At 1 atm of pressure a volume of 22 liters of N2 gas is passed in a closed system over a boat containing Hg liquid at 100°C. The flow of N2 is slow to allow the gas to become saturated with mercury. At 20°C and 1 atm, the nitrogen was found to contain 0.0647g of Hg. Calculate the vapor pressure of Hg at 100°C.
Raoult's Law (Ideal Solution):
PHg = XHgP°Hg
Ideal Gas Law:
PV = nRT
The Attempt at a Solution
My endgame here is to use Raoult's Law to calculate the partial pressure of mercury. To do that, though, I will need the mole fraction XHg and the pressure the mercury would exert if it were alone in the container P°Hg. As far as the latter goes, I suspect I can use the ideal gas law to calculate the pressure of mercury when nitrogen is not involved.
This is where I run into problems. I'm not sure how to synthesize the information given into the information I need. I could calculate a mole fraction for the system at 20°C, again via the ideal gas law, but I'm not sure how I can relate this to either P°Hg or XHg for the same system at 100°C.
Any insight anyone can provide would be incredibly helpful and greatly appreciated.