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How many gas molecules are there?
The best laboratory vacuum has a pressure of about 1.00x10^-18 atm, or 1.01x10^-13 Pa. How many gas molecules are there per cubic centimeter in such a vacuum at 293 K?
The formula is PV=nRT where P=1.00x10^-18 atm, R=8.31, T=293 K, but is the question asking to solve for V or n? Because the answer is 25 molecules/cm^3 and I think I should solve for V which is the Volume but what's the value of n in this case? Is it 6.02x10^23?
But how do you solve for V? Is it 1.01x10^-13 Pa?
Snoopie: If it's not 8.31, then what's R?
2 Answers
- GroverLv 79 years agoFavorite Answer
Solve for n. Use 1cm^3 (or its equivalent, depending on the units you use for R) for the V.
(That's why the units are atom/cm^3)
Once you've solved for n, multiply by 6.02E23.
Get a value for R using the units in the problem.
R = PV / nT = 1atm x 22400cm^3 / (1mole x 273K) = 82.1atm cm^3 /molek
Now solve for n
n=PV / RT = 1E-18atm x 1cm^3 / (82.1atmcm^3 / moleK x 293K) = 4.12E-23 moles.
Finally solve for number of particles:
4.12E-23moles x 6.02E23particle/mole = 25 particles in 1cm^3.
It will be very useful for you to be able to match units to variables.
P is in atm, kPa, Pa, torr, mmHg, psi and others.
V is in cm^3, L, m^3, and others
The value for R depends on the units for P and V.
- Anonymous9 years ago
Are you sure you are using the right R constant, there is also the Boltzmann constant that includes avogadro number.
