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### Topic: Ideal gas eqn to caluculate no. of molecules  (Read 483 times)

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#### lolhaha

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##### Ideal gas eqn to caluculate no. of molecules
« 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.

#### Borek

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##### Re: Ideal gas eqn to caluculate no. of molecules
« Reply #1 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.
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#### lolhaha

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##### Re: Ideal gas eqn to caluculate no. of molecules
« Reply #2 on: March 30, 2020, 01:35:02 PM »
Thanks Borek

#### mjc123

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##### Re: Ideal gas eqn to caluculate no. of molecules
« Reply #3 on: March 30, 2020, 06:25:05 PM »
The value they give for mean kinetic energy is actually kT, not 3/2 kT.

#### Enthalpy

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##### Re: Ideal gas eqn to caluculate no. of molecules
« Reply #4 on: March 31, 2020, 04:50:16 AM »
A pressure equalling an energy?

#### Borek

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##### Re: Ideal gas eqn to caluculate no. of molecules
« Reply #5 on: March 31, 2020, 06:27:18 AM »
A pressure equalling an energy?

Actually PV.
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#### MNIO

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##### Re: Ideal gas eqn to caluculate no. of molecules
« Reply #6 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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