For a gas with molar mass M at temperature T, what is the relationship between RMS speed and molar mass?

Practice Questions

1 question

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

Questions & Step-by-step Solutions

1 item

Q: For a gas with molar mass M at temperature T, what is the relationship between RMS speed and molar mass?

Solution: The RMS speed is given by v_rms = sqrt((3RT)/M). This shows that v_rms is inversely proportional to the square root of the molar mass M.

Steps: 6

Step 1: Understand that RMS speed (v_rms) 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 and T is the temperature.
Step 3: Identify that M represents the molar mass of the gas.
Step 4: Notice that in the formula, M is in the denominator under the square root.
Step 5: Realize that if M increases (the molar mass gets larger), the value of v_rms decreases because they are inversely related.
Step 6: Conclude that RMS speed is inversely proportional to the square root of the molar mass M.

For a gas with molar mass M at temperature T, what is the relationship between RMS speed and molar mass?

Practice Questions

Questions & Step-by-step Solutions

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