For a gas with molar mass M at temperature T, what is the relationship between R

₹0.0

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

Options:

Correct Answer: v_rms is inversely proportional to M

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.

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

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

Correct Answer: RMS speed is inversely proportional to the square root of molar mass.

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.

RMS Speed – The root mean square speed of gas molecules, which is a measure of the average speed of particles in a gas.
Molar Mass – The mass of one mole of a substance, typically expressed in grams per mole (g/mol).
Inversely Proportional Relationship – A relationship where one quantity increases as the other decreases; in this case, RMS speed decreases as molar mass increases.
Gas Laws – The principles governing the behavior of gases, including the ideal gas law and kinetic molecular theory.