# Assume that you have a solution of an unknown solute in cyclohexane. If the solution has a freezing-point depression of 9.50Celcius, what is the molality of this solution? (The molal freezing-point constant of cyclohexane is 20.2 C/m)

##### 1 Answer

We obtain a molality dependent on the assumed van't Hoff factor of

#m ~~ 0.470# #"molal"#

We refer to the **freezing point depression** given by

#DeltaT_f = T_f - T_f^"*" = -iK_fm# ,where:

#T_f# is thefreezing pointin#""^@ "C"# of the solution, and#"*"# indicates pure solvent.#i# is thevan't Hoff factorof the solute, the effective number of dissociated particles per formula unit. For nonelectrolytes, this would be#1# , butwe have no idea what this solute is...#K_f = 20.2^@ "C/m"# is thefreezing point depression constantof cyclohexane at its normal freezing point.#m# is themolalityin#"mol solute/kg solvent"# .

The **molality expression** is therefore

#color(blue)(m) = -(DeltaT_f)/(iK_f) = -1/i (-9.50^@ "C")/(20.2^@ "C/m")#

#= color(blue)(0.470/i)# #color(blue)("mol solute/kg solvent")#

So we will have to provide a van't Hoff factor to determine the molality here.

Since this is a **fairly high molality** (high being higher than *nonelectrolyte*.

That means

Of course, had the change in temperature been low enough that