# Does freezing point depression depend on the charge of the solvated ions?

Assuming an ideal solution, which of these 0.10 M solutions would have the least freezing point depression?

$\ce{HCl}$

$\ce{NaBr}$

$\ce{KNO3}$

$\ce{MgSO4}$

They all produce solutions with two ions per formula unit, but the correct answer is somehow supposed to be $\ce{MgSO_4}$. How is this? I don't think it can be due to the weak basicity of sulfate; that should in fact increase the ions present and have an even greater freezing point depression.

• Frankly I think that the problem is posed poorly. First the problem states to "assume an ideal solution," then wants an answer that requires some sort of non-ideal behavior. // I'd expect that the answer has to do with the hydrated $\ce{Mg^{2+}}$ and $\ce{SO4^{2-}}$ species attracting one another in solution. So the attracted clusters behave more like one molecule of $\ce{MgSO4}$ rather than two ions. This isn't "ideal" behavior. – MaxW Apr 21 '16 at 19:01
• @MaxW Isn't every ionic compound subject to ion-pair formation? – Yunfei Ma Apr 21 '16 at 22:28
• Yes, but $\ce{MgSO4}$ is the only compound that has a charge of 2 on the anion and cation. All the other anions and cations have a charge of 1. – MaxW Apr 22 '16 at 0:57

First let's gather the data from the CRC Handbook of Chemistry and Physics, 92nd edition (mol/L is moles per liter). The data below is reported as molarity rather than molality since the problem is posed in molarity. However in a solution as dilute as 0.1 M the difference shouldn't be large.

         wt%      mol/L      Delta-F
HCl     0       0        0.00
0.5     0.137   -0.49
1       0.275   -0.99
2       0.553   -2.08
3       0.833   -3.28
4       1.117   -4.58
5       1.403   -5.98
least squares fit Delta-f = = -3.4683*[HCL] - 0.5624*[HCL]^2
[HCL] =0.1 M, Delta-f = -0.35

wt%      mol/L      Delta-F
NaBr    0       0.00     0.00
0.5     0.049   -0.17
1       0.098   -0.34
2       0.198   -0.69
3       0.301   -1.04
4       0.405   -1.39
5       0.512   -1.76
least squares fit Delta-f = = -3.4823*[NaBr] + 0.0930*[NaBr]^2
[NaBr] =0.1 M, Delta-f = -0.35

wt%      mol/L      Delta-F
KNO3   0        0        0.00
0.5      0.05    -0.17
1        0.099   -0.33
2        0.2     -0.64
3        0.302   -0.94
4        0.405   -1.22
5        0.509   -1.50
least squares fit Delta-f = = -3.4264*[KNO3] + 0.9923*[KNO3]^2
[KNO3] =0.1 M, Delta-f = -0.33

wt%      mol/L      Delta-F
MgSO4  0        0        0.00
0.5      0.042    -0.10
1        0.084    -0.19
2        0.169    -0.36
3        0.257    -0.52
4        0.346    -0.69
5        0.437    -0.87
least squares fit Delta-f = = -2.3466*[MgSO4] + 0.9726*[MgSO4]^2
[MgSO4] =0.1 M, Delta-f = -0.22


So there is a difference. 0.1 molar $\ce{MgSO4}$ has a freezing point depression of 0.22 degrees Celsius whereas the other 0.1 molar salts are about 0.35 degrees.

As far as the "answer" goes the problem is very poorly worded. First the problem states to "assume an ideal solution," then poses the problem in such a manor that some sort of non-ideal behavior must be assumed to obtain an answer. "Ideal behavior" for electrolytes only occurs in very dilute solutions. A 0.1 molar solution is much too concentrated for ideal electrolyte behavior.

Without any "lookup" of data the only solution seems to be some hand-waving about $\ce{MgSO4}$ being the only salt with divalent ions so the effective dissociation is smaller because of forming ion-pairs in solution.