Kinetic Theory of Gases and speed of oxygen molecules

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SUMMARY

The discussion focuses on calculating the root mean square (rms) speed of oxygen molecules in a syringe under specific conditions. The syringe has a volume of 20 ml and contains air as an ideal gas, composed of 20% oxygen (O2) and 80% nitrogen (N2). The relevant constants include Boltzmann's constant (k = 1.38×10-23 J/K) and the molar mass of oxygen (32 g/mol). The correct rms speed calculation involves using the mass of a single oxygen molecule, which is derived from the molar mass divided by Avogadro's number, leading to a final rms speed of approximately 6.13 m/s after correcting the mass calculation.

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Homework Statement



A syringe of volume 20 ml has just been used and now lies empty on the doctor's desk. The pressure in the office is 100,000 Pa. Assume that the air is an ideal gas consisting of nitrogen N2 (80%) and oxygen O2 (20%) molecules. k=1.38×10-23 J/K and the molar mass of oxygen is 32 g/mol.

The syringe must be heated to high temperatures to sterilize it. When the syringe is at its maximum temperature, the number of oxygen molecules is 6.5 x 1019 (but the pressure, volume, and percent oxygen remain the same), what is the rms speed of the oxygen molecules?

Homework Equations



Kinetic theory of Gas

KE=m(v^2)/2=3KT/2

The Attempt at a Solution

m=32/6.5e19=4.9e-22kgNot sure if this is right..
k=1.38e-23
T=445.93

v=sq rt(3(1.38e-23)(445.93)/4.9e-22)

so i got 6.13m/s but its wrong, can someone explain to me what i did wrong?
 
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figured it out, mass should of been .032Kg/6.022e23
 

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