In a mixture of gases, how does the RMS speed depend on the individual gas components?
Practice Questions
1 question
Q1
In a mixture of gases, how does the RMS speed depend on the individual gas components?
It depends only on the lightest gas
It is the weighted average of the RMS speeds of the components
It is the sum of the RMS speeds of the components
It is independent of the gas components
The RMS speed of a mixture of gases is the weighted average of the RMS speeds of the individual components, taking into account their molar masses.
Questions & Step-by-step Solutions
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Q
Q: In a mixture of gases, how does the RMS speed depend on the individual gas components?
Solution: The RMS speed of a mixture of gases is the weighted average of the RMS speeds of the individual components, taking into account their molar masses.
Steps: 7
Step 1: Understand what RMS speed is. RMS speed stands for Root Mean Square speed, which is a way to measure the average speed of gas particles in a mixture.
Step 2: Recognize that a mixture of gases can contain different types of gases, each with its own molar mass.
Step 3: Know that the RMS speed of each individual gas depends on its molar mass. Lighter gases have higher RMS speeds, while heavier gases have lower RMS speeds.
Step 4: To find the RMS speed of the entire mixture, you need to calculate the RMS speed for each gas in the mixture.
Step 5: Use the formula for the RMS speed of each gas, which is based on its temperature and molar mass.
Step 6: Combine the individual RMS speeds using a weighted average. This means you consider how much of each gas is present in the mixture (their proportions).
Step 7: The final result gives you the RMS speed of the entire gas mixture, reflecting the contributions of each gas based on their speeds and amounts.
