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

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

Options:

Correct Answer: Decreases by sqrt(2)

Solution:

RMS speed is inversely proportional to the square root of molar mass, so if M is doubled, v_rms decreases by sqrt(2).

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

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

Step 1: Understand that RMS speed (v_rms) is a measure of the speed of gas molecules.
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 the new molar mass as 2M.
Step 4: Substitute 2M into the RMS speed formula: v_rms_new = sqrt(3RT/(2M)).
Step 5: Simplify the new RMS speed: v_rms_new = sqrt(3RT/M) * sqrt(1/2) = v_rms * (1/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, as described by the equation v_rms = sqrt(3RT/M).