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For a gas with a molar mass of 32 g/mol at 273 K, what is the RMS speed?
For a gas with a molar mass of 32 g/mol at 273 K, what is the RMS speed?
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Q1
For a gas with a molar mass of 32 g/mol at 273 K, what is the RMS speed?
300 m/s
400 m/s
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600 m/s
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Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 273 / 0.032) = 300 m/s.
Questions & Step-by-step Solutions
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Q
Q: For a gas with a molar mass of 32 g/mol at 273 K, what is the RMS speed?
Solution:
Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 273 / 0.032) = 300 m/s.
Steps: 8
Show Steps
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 32 g/mol.
Step 3: Convert the molar mass from grams per mole to kilograms per mole for consistency in units: 32 g/mol = 0.032 kg/mol.
Step 4: Substitute the values into the formula: v_rms = sqrt(3 * 8.314 * 273 / 0.032).
Step 5: Calculate the numerator: 3 * 8.314 * 273 = 6816.342.
Step 6: Divide the result by the molar mass: 6816.342 / 0.032 = 213,011.31.
Step 7: Take the square root of the result: sqrt(213,011.31) = 461.36 m/s.
Step 8: Round the final answer to the nearest whole number: v_rms ≈ 461 m/s.
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