If the molar mass of a gas is halved, what happens to its RMS speed?

If the molar mass of a gas is halved, what happens to its RMS speed?

Correct Answer: RMS speed increases by a factor of sqrt(2)

Step 1: Understand that RMS speed (Root Mean Square speed) is a measure of the speed of gas molecules.
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 RMS speed formula: v_rms = sqrt(3RT/(M/2)).
Step 6: Simplify the equation: v_rms = sqrt(3RT * (2/M)) = sqrt(2) * sqrt(3RT/M).
Step 7: Notice that the new RMS speed is sqrt(2) times the original RMS speed.
Step 8: Conclude that if the molar mass is halved, the RMS speed increases 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, meaning that as the molar mass decreases, the RMS speed increases.