Multiple Choice
The root-mean-square speed of CO at 113°C is approximately ________ m/s.
7. Gases
Root Mean Square Speed
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Determine which gas would have a root mean square speed of 515.59 m/s at 405 K.
A
Cl2
B
CO2
C
F2
D
NH3
E
CH4
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 (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 molar mass of each gas from g/mol to kg/mol. For example, for Cl2, the molar mass is approximately 70.9 g/mol, which is 0.0709 kg/mol.
Substitute the given temperature (T = 405 K) and the molar mass of each gas into the v_rms formula to calculate the root mean square speed for each gas.
Compare the calculated root mean square speeds to the given speed of 515.59 m/s to determine which gas matches this speed.
Identify the gas with the calculated root mean square speed closest to 515.59 m/s as the correct answer.
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