Question

Ultra high vacuum chambers are capable of sustaining pressures as low as 10^-12 torr. How many molecules per mL are there inside this apparatus at 10^-12 torr and 300K? what is the corresponding molar volume at this temperature and pressure?

Answer 1

P = 10^-12 torr

find molecules per mL = 1/1000 L = 10^-3 L

T = 300K

then...

Apply Ideal Gas Law,

PV = nRT

where

P = absolute pressure

V = total volume of gas

n = moles of gas

T = absolute Temperature

R = ideal gas constant

PV = nRT

solve for:

n = PV/(RT)

V = 10^-3 L; R = 62.4 Ltorr/jmolK; T = 300 K

n = (10^-12)(10^-3)/(62.4 *300) = 5.34188*10^-20 mol

1 mol = 6.022*10^23 molecules

molecule = 5.34188*10^-20 mol * (6.022*10^23 molecules / mol ) = 32168.80136 mnolecules

na = 32168 molecules per liter

molar volume

v = Volume / mol = 1 mL /(5.34188*10^-20) = 1.872*10^19 mL / mol