What is the RMS speed of a gas with a molar mass of 0.032 kg/mol at 273 K?

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Question: What is the RMS speed of a gas with a molar mass of 0.032 kg/mol at 273 K?

Options:

Correct Answer: 400 m/s

Solution:

Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 273 / 0.032) which is approximately 400 m/s.

What is the RMS speed of a gas with a molar mass of 0.032 kg/mol at 273 K?

What is the RMS speed of a gas with a molar mass of 0.032 kg/mol at 273 K?

Step 1: Identify the formula for RMS speed, which is v_rms = sqrt(3RT/M).
Step 2: Identify the values needed for the formula: R (the gas constant) is 8.314 J/(mol·K), T (temperature) is 273 K, and M (molar mass) is 0.032 kg/mol.
Step 3: Substitute the values into the formula: v_rms = sqrt(3 * 8.314 * 273 / 0.032).
Step 4: Calculate the numerator: 3 * 8.314 * 273.
Step 5: Calculate the denominator: 0.032.
Step 6: Divide the result from Step 4 by the result from Step 5.
Step 7: Take the square root of the result from Step 6 to find v_rms.
Step 8: The final result is approximately 400 m/s.

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