Multiple Choice
Calculate the root mean square velocity in m/s of dinitrogen pentoxide gas at 99.5 °C, given that the molar mass of dinitrogen pentoxide is 108 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 252 K?
A
SO3
B
CO
C
CO2
Verified step by step guidance1
To determine which gas has the highest root-mean-square (rms) speed, we use the formula for rms speed: \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas in kg/mol.
First, convert the molar masses of the gases from grams per mole to kilograms per mole. For example, the molar mass of CO is approximately 28.01 g/mol, which is 0.02801 kg/mol.
Next, substitute the values for \( R \) (8.314 J/(mol·K)), \( T \) (252 K), and the molar mass \( M \) for each gas into the rms speed formula.
Calculate the rms speed for each gas: CO, CO2, and SO3. Remember that a lower molar mass will result in a higher rms speed, as the molar mass is in the denominator of the formula.
Compare the calculated rms speeds for each gas. The gas with the highest rms speed will be the one with the smallest molar mass, which in this case is CO.
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