Hi Tatum!
At any time, there will be some molecules in the gas phase above a sample of liquid. The pressure of those gas molecules is the vapor pressure. Basically, if the volume of the container is large enough, all of the water will be vapor rather than liquid. We can calculate what V this mass of water as a gas would occupy if it is at the vapor pressure we are given.
So here we are talking about water in the gas phase. It would make sense for us to pull out our ideal gas law.
PV = nRT
What variables do we know? We know the vapor pressure of water. We know the temperature. We know we are looking for the volume, so that's our unknown variable. If we want to find it we need to also know the number of moles. But we can get that from the mass that they give us.
0.582 g x (mol/18.015 g) = 0.032306 mol
Great! Before we can plug this in to the ideal gas law though, we need to make sure the units are right. If we use 0.08206 L atm/mol K for the gas constant R, then our units for pressure need to be in atmospheres.
23.8 torr x (1 atm/760 torr) = 0.031316 atm
We also the temperature in kelvin.
25 C + 273 = 298 K
Now we can plug in everything we know, and get the volume.
V = nRT / P
V = ( 0.032306 mol x 0.08206 L atm/mol K x 298 K ) / 0.031316 atm
All the units cancel except for L.
I get 25.2 L.
