For a gas at a constant temperature, if the molar mass is halved, what happens t

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

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

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.

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.