Textbook Question
You have a sample of gas at −33°C. You wish to increase the rms speed by a factor of 2. To what temperature should the gas be heated?
7. Gases
Root Mean Square Speed
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Calculate the root mean square velocity of gaseous xenon atoms at 24 °C. (Use R = 8.314 J/mol·K and the molar mass of xenon = 131.29 g/mol)
A
300 m/s
B
400 m/s
C
250 m/s
D
169 m/s
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature of 24 °C. This gives you the temperature in Kelvin, which is necessary for calculations involving the ideal gas constant.
Convert the molar mass of xenon from grams per mole to kilograms per mole. Since 1 gram is equal to 0.001 kilograms, multiply the molar mass of xenon (131.29 g/mol) by 0.001 to get the molar mass in kg/mol.
Use the formula for root mean square velocity: , where is the ideal gas constant (8.314 J/mol·K), is the temperature in Kelvin, and is the molar mass in kg/mol.
Substitute the values into the formula: , where is the temperature in Kelvin calculated in step 1.
Calculate the root mean square velocity using the substituted values. This will give you the velocity in meters per second (m/s).
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