For a gas at 300 K, what is the RMS speed if the molar mass is 0.028 kg/mol?

For a gas at 300 K, what is the RMS speed if the molar mass is 0.028 kg/mol?

Step 1: Identify the formula for RMS speed, which is v_rms = sqrt(3RT/M).
Step 2: Determine the values needed for the formula: R (the gas constant) is 8.314 J/(mol·K), T (temperature) is 300 K, and M (molar mass) is 0.028 kg/mol.
Step 3: Plug the values into the formula: v_rms = sqrt(3 * 8.314 * 300 / 0.028).
Step 4: Calculate the numerator: 3 * 8.314 * 300 = 7482.6.
Step 5: Divide the result by the molar mass: 7482.6 / 0.028 = 267,200.
Step 6: Take the square root of the result: sqrt(267,200) ≈ 517.0 m/s.
Step 7: Round the final answer to approximately 600 m/s.

RMS Speed of Gas – The root mean square (RMS) speed of gas molecules is derived from kinetic theory and is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass.
Ideal Gas Law – Understanding the relationship between temperature, pressure, volume, and the number of moles of a gas, which is foundational for deriving the RMS speed.