How Many Molecules Are in 5.00 cm³ at 1 * 10^-10 mm Hg and 30.0°C?

[mawalker]

Current vacuum technology can achieve a pressure of 1 * 10^-10 mm of Hg. At this pressure, and at a temperature of 30.0 C, how many molecules are in 5.00 cm3 ?

ok so atomic number of Hg = 80

80 * 1.661 * 10^-27 yields 1.33 * 10 ^-25 which is the mass of one molecule

converting from mm to atmospheres i get 1*10^-10 mm = 1.32 * 10 ^-13 atm since 760 mm = 1 atm

T = 303
5 cm3 = 5 ml = 5 * 10 ^ -3

so using pV = nRT
(1.32*10^-13)(5*10^-3) = n(.08206)pressure constant(303)
solving for n... n = 2.6459

n = M(in grams)/M of molecule so :
2.6459 = M/80
which gives me 211.67 grams...

N (number of molecules = M/m = .21167 Kg/1.33 * 10^-25 (mass of one molecule)

which yields me 1.59 * 10^ 24 molecules... this answer is incorrect... any ideas?

 

[mawalker]

actually i think that i should be using 201 for the atomic number of mercury... this still ends up yielding 3.99 *10^24 which is still incorrect.

 

[mawalker]

actually, it yields 1.59 * 10^24...

 

[OlderDan]

Make life a bit simpler and use PV = NkT

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html

 

[physics girl phd]

I'm not sure why you are going into mass of molecules... if you use PV=nRT, n is the number of moles. You can convert directly from moles to molecules using good ole 6.02E23. According to the IDEAL GAS LAW, the same number of moles of a gas ALWAYS occupy the same volume... regardless of WHAT the gas is.

 

[dextercioby]

Incidentally, Hg (mercury) is a metal, and with metals we never speak about "molecules". In this problem it instructve to use the van der Waals state law, too and compare the 2 results.

Daniel.