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

Title: Ideal gas eqn to caluculate no. of molecules
Post 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.

Title: Re: Ideal gas eqn to caluculate no. of molecules
Post by: Borek on March 30, 2020, 12:57:23 PM

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.

Title: Re: Ideal gas eqn to caluculate no. of molecules
Post by: lolhaha on March 30, 2020, 01:35:02 PM

Thanks Borek :D

Title: Re: Ideal gas eqn to caluculate no. of molecules
Post by: mjc123 on March 30, 2020, 06:25:05 PM

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

Title: Re: Ideal gas eqn to caluculate no. of molecules
Post by: Enthalpy on March 31, 2020, 04:50:16 AM

A pressure equalling an energy?

Title: Re: Ideal gas eqn to caluculate no. of molecules
Post by: Borek on March 31, 2020, 06:27:18 AM

Quote from: Enthalpy on March 31, 2020, 04:50:16 AM

A pressure equalling an energy?

Actually PV.

Title: Re: Ideal gas eqn to caluculate no. of molecules
Post by: MNIO on April 01, 2020, 09:38:41 PM

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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