Question

Question #e1c07

Answer 1

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`

The formula for freezing point depression is

`ΔT_"f" = iK_"f"m`

For water, `K_"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_"f"` are constants, `ΔT_"f" ∝ m`.

The observed freezing point depression is only `"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 `"0.038 mol/kg"`.

The solution must be non-ideal.

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

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