Textbook Question
WF6 is one of the heaviest known gases. How much slower is the root-mean-square speed of WF6 than He at 300 K?
7. Gases
Root Mean Square Speed
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Calculate the root mean square speed of gaseous krypton atoms at 27 °C. Given that the molar mass of krypton is 83.8 g/mol, which of the following is the correct root mean square speed?
A
400 m/s
B
300 m/s
C
200 m/s
D
500 m/s
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius: \( T = 27 + 273.15 \).
Use the formula for root mean square speed \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant \( 8.314 \text{ J/mol·K} \), \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.
Convert the molar mass of krypton from grams per mole to kilograms per mole by dividing by 1000: \( M = \frac{83.8}{1000} \text{ kg/mol} \).
Substitute the values into the root mean square speed formula: \( v_{rms} = \sqrt{\frac{3 \times 8.314 \times T}{M}} \).
Calculate the expression inside the square root and then take the square root to find the root mean square speed.
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