg-m²/s²). What is the rms speed of O, molecules at 307 K? rms speed: m/s What is the rms speed of He atoms at 307 K? rms speed: m/s
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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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![**Understanding RMS Speed of Gas Molecules: An Educational Overview**
The average kinetic energy of molecules in a gas sample depends solely on the temperature, \( T \). Given the same kinetic energies, lighter molecules will travel faster than heavier molecules. This relationship is defined by the equation for root mean square (rms) speed:
\[
\text{rms speed} = \sqrt{\frac{3RT}{\mathcal{M}}}
\]
where:
- \( R = 8.314 \, \text{J/(mol}\cdot\text{K)} \) is the universal gas constant,
- \( \mathcal{M} \) represents the molar mass in kilograms per mole.
**Note:** A joule (J) is equivalent to a kilogram-meter squared per second squared (\(\text{kg}\cdot\text{m}^2/\text{s}^2\)).
**Calculation Example:**
1. **RMS Speed of \( \text{O}_2 \) Molecules at 307 K:**
Calculate rms speed: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Result: \(\underline{\hspace{2cm}}\) m/s
2. **RMS Speed of He Atoms at 307 K:**
Calculate rms speed: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Result: \(\underline{\hspace{2cm}}\) m/s
This module serves as a practical application exercise, enhancing comprehension of molecular dynamics in gases based on temperature and molecular weight.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6797ee8f-35b0-45f9-be91-6b4961db7d8a%2Fc77cd353-b963-448b-bb9d-40464a250224%2Fgghxb4w_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding RMS Speed of Gas Molecules: An Educational Overview**
The average kinetic energy of molecules in a gas sample depends solely on the temperature, \( T \). Given the same kinetic energies, lighter molecules will travel faster than heavier molecules. This relationship is defined by the equation for root mean square (rms) speed:
\[
\text{rms speed} = \sqrt{\frac{3RT}{\mathcal{M}}}
\]
where:
- \( R = 8.314 \, \text{J/(mol}\cdot\text{K)} \) is the universal gas constant,
- \( \mathcal{M} \) represents the molar mass in kilograms per mole.
**Note:** A joule (J) is equivalent to a kilogram-meter squared per second squared (\(\text{kg}\cdot\text{m}^2/\text{s}^2\)).
**Calculation Example:**
1. **RMS Speed of \( \text{O}_2 \) Molecules at 307 K:**
Calculate rms speed: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Result: \(\underline{\hspace{2cm}}\) m/s
2. **RMS Speed of He Atoms at 307 K:**
Calculate rms speed: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Result: \(\underline{\hspace{2cm}}\) m/s
This module serves as a practical application exercise, enhancing comprehension of molecular dynamics in gases based on temperature and molecular weight.
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