For a gas at a constant temperature, if the molar mass is halved, what happens to the RMS speed?
Practice Questions
1 question
Q1
For a gas at a constant temperature, if the molar mass is halved, what happens to the RMS speed?
Increases by a factor of sqrt(2)
Increases by a factor of 2
Decreases by a factor of 2
Remains the same
The RMS speed is inversely proportional to the square root of the molar mass. If the molar mass is halved, the RMS speed increases by a factor of sqrt(2), which is approximately 1.414, but in terms of doubling the speed, it is considered to increase by a factor of 2.
Questions & Step-by-step Solutions
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Q
Q: For a gas at a constant temperature, if the molar mass is halved, what happens to the RMS speed?
Solution: The RMS speed is inversely proportional to the square root of the molar mass. If the molar mass is halved, the RMS speed increases by a factor of sqrt(2), which is approximately 1.414, but in terms of doubling the speed, it is considered to increase by a factor of 2.
Steps: 7
Step 1: Understand that RMS speed (Root Mean Square speed) is a measure of the average 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 temperature (T) and gas constant (R) are constant, the RMS speed depends on the molar mass (M).
Step 4: Remember that RMS speed is inversely proportional to the square root of the molar mass. This means that if M decreases, v_rms increases.
Step 5: If the molar mass is halved (M becomes M/2), we can substitute this into the formula: v_rms = sqrt(3RT/(M/2)) = sqrt(6RT/M).
Step 6: Notice that this new RMS speed is sqrt(2) times the original RMS speed because sqrt(6) is sqrt(2) times sqrt(3).
Step 7: Conclude that halving the molar mass increases the RMS speed by a factor of sqrt(2), which is approximately 1.414.
