Chemical Forums
Chemistry Forums for Students => High School Chemistry Forum => Topic started by: lolhaha on March 30, 2020, 08:05:11 AM

Hello. Encountered the following question:
"Calculate the number of molecules in 1cm^3 of an ideal gas at 27C and a pressure of 10mm Hg. Mean kinetic energy of a molecule at 27C is 4*10^14 erg; the density of mercury is 13.6gm/cm^3"
I tried solving this using PV = nRT (as it is applicable to ideal gases)
(10/760) atm * (1/1000)L = n * 0.0821 (L)(atm) * 300K ... [760mmHg = atmospheric pressure]
n = no. of moles ~= 5.34 * 10^(7)
no. of molecules ~= 3.22 * 10^17
HOWEVER: the question is solved using the given mean KE value and using the relation  P = 2/3 KE
The final answer given is 4.9*10^17 molecules
My question is  why is my approach wrong?
Isn't the use of the ideal gas equation correct?
Thanks a lot.

I see nothing wrong with your result.
Fact that the answer found with the approach from kinetic theory of gases gives different result means just that the data given is inconsistent.

Thanks Borek :D

The value they give for mean kinetic energy is actually kT, not 3/2 kT.

A pressure equalling an energy?

A pressure equalling an energy?
Actually PV.

from the kinetic theory for gases
3 (8.324 J/molK) 300.15K 1x10^7 erg 6x10^14 erg
KE =  x  x  x  = 
2 6.022x10^23 molecules / mol 1 1 J molecule
were did you get 4x10^14 erg?
was the 3/2 factor left off?
what was your next equation? P = 2/3 * KE ?
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