Multiple Choice
Calculate the root mean square velocity of carbon monoxide (CO) at 316 K. (Use R = 8.314 J/mol·K and the molar mass of CO = 28.01 g/mol)
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7. Gases
Root Mean Square Speed
Multiple Choice
The root-mean-square speed of CO at 113°C is approximately ________ m/s.
A
700 m/s
B
600 m/s
C
515 m/s
D
400 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 gas molecules. It is given by the formula: , where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Convert the given temperature from Celsius to Kelvin. The formula for conversion is: . For 113°C, calculate the temperature in Kelvin.
Identify the molar mass of carbon monoxide (CO). CO consists of one carbon atom and one oxygen atom. Use the periodic table to find the atomic masses: Carbon (C) is approximately 12.01 g/mol and Oxygen (O) is approximately 16.00 g/mol. Add these values to find the molar mass of CO.
Substitute the values for R (8.314 J/mol·K), the temperature in Kelvin, and the molar mass of CO into the root-mean-square speed formula: .
Calculate the root-mean-square speed using the substituted values. This will give you the approximate speed in meters per second (m/s).
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