Assuming equal concentrations and complete dissociation, rank these aqueous solutions by their freezing points. nh4cl cobr3 k2so4

CoBr3 < K2SO4 < NH4 Cl

Justification:

1) The depression of the freezing point of a solution is a colligative property, which means that it depends on the number of particles of solute dissolved.

2) The formula for the depression of freezing point is:

ΔTf = i * Kf * m

Where i is the van't Hoof factor which accounts for the dissociation of the solute.

Kf is the freezing molal constant and only depends on the solvent

m is the molality (molal concentration).

3) Since, you are assuming equal concentrations and complete dissociation of the given solutes, the solute with more ions in the molecular formula will result  in the solution with higher depression of the freezing point (lower freezing point).

4) These are the dissociations of the given solutes:

a) NH4 Cl (s) --> NH4(+)(aq) + Cl(-) (aq) => 1 mol --> 2 moles

b) Co Br3 (s) --> Co(3+) (aq) + 3Br(-)(aq) => 1 mol --> 4 moles

c) K2SO4 (s) --> 2K(+) (aq) + SO4 (2-) (aq) => 1 mol --> 3 moles

5) So, the rank of solutions by their freezing points is:

CoBr3 < K2SO4 < NH4 Cl

The freezing order from the largest to the smallest is:

NH4Cl> K2SO4> COBr3

Further explanation

For electrolyte solutions:

ΔTb = Kb.m. i

ΔTf = Kf.m. i

Kb = molal boiling point increase

Kf = molal freezing point constant

m = molal solution

i = van't Hoff factor

i = 1 + (n-1) α

The formula above shows that the freezing point depends on

•molal value

•degree of ionization/dissociation

•number of ions in solution

In the statement of the matter, it is known that there are solutions which have the same concentration and are completely dissociated (α = 1)

So the value of the freezing point drop depends only on the number of ions in the solution

The more ions produced, the greater the value of the freezing point (the freezing point is smaller)

There are several solutions

•1. NH4Cl ionization:

NH4Cl ---> NH4+ + Cl-

There are 2 ions in the solution

•2. COBr3 ionization:

COBr3 ---> CO3++ 3Br-

There are 4 ions in the solution

•3. ionization K2SO4

K2SO4 ---> 2K ++ SO42-

There are 3 ions in the solution

So the order of freezing from the largest to the smallest is:

NH4Cl> K2SO4> COBr3

Learn more

The freezing point of a solution

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Keywords: freezing point,  properties, van't Hoff factor

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