For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
Practice Questions
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Q1
For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
v_rms is directly proportional to M
v_rms is inversely proportional to M
v_rms is independent of M
v_rms is proportional to M^2
The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.
Questions & Step-by-step Solutions
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Q
Q: For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
Solution: The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.
Steps: 6
Step 1: Understand what RMS speed is. RMS speed (v_rms) is a measure of the average 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 in Kelvin, and M is the molar mass.
Step 3: Identify the relationship between RMS speed and molar mass. The formula shows that v_rms is divided by the square root of M.
Step 4: Recognize that if M (molar mass) increases, the value of sqrt(M) also increases.
Step 5: Since v_rms is divided by sqrt(M), an increase in M means that v_rms will decrease.
Step 6: Conclude that RMS speed is inversely proportional to the square root of molar mass.
