How do you calculating freezing point from molality?

One of the colligative properties of solutions is freezing-point depression.

This phenomenon helps explain why adding salt to an icy path melts the ice, or why seawater doesn't freeze at the normal freezing point of #0# #""^"o""C"#, or why the radiator fluid in automobiles don't freeze in the winter, among other things.

The equation for freezing point depression is given by

#ulbar(|stackrel(" ")(" "DeltaT_f = imK_f" ")|)#

where

• #DeltaT_f# represents the change in freezing point of the solution

• #i# is called the van't Hoff factor, which is essentially the number of dissolved particles per unit of solute (for example, #i = 3# for calcium chloride, because there is #1# #"Ca"^(2+) + 2# #"Cl"^(-)#).

• #m# is the molality of the solution, the number of moles of solute dissolved per kilogram of solvent:

#"molality" = "mol solute"/"kg solvent"#

• #K_f# is the molal freezing-point depression constant for the solvent, which the following table lists some values for certain solvents:

(the far-right column shows the #K_f#)

Once you've calculated the change in freezing point, to find the new freezing point, you subtract the #DeltaT_f# quantity from the normal freezing point of the solvent:

#ul("new f.p." = "normal f.p." - DeltaT_f#

(I'd like to point out that depending on how you're taught, the #DeltaT_f# quantity may be negative (possibly because the constant #K_f# was negative). Just know that the magnitude of the #DeltaT_f# quantity (regardless of sign) represents by how much the freezing point is lowered.)