For a gas with molar mass M, what is the RMS speed at 300 K?

For a gas with molar mass M, what is the RMS speed at 300 K?

Step 1: Identify the formula for RMS speed, which is v_rms = sqrt(3RT/M).
Step 2: Understand that R is the universal gas constant, which is approximately 8.314 J/(mol·K).
Step 3: Recognize that M is the molar mass of the gas in kg/mol.
Step 4: Set the temperature T to 300 K in the formula.
Step 5: Substitute the values of R and M into the formula: v_rms = sqrt(3 * 8.314 * 300 / M).
Step 6: Calculate the value inside the square root to find v_rms.

RMS Speed – The root mean square (RMS) speed of gas molecules is a measure of the average speed of particles in a gas, derived from kinetic theory.
Ideal Gas Law – The relationship between pressure, volume, temperature, and number of moles of an ideal gas, which is relevant for understanding gas behavior.
Molar Mass – The mass of one mole of a substance, which is crucial for calculating the RMS speed in relation to the gas's molecular weight.
Gas Constant (R) – A constant used in the ideal gas law and related equations, which varies depending on the units used.