If the molar mass of a gas is halved, what happens to its RMS speed?
Practice Questions
1 question
Q1
If the molar mass of a gas is halved, what happens to its RMS speed?
Increases by a factor of sqrt(2)
Increases by a factor of 2
Decreases by a factor of sqrt(2)
Remains the same
If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.
Questions & Step-by-step Solutions
1 item
Q
Q: If the molar mass of a gas is halved, what happens to its RMS speed?
Solution: If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.
Steps: 8
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)).
