Calculating the Mass of a Gas Molecule Using Kinetic Theory

AI Thread Summary
To calculate the mass of a gas molecule using kinetic theory, the rms velocity formula u = √(3RT/M) is applied, where u is the rms speed, R is the gas constant, and M is the molar mass. Given an rms speed of 1631 m/s and a temperature of 320 K, the molar mass can be calculated as M = 3RT/u², resulting in a value of approximately 3 x 10^-3 kg/mol. To find the mass per molecule, the molar mass must be converted to kg/molecule by dividing by Avogadro's number (6.02 x 10^23). Alternatively, the equation u = √(3kT/m) can be used for a direct calculation of mass. The discussion emphasizes the importance of unit conversion in determining the mass of individual gas molecules.
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Homework Statement


A sample of an ideal gas is at a temperature of 320 K. The rms molecular speed at this temperature is measured as 1631 m/s. Calculate the mass of a molecule of this gas


Homework Equations



rms velocity , u = √(3RT/M )

The Attempt at a Solution



Given u = 1631 m / s
Temperature , T = 320 K
R = gas constant = 8.314 J/ mol . K
Molar mass of the gas molecule , M = 3RT / u 2
= 3 * 10^-3 Kg / mol
 
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Right. You can convert to kg/molecule now, or you can use u=sqrt(3kT/m) instead of u=sqrt(3RT/M) and get the answer directly.
 
so do i just multply by 6.02e23?
 
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