Freezing-Point depression equation question

[Zellmer, Robert]

I got the following question from a fellow student:

“I noticed that in one of the problems in the closer look of chapter 13.5 that
∆Tf was a positive number, but I thought since ∆Tf = -i*Kf*m that ∆Tf was
always a negative number. Could you help clear this up for me?”


There’s two ways to write and use the f.p. depression eqn.  I went over this
in lecture.  Which eqns to use depends on how you’re looking at things.

The book uses T_final -T_initial for all deltaT calculations.  Based on this for
the delT_f you have to include a negative sign in the eqn below,

delT_f = - i*m*Kf

Then delT_f is related to the f.p of solution and solvent in the following way:

delT_f = fp_soln – fp_solvent             (final is solution and initial is solvent)


You could use what I used in my notes in lecture and what’s in the lab
manual,

delT_f = i*m*Kf           (no negative sign)

Then you would think in the following way and use the following eqn.,

fp_soln = fp_solvent – delT_f

since the fp of the soln must be less than that of the pure solvent for a
nonvolatile solute.

Chose one way or the other to think of the delT_f eqn (w. or w/o the
negative sign) and then remember how to relate the delT_f to
the fp of the soln and fp of the solvent.


For bp elevation it doesn’t really matter.

delT_b = i*m*Kb

Using the books definition for this delT_b as T_final – T_initial
would give the following,

delT_b = bp_soln – bp_solvent > 0

If you think of it as I did above, you know the bp of the soln has
to be higher than the bp of the solvent and you can write the
following,

bp_soln = bp_solv + delT_b

Note, rearranging this eqn for delT_b gives the previous eqn.

It’s only the fp depression stuff that presents a possible problem.

Dr. Zellmer

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