If the RMS speed of a gas is 400 m/s and its molar mass is 16 g/mol, what is the temperature of the gas?
Practice Questions
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Q1
If the RMS speed of a gas is 400 m/s and its molar mass is 16 g/mol, what is the temperature of the gas?
200 K
400 K
800 K
1600 K
Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T: T = (M * v_rms^2) / (3R). Substituting M = 0.016 kg/mol and v_rms = 400 m/s gives T = 400 K.
Questions & Step-by-step Solutions
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Q
Q: If the RMS speed of a gas is 400 m/s and its molar mass is 16 g/mol, what is the temperature of the gas?
Solution: Using the formula v_rms = sqrt((3RT)/M), we can rearrange to find T: T = (M * v_rms^2) / (3R). Substituting M = 0.016 kg/mol and v_rms = 400 m/s gives T = 400 K.
Steps: 11
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 = (M * v_rms^2) / (3R).
Step 3: Convert the molar mass from grams to kilograms: 16 g/mol = 0.016 kg/mol.
Step 4: Substitute the values into the formula: M = 0.016 kg/mol and v_rms = 400 m/s.
Step 5: Calculate v_rms^2: 400 m/s * 400 m/s = 160000 m^2/s^2.
Step 6: Substitute the values into the rearranged formula: T = (0.016 kg/mol * 160000 m^2/s^2) / (3R).
Step 7: Use the value of R (the gas constant): R = 8.314 J/(mol·K).
