1) ( temperature. Let Vị = the most probable velocity for dipropyl ether. Let V2 = the most probable velocity for dimethyl ether. , Dipropyl ether and dimethyl ether exist as a mixed ideal gas at a common Calculate Vi / V2.
1) ( temperature. Let Vị = the most probable velocity for dipropyl ether. Let V2 = the most probable velocity for dimethyl ether. , Dipropyl ether and dimethyl ether exist as a mixed ideal gas at a common Calculate Vi / V2.
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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![### Problem Statement
1) Dipropyl ether and dimethyl ether exist as a mixed ideal gas at a common temperature. Let \( V_1 \) represent the most probable velocity for dipropyl ether, and \( V_2 \) represent the most probable velocity for dimethyl ether.
Calculate \( V_1 / V_2 \).
### Explanation
This question involves calculating the ratio of the most probable velocities of two different gases within an ideal gas mixture. It hinges on the principles of kinetic molecular theory, which implies that the most probable speed is related to the mass of the gas molecules and the temperature of the gas.
A typical approach would involve using the formula for the most probable speed given by:
\[ V_{\text{mp}} = \sqrt{\frac{2kT}{m}} \]
where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the molar mass of the gas. In this problem, for each gas (dipropyl ether and dimethyl ether), the ratio can be calculated since the temperature \( T \) is constant. Thus,
\[ \frac{V_1}{V_2} = \sqrt{\frac{m_2}{m_1}} \]
where \( m_1 \) and \( m_2 \) are the molar masses of dipropyl ether and dimethyl ether, respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b22dc5-b81c-452b-a8fe-ec73685697af%2Fe627a805-51b4-4f49-b6ab-6d5ca197f482%2Fk03ym3k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
1) Dipropyl ether and dimethyl ether exist as a mixed ideal gas at a common temperature. Let \( V_1 \) represent the most probable velocity for dipropyl ether, and \( V_2 \) represent the most probable velocity for dimethyl ether.
Calculate \( V_1 / V_2 \).
### Explanation
This question involves calculating the ratio of the most probable velocities of two different gases within an ideal gas mixture. It hinges on the principles of kinetic molecular theory, which implies that the most probable speed is related to the mass of the gas molecules and the temperature of the gas.
A typical approach would involve using the formula for the most probable speed given by:
\[ V_{\text{mp}} = \sqrt{\frac{2kT}{m}} \]
where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the molar mass of the gas. In this problem, for each gas (dipropyl ether and dimethyl ether), the ratio can be calculated since the temperature \( T \) is constant. Thus,
\[ \frac{V_1}{V_2} = \sqrt{\frac{m_2}{m_1}} \]
where \( m_1 \) and \( m_2 \) are the molar masses of dipropyl ether and dimethyl ether, respectively.
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