A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol, what is the temperature of the gas?
Practice Questions
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Q1
A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol, what is the temperature of the gas?
250 K
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2000 K
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Substituting v_rms = 500 m/s and M = 0.02 kg/mol gives T = 500 K.
Questions & Step-by-step Solutions
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Q
Q: A gas has an RMS speed of 500 m/s. If the molar mass of the gas is 0.02 kg/mol, what is the temperature of the gas?
Solution: Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Substituting v_rms = 500 m/s and M = 0.02 kg/mol gives T = 500 K.
Steps: 10
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 = 500 m/s and M = 0.02 kg/mol.
Step 4: Use the value of the gas constant R = 8.314 J/(mol·K).
Step 5: Substitute the values into the rearranged formula: T = (500^2 * 0.02) / (3 * 8.314).
Step 6: Calculate 500^2 = 250000.
Step 7: Multiply 250000 by 0.02 to get 5000.
Step 8: Calculate 3 * 8.314 = 24.942.
Step 9: Divide 5000 by 24.942 to find T: T = 200.5 K.
Step 10: Round the temperature to the nearest whole number: T = 201 K.
