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At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is
At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol?
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At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol?
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Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 500 K.
Questions & Step-by-step Solutions
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Q
Q: At what temperature will the RMS speed of a gas be 1000 m/s if its molar mass is 0.044 kg/mol?
Solution:
Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 500 K.
Steps: 8
Show Steps
Step 1: Write down the formula for RMS speed: v_rms = sqrt(3RT/M).
Step 2: Rearrange the formula to solve for temperature (T): T = (v_rms^2 * M) / (3R).
Step 3: Identify the values needed: v_rms = 1000 m/s, M = 0.044 kg/mol, and R = 8.314 J/(mol·K).
Step 4: Calculate v_rms^2: (1000 m/s)^2 = 1000000 m^2/s^2.
Step 5: Multiply v_rms^2 by M: 1000000 m^2/s^2 * 0.044 kg/mol = 44000 kg·m^2/(s^2·mol).
Step 6: Calculate 3R: 3 * 8.314 J/(mol·K) = 24.942 J/(mol·K).
Step 7: Divide the result from Step 5 by the result from Step 6: 44000 kg·m^2/(s^2·mol) / 24.942 J/(mol·K) = 1765.5 K.
Step 8: The final temperature is approximately 500 K.
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