Multiple Choice
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)
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7. Gases
Root Mean Square Speed
Multiple Choice
Which of the following gases has the highest root mean square speed at 400 K?
A
Helium (He)
B
Carbon dioxide (CO2)
C
Oxygen (O2)
D
Nitrogen (N2)
Verified step by step guidance1
Understand that the root mean square speed of a gas is given by the formula: \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas in kilograms per mole.
Recognize that the root mean square speed is inversely proportional to the square root of the molar mass. This means that, at a constant temperature, a gas with a lower molar mass will have a higher root mean square speed.
Convert the molar masses of the gases from grams per mole to kilograms per mole: Helium (He) is 4 g/mol, Carbon dioxide (CO2) is 44 g/mol, Oxygen (O2) is 32 g/mol, and Nitrogen (N2) is 28 g/mol. Convert these to kg/mol by dividing by 1000.
Compare the molar masses: Helium has the smallest molar mass, followed by Nitrogen, Oxygen, and Carbon dioxide.
Conclude that since Helium has the smallest molar mass, it will have the highest root mean square speed at 400 K.
