In the RMS speed formula v_rms = sqrt(3 R T / M), what does M represent?

In the RMS speed formula v_rms = sqrt(3 R T / M), what does M represent?

• A. Molar mass
• B. Mass of a single molecule
• C. Initial length
• D. Number of molecules

Answer: (A)

M stands for molar mass, the mass of one mole of the gas. In this formula, R is the universal gas constant and T is temperature, so RT has units of energy per mole. Dividing by M (which is in kilograms per mole) gives units of energy per mass, which works out to velocity squared when you take the square root. That makes v_rms have the correct units of meters per second. If M were the mass of a single molecule, you’d be using a per-molecule form like v_rms = sqrt(3k_B T / m) with Boltzmann’s constant k_B, not RT divided by molar mass. The other options—initial length or number of molecules—don’t appear in this expression.

M stands for molar mass, the mass of one mole of the gas. In this formula, R is the universal gas constant and T is temperature, so RT has units of energy per mole. Dividing by M (which is in kilograms per mole) gives units of energy per mass, which works out to velocity squared when you take the square root. That makes v_rms have the correct units of meters per second.

If M were the mass of a single molecule, you’d be using a per-molecule form like v_rms = sqrt(3k_B T / m) with Boltzmann’s constant k_B, not RT divided by molar mass. The other options—initial length or number of molecules—don’t appear in this expression.