Average Translational Kinetic Energy of 1 Molecule: Solve for N

AI Thread Summary
To find the average translational kinetic energy of one molecule of a monatomic ideal gas, the equation PV = NRT is used, where N is the number of moles. Given that 1 mole contains approximately 6.03 x 10^23 molecules, the number of moles for 1.2 x 10^23 molecules is calculated as 1.2/6.02. Using the ideal gas law, the temperature T is derived as 39,425 K, which, while mathematically correct, is not realistic for a room-temperature gas. This discrepancy highlights the importance of understanding the physical context of the calculations.
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Homework Statement


1.2 x10^23 molecules of a monatomic ideal gas occupies the volume of 0.63 m3 at
atmospheric pressure. Find the average translational kinetic energy of one molecule.


Homework Equations



PV = NRT

K = 3/2*kB*T

The Attempt at a Solution



T = PV/NR

But.. what's N(moles)?
 
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One mole of anything = 6.03*10^23 molecules of that thing. BTW, you can also use PV=nkT. That way, you can directly plug in 1.2 x10^23 into "n".
 
In this equation usually moles: here 1.2/6.02= n. The 10^23 on top and bottom cancel.
 
Ok so I get T = 39425 K :S
 
That's correct, although not realistic. 1.2*10^23 of a room-temperature gas would take up around 5 L.
 
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