Textbook Question
You have a sample of gas at 0 C. You wish to increase therms speed by a factor of 3. To what temperature shouldthe gas be heated?
7. Gases
Root Mean Square Speed
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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)
A
450 m/s
B
500 m/s
C
515 m/s
D
483 m/s
Verified step by step guidance1
First, understand the formula for root mean square velocity (v_rms) which is given by: , where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass in kg/mol.
Convert the molar mass of carbon monoxide (CO) from grams per mole to kilograms per mole. Since 1 g = 0.001 kg, the molar mass of CO is kg/mol.
Substitute the values into the formula: R = 8.314 J/mol·K, T = 316 K, and M = 0.02801 kg/mol. The equation becomes: .
Calculate the numerator of the fraction: .
Finally, divide the result from the previous step by the molar mass in kg/mol, and take the square root of the entire expression to find the root mean square velocity.
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