Multiple Choice
Calculate the root mean square speed of gaseous krypton atoms at 27 °C. Given that the molar mass of krypton is 83.8 g/mol, which of the following is the correct root mean square speed?
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7. Gases
Root Mean Square Speed
Multiple Choice
What is the root-mean-square speed of a carbon monoxide molecule at 27°C?
A
700 m/s
B
400 m/s
C
515 m/s
D
600 m/s
Verified step by step guidance1
First, understand the concept of root-mean-square speed (v_rms), which is a measure of the average speed of particles in a gas. It is derived from the kinetic theory of gases.
The formula for calculating the root-mean-square speed is: , where R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and M is the molar mass of the gas in kg/mol.
Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: .
Determine the molar mass of carbon monoxide (CO). Carbon has a molar mass of approximately 12.01 g/mol and oxygen has a molar mass of approximately 16.00 g/mol. Add these values to find the molar mass of CO: g/mol, then convert to kg/mol by dividing by 1000.
Substitute the values for R, T, and M into the root-mean-square speed formula and solve for v_rms. Ensure all units are consistent, particularly converting the molar mass to kg/mol.
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