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What am I missing? I cannot reconcile the difference between what the internet says the freezing point of CaCl2 is vs the calculation, which means my calculation must be off, but I am not sure how.

Example Calculation:

  • A Solute of 1700g of CaCl2 would equate to ~15.32 Moles @ 110.98 Atomic Mass.
  • Mix in 1 Gallon of water, or 3.785 kg.
  • This represents a ~31% solution (1700/(1700+3785))
  • Molality would be 4.047 (15.32 / 3.875)
  • With a Van't Hoff of 3...
  • The Freezing Point Depression would be -22.52C (3*1.855*4.047)

I think all of that is right, but when I look at the tables online they show that a 31% CaCl2 solution would have a freezing point of ~-34C - ~-37C

These sites shows a 30% concentration to have a freezing point of ~-46.1C:

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They didn't come up with the number. They went out into the field and actually measured it. Chemistry is an experimental science, you know.

Your calculations are fine; it is just they were never supposed to work in the first place. When you calculate the freezing point depression like that, you use the linear approximation, and all approximations have their limits. You can't apply it to a concentrated solution; the error will be too great, just as you observed.

Look at them graphs by your links, they are pretty far from being linear; they are bent. (We may apply some hand-waving about molarity and molality not being the same thing, but it doesn't explain the effect away completely). Look at the left corner of the graph with a magnifying glass (related picture: Why do increasing concentrations of zinc chloride not linearly decrease the freezing point?). What would you call that section of the curve? Almost linear, shall we say? Well, that's where our approximation is almost precise.

So it goes.

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