Chemistry Lab - Molality of a Solution

Question

Hello,

 

I am finishing up my chemistry lab,  and am having trouble solving a question.  I clearly am missing something here, but I cannot figure out what it is.

 

The question reads.

 

Arrange a 1.0 molal solution of the following solutes in order of decreasing freezing points.  It also asks to indicate my reasoning.

 

a) C₂H₅OH    b) Cr₂3⁺(SO₄^2-)₃    c) K₂⁺CR₂O₇^2-  d)  Na₃⁺PO₄^3-

 

to complete this, do I need to add up the compounds?  Do I use T_f=K_f m?  Or am I just looking at the + and or - of the compounds, and if they are ionic, covalent and such?  I think I am looking into this more then I need to,  but cannot figure it out.  Hopefully someone is able to help. 

Answer 1

Since all solutes are present at the same concentration, i.e. 1.0 molal, the depression in freezing point will depend only on the van't Hoff factor (i).  The equation you present isn't exactly correct.  Instead of Tf = Kfm, it should more correctly be written as ∆T = Kmi where i = van't Hoff factor.  This is the number of particles that result from the dissociation of the solute.  So, what you have is the following:

(a) C2H5OH is covalent and does not dissociate/ionize so i = 1

(b) Cr₂(SO₄)₃ is ionic and ionizes into 2Cr³⁺ and 3SO₄^2- so  i = 5

(c) K₂Cr₂O₇ is ionic and ionizes into 2K⁺ and 1Cr₂O₇^2- so i = 3

(d) Na₃PO₄ is ionic and ionizes into 3Na⁺ and 1PO₄^3- so i = 4

So, (b) will decrease the freezing point the most and (a) will decrease it the least.  When it asks for them in order of decreasing freezing points, I assume that means from the lowest freezing point depression to the highest freezing point depression, which would be (a) < (c) < (d) < (b).  It's a little confusing to ask it this way, since a freezing point of say -1ºC is higher than a freezing point of say - 5ºC but the solute that causes the -5º freezing point has a greater effect than that which causes the -1º freezing point.