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If the molar mass of a gas is doubled, how does the RMS speed change?
If the molar mass of a gas is doubled, how does the RMS speed change?
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Practice Questions
1 question
Q1
If the molar mass of a gas is doubled, how does the RMS speed change?
Increases by sqrt(2)
Decreases by sqrt(2)
Remains the same
Increases by 2
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The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).
Questions & Step-by-step Solutions
1 item
Q
Q: If the molar mass of a gas is doubled, how does the RMS speed change?
Solution:
The RMS speed is inversely proportional to the square root of the molar mass. If M is doubled, v_rms decreases by sqrt(2).
Steps: 6
Show Steps
Step 1: Understand that RMS speed (v_rms) is a measure of the speed of gas particles.
Step 2: Know that the formula for RMS speed is v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass.
Step 3: Recognize that if the molar mass (M) is doubled, we can represent this as M' = 2M.
Step 4: Substitute M' into the RMS speed formula: v_rms' = sqrt(3RT/(2M)).
Step 5: Simplify the new RMS speed: v_rms' = sqrt(1/2) * sqrt(3RT/M) = v_rms/sqrt(2).
Step 6: Conclude that if the molar mass is doubled, the RMS speed decreases by a factor of sqrt(2).
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