I have this awful problem due tomorrow; if anyone can help it would be much appreciated.
Most introductory chemistry texts provide a formula for the freezing point depression/boiling point of elevations:
delta-T(f,b)= K(f,b) * m
(m = molality)
In fact, these are derived equations for dilute solutions. They are generated from the more general relationships....
ln Xsolv= delta-b/R [(1/T) - (1/Tb)]
-ln Xsolv= delta-Hf/R [(1/T) - (1/Tf)]
Please derive the latter from the former for boiling point elevation, and indicate which values are contained in the super-constant Kb. (This is a difficult derivation; you'll find some assumptions are made based on the fact that the solution is dilute.)
Two question first on just what's being asked:
1. I'm going to start with the first equation and end up with one of the next two, correct?
2. What does it mean "Indicate which values are contained in the super-constant Kb"?
Here are my thoughts so far, looking just at the variables in both equations:
I know that...
ln P2/P1= delta-Hfusion/R [(1/T2)-(1/T1)]
dT/dP= delta-Hfusion/T [V1 - V2]
Μu(i)= Μu°i + RT ln a(i)
And in dilute systems a(i) --> 1
P(i)= Xi*P°i
P(t)= XB(P°B - P°A) + P°A
I looked through my worksheets and tried to pull out anything that looked useful, but I'm not sure how to piece it all together. Any help would be much appreciated.