Multiple Choice
Which of the following gases has the highest root-mean-square speed at 252 K?
7. Gases
Root Mean Square Speed
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Which of the following gases has the highest root mean square speed at 400 K?
A
Nitrogen (N2)
B
Carbon Dioxide (CO2)
C
Helium (He)
D
Oxygen (O2)
Verified step by step guidance1
Understand that the root mean square speed (v_rms) of a gas 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 in kg/mol.
Recognize that the root mean square speed is inversely proportional to the square root of the molar mass of the gas. This means that lighter gases will have higher root mean square speeds at the same temperature.
Convert the molar masses of the gases from g/mol to kg/mol: Nitrogen (N2) is approximately 28.02 g/mol, Carbon Dioxide (CO2) is approximately 44.01 g/mol, Helium (He) is approximately 4.00 g/mol, and Oxygen (O2) is approximately 32.00 g/mol.
Compare the molar masses: Helium has the smallest molar mass, which means it will have the highest root mean square speed at the same temperature.
Conclude that Helium (He), having the lowest molar mass, will have the highest root mean square speed at 400 K among the given gases.
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