Calculating Boiling Point Elevation for a Solution with Dissociating Solutes

[philistinesin]

Here's the question:

What is the boiling point of a solution that contains 1.25 mol $$CaCl_2$$ in 1400g of water?

Now, I know that I have to take into account the fact that $$CaCl_2$$ disassociates in water to form ions.

I thought the effective molality here would be 3 * 1.75 m since there are 3 ions. But, the book saids it's 2 * 1.75 m.

I'm confused as to why that is.

 

[so-crates]

Use your boiling point elevation equation $$\Delta T = imK_b$$

The reason why the molality is what it should be has to do with the 'Van't Hoff Factor', i, which is multiplied by the molality of the solution to get the 'effective' molality.

 

[chem_tr]

Molality, if I'm remembering it correctly, is defined as the mole amount of a solution whose solvent weighs 1000 grams. So the CaCl₂ solution you are dealing with is of 0.893 molal. So a recalculation and using this value may give the answer you're looking for.