Multiple Choice
What is the root-mean-square speed of a carbon monoxide molecule at 27°C?
7. Gases
Root Mean Square Speed
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The root mean square speed of gas molecules is 283.0 m/s at a given temperature T when the recorded molar mass is 42.0 g/mol. What would be the root mean square speed for a gas with a molar mass of 152.0 g/mol?
A
103.7 m/s
B
128.2 m/s
C
148.8 m/s
D
177.2 m/s
E
205.1 m/s
Verified step by step guidance1
Understand that the root mean square speed (v_rms) of gas molecules is given by the formula: , where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass in kg/mol.
Recognize that the problem provides the root mean square speed for a gas with a molar mass of 42.0 g/mol, which needs to be converted to kg/mol by dividing by 1000, resulting in 0.042 kg/mol.
Use the given root mean square speed of 283.0 m/s to set up the equation: = 283.0 m/s. Solve for the term .
Calculate the new root mean square speed for a gas with a molar mass of 152.0 g/mol, which is 0.152 kg/mol. Use the equation: .
Compare the calculated root mean square speed with the given options to determine the correct answer.
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