which of the following would be expected to have the lowest freezing temperature?

a. .1 M Ca(NO3)2
b. .1 M NaC2H3O2
c. .1 M CuSO4
d. .1 M HC2H3O2
e. .1 M C2H5OH

Here is what you do Mary.
delta T = Kb*i*m
Kb is the same for all.
m is the same for all.
i is the number of particles in solution. I assume the solvent is water.
Ca(NO3)2 gives 3 particles when it ionizes. One Ca ion and 2 nitrate ions to make a total of 3.
Go through the group. The one with the largest i will be the one with the largest delta T and therefore the lowest freezing point.

so it's a right? because all of the others only yeild 2 particles when they ionize

That's correct! Among the given options, Ca(NO3)2 would be expected to have the lowest freezing temperature because it yields the highest number of particles when it ionizes in water. As you mentioned, Ca(NO3)2 will dissociate into three ions: one Ca²⁺ ion and two NO₃⁻ ions, giving a total of three particles in the solution. On the other hand, the other options only yield two particles when they ionize. Therefore, Ca(NO3)2 has the largest "i" value and would result in the largest change in freezing point, indicating the lowest freezing temperature.