[lolhaha]

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.

[Borek]

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.

[lolhaha]

Thanks Borek

[mjc123]

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

[Enthalpy]

A pressure equalling an energy?

[Borek]

A pressure equalling an energy?

Actually PV.

[MNIO]

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 ?

**********