If the molar mass of a gas is doubled, how does the RMS speed change?

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Question: If the molar mass of a gas is doubled, how does the RMS speed change?

Options:

Correct Answer: Decreases by sqrt(2)

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).

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?

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).

RMS Speed and Molar Mass Relationship – The root mean square (RMS) speed of a gas is inversely proportional to the square root of its molar mass, described by the equation v_rms = sqrt(RT/M), where R is the gas constant and T is the temperature.