# Question e1c07

Feb 29, 2016

The freezing point depression is less than predicted because of the formation of ion pairs.

#### Explanation:

"K"_3["Fe(CN)"_6]_3 is an ionic compound.

It dissociates in water to form 4 mol of ions for each mole of compound.

"K"_3["Fe(CN)"_6]("aq") → "3K"^+("aq") + ["Fe(CN)"_6)]^"3-"("aq"); i = 4

ΔT_"f" = iK_"f"m

For water, ${K}_{\text{f" = "1.86 °C·kg·mol"^"-1}}$

The predicted freezing point depression of the solution is

ΔT_"f" = "4 × 1.86 °C·"color(red)(cancel(color(black)("kg·mol"^-1))) × 0.05 color(red)(cancel(color(black)("mol·kg"^-1))) = "0.37 °C"

Since $i$ and ${K}_{\text{f}}$ are constants, ΔT_"f" ∝ m.

The observed freezing point depression is only $\text{0.28 °C}$.

This is (0.28 color(red)(cancel(color(black)("mol/kg"))))/(0.37 color(red)(cancel(color(black)("mol/kg")))) × 100 % = 75.7 % of the theoretical value.

The effective concentration is also 75.7 % "of 0.05 mol/kg"# or $\text{0.038 mol/kg}$.

The solution must be non-ideal.

Most likely, some of the ions exist in solution as ion pairs like $\left\{\text{K"^+,["Fe(CN)"_6)]^"3-"}^"2-"("aq}\right)$.

Each ion pair behaves as if it were a single particle.