Effect of two ionic solutes with different Van't Hoft factors on colligative properties?

Question

Colligative properties of a solution are affected only by the number of solute particles in the solution. To calculate the boiling point elevation of a solution you would do i * K * m = CBP where i is the Van't Hoft factor, K is the molal boiling point constant, m is the molality, and CBP is the change in boiling point. My question is what if you had two solutes with different i factors say sodium chloride and calcium chloride and put them in water to make 1 kg of solution. How would you determine the change in boiling point? Would you simply add up the molalities? Then what would be the i factor? Would you calculate the change that sodium chloride alone would make and add that to the change calcium chloride would make alone? Make as many assumptions as needed.

Answer 1

This is a very difficult and interesting question. I am not sure how to tackle this issue but here's my opinion.

First of all i=Pel/P0 where Pel is the real value of the colligative property of the electrolyte solution and P0 the one you would expect for complete dissociation.
The problem is that i is a function of concentration: it approximates a constant value when you approximate infinite dilution. So even if you had NaCl to begin with and dissolved a significant amount of the same solute i would change...

**Parenthesis:It is also a function of the degree of dissociation so if you have a weak electrolyte or formation of one with low solubility you will have even more things to consider. In the case of NaCl and CaCl2 there shouldn't be such a problem.

Considering that i changes with m even for the same solute I would go for a common "hybrid" i representing the difference of the solution compared to one that has the same number of particles when there is complete dissociation of all. Thus adding up the molalities. I think it would be:
CBPe=ihybrid*K*(mNaCl+mCaCl2) and
CBP0=K(2mNaCl+3mCaCl2)

However you can only measure experimentaly ihybrid. So if you have only values for iNacl and iCaCl2 at infinite dilution and want to calculate CBP then you don't have much of a choice:
CBP=iNaCl*Km*NaCl+iCaCl2*K*mCaCl2
Of course for this to be true you are assuming that i is not a function of m any more (good enough for extremely dilute solutions) and that the presence of one electrolyte has no effect on the other.

You should ask one of your professors who's working on this stuff.
Please e-mail the answer-I am really curious.

Answer 2

yes. right, well done. Just trying to get someone else to do your homework right?
How lazy is that...