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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?