Textbook Question
A big-league fastball travels at about 45 m/s. At what temperature (°C) do helium atoms have this same average speed?
7. Gases
Root Mean Square Speed
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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.
A
520 m/s
B
640 m/s
C
580 m/s
D
450 m/s
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius. This is necessary because the root mean square velocity formula requires temperature in Kelvin.
Use the formula for root mean square velocity: \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.
Convert the molar mass of dinitrogen pentoxide from grams per mole to kilograms per mole by dividing by 1000, since the formula requires the molar mass in kg/mol.
Substitute the values for \( R \), \( T \), and \( M \) into the root mean square velocity formula. Ensure all units are consistent, particularly that the molar mass is in kg/mol and temperature is in Kelvin.
Calculate the square root of the result from the previous step to find the root mean square velocity in meters per second (m/s).
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