# Can one predict the entropy change for aqueous phase reactions without calculation?

I have seen several sources that claim aqueous solutions always have more entropy than pure liquids or solids, however, some aqueous ions have negative standard entropy. This opens the possibility of solubility reactions with negative standard entropy change. For example, \begin{align} \ce{NaF (s) &<=> Na+ (aq) + F- (aq)}&&\Delta S^{\circ} =-6.26 \ \mathrm{J/(mol\cdot K)}\\ \ce{AlCl3 (s) &<=> Al^3+ (aq) + 3 Cl- (aq)}&&\Delta S^{\circ} =-261.5 \ \mathrm{J/(mol\cdot K)}\\ \ce{AlF3 (s) &<=> Al^3+ (aq) + 3 F- (aq)}&&\Delta S^{\circ} =-429.58 \ \mathrm{J/(mol\cdot K)} \end{align}

I have used thermodynamic data from this source.

So it seems to me that it is impossible to easily predict whether the entropy change for a reaction involving an aqueous phase is either positive or negative without calculation (unless a gas phase is involved, in which case the aqueous phase is moot)

Am I missing something, or are all the sources that claim an aqueous phase always has more entropy than a liquid phase oversimplifying the situation or just plain wrong?

I brought up the example of aluminum chloride to a chemistry instructor who then said that it is possible for molecular compounds to have negative entropy change when dissolved, but never for ionic compounds. Yet both sodium fluoride and aluminum fluoride are ionic, and seem to have a negative entropy change when dissolved.

I understand why the standard entropies are negative, and about solvation shells. What I'm asking is whether the change in entropy can be predicted at a glance instead of looking up values and calculating as I have done. Many textbooks claim all of these reactions should have a positive $\Delta S^{\circ}$ simply because "aqueous solutions have more entropy than solids or liquids." The instructor I talked to claimed that $\ce{AlCl3}$ will have negative $\Delta S^{\circ}$ because it is a molecular solid whereas $\ce{NaF}$ and $\ce{AlF3}$ should have positive $\Delta S^{\circ}$ because they are ionic solids. Are the textbooks and this instructor incorrect?

• BTW, aluminum chloride is also pretty much ionic when dissolved. Apr 11 '16 at 22:47

Some ions when dissolved in water may form a solvation shell that orders the solvent molecules in a way that the entropy decrease through this ordering outweighs the entropy increase through the ions leaving the crystal structure. Then you would have an overall decrease in entropy when dissolving the salt.

Small ions with high charge have a tendency for this.

When textbooks say (and many do) that we can predict the sign of $$\Delta _{solution} S^\circ$$, and that it is positive, they are wrong. Many salts have a negative solution entropy changes, as you already saw. The problem is that they are neglecting that water is part of the system in a solution process, and that the number of microstates for the water, and hence its entropy, can decrease when ions are dissolved in it. In pure water the molecules are constantly changing their orientation, but in an ionic solution water molecules in the hydration sphere become oriented, and so lose orientational (really rotational) entropy.

• Welcome to Chemistry SE! Take the Tour to familiarize yourself with this forum. Feb 26 at 11:58

When a source says that the entropy change is positive when a solid/liquid is dissolved in water, what they're trying to say is that the system becomes more disordered relative to the solid or liquid alone. This intuitively makes sense, on the basis that the now-dissolved ion/molecule is "freed" from the bonds that once held it in place. It can roam freely through the entire volume of the solution now, rather than when it was all clumped together as a solid or liquid.

Now, why are the calculations seemingly showing otherwise? The $\Delta S$ you have calculated above is the change in terms of hydration rather than dissolution. A negative $\Delta S_{hydration}$ is sensible because some ions do in fact impose a local order (relative to the proton) whereas others do not. However, if you want to look at the entropy of solution (which is then comparable to enthalpy of solution), you have to consider the case of infinite dilution.

Infinite dilution, by definition, is such that no more change in concentration is achieved despite adding more solvent. Assuming that the substance dissolves in the first place, at infinite dilution the individual solute molecules/ions are probably substantially far apart from each other such that they no longer interact with each other - they are totally free from each other but not the solvent. So relative to their 'bound state' of solid and liquid, dissolving the substance will then result in a $\Delta S$ that must be positive.

• Note that the reference state is not one with infinitely dilute concentration (which would result in a nonsensical value of the entropy), but rather the interactions between ions are as in an infinitely dilute solution. Mar 1 at 8:47

The order of decreasing entropy from the state with highest to lowest entropy is- gas>aqueous>liquid>solid. Hence, just know that the entropy is positive when state changes from either liquid or solid to aqueous and it is negative when there is change of state from gas to aqueous.