For a gas at a certain temperature, if the molar mass is halved, what happens to the RMS speed?

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Increases by a factor of 2
Increases by a factor of sqrt(2)
Decreases by a factor of 2
Remains the same

Questions & Step-by-step Solutions

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Q: For a gas at a certain temperature, if the molar mass is halved, what happens to the RMS speed?

Solution: RMS speed is inversely proportional to the square root of molar mass. Halving the molar mass increases the RMS speed by a factor of sqrt(2).

Steps: 7

Step 1: Understand that RMS speed (Root Mean Square speed) is a measure of the speed of gas particles.
Step 2: Know the formula for RMS speed: 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 in this formula, the RMS speed is inversely related to the square root of the molar mass (M).
Step 4: If the molar mass (M) is halved, it means M becomes M/2.
Step 5: Substitute M/2 into the formula: v_rms = sqrt(3RT/(M/2)) = sqrt(3RT * (2/M)) = sqrt(2) * sqrt(3RT/M).
Step 6: This shows that the new RMS speed is sqrt(2) times the original RMS speed.
Step 7: Conclude that halving the molar mass increases the RMS speed by a factor of sqrt(2).

For a gas at a certain temperature, if the molar mass is halved, what happens to the RMS speed?

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