Concept:The root mean square (RMS) velocity of a gas is derived from the Kinetic Molecular Theory and shows how the speed of gas molecules relates to temperature and molar mass.
Formula:$$ C_{rms} = \sqrt{\frac{3RT}{M}} $$
Solution:- In the formula, \( C_{rms} \) represents the root mean square velocity, \( R \) is the ideal gas constant, \( T \) is absolute temperature, and \( M \) is the molar mass of the gas.
- From the equation, we can see that \( C_{rms} \propto \sqrt{T} \) and \( C_{rms} \propto \frac{1}{\sqrt{M}} \).
- Therefore, the RMS velocity is inversely proportional to the square root of the molar mass.
Why other options are incorrect:- Option A: It is directly proportional to the square root of Temperature, not inversely.
- Options B & D: Pressure and Volume do not directly appear in this formulation of the RMS velocity equation.
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