Question #e1c07

1 Answer
Feb 29, 2016

Answer:

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.