Question

How do you calculating freezing point from molality?

Answer 1

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.)