We’ve already discussed solution chemistry at great length, so we understand the process by
which an ionic solid can dissolve and dissociate in aqueous solution. We have also discussed the
basics regarding thermodynamics and spontaneity, so we understand the difference between
a spontaneous and nonspontaneous process. Let’s now combine these two concepts
to examine the free energy of dissolution. As we recall, in order for something like sodium
chloride to dissolve in water, the individual ions must become solvated. That is to say, the
ions must separate from one another, leaving the lattice, and become surrounded by water molecules
so as to generate ion-dipole interactions. The positively charged sodium ions will interact with
the negative end of the net dipole on a number of water molecules, and the negatively charged
chloride ions will interact with the positive end of the net dipole on a number of water molecules.
This is what prompts dissolution, because the system would be moving to a much higher energy
in breaking the ionic bonds and pulling all the ions apart. That is to say, the lattice energy
of the ionic solid is lost, and must then be accounted for by the hydration energy,
or the energy released when the ions generate all of these new interactions in solution.
We have already learned about the Gibbs free energy equation, delta G equals delta H minus
T delta S, where delta H is the change in enthalpy, and delta S is the change
in entropy. And we know that a negative value for delta G will correspond to a spontaneous process.
Of course we also know that sodium chloride dissolves spontaneously in water. Anyone can
demonstrate this for themselves in the kitchen, so this process must have a negative delta G value.
The question is whether the spontaneity is driven by enthalpic or entropic favorability, or both.
Let us therefore get quantitative. The lattice energy and hydration energy of sodium chloride
are tabulated values that we can easily look up. As it turns out,
the lattice energy is 778 kilojoules per mole. What this means is that 778 kilojoules of energy
would be required to separate every ion in one mole of sodium chloride,
such that no electrostatic interactions are being made any longer. Additionally,
the hydration energy of sodium chloride is negative 774 kilojoules per mole.
This means that 774 kilojoules of energy would be released if all of the ions in one mole of sodium
chloride were to go from totally isolated to being fully hydrated by water molecules,
making as many ion-dipole interactions as possible and bringing the system to a lower energy.
When we add these values together, we get the change in enthalpy for the dissolution of sodium
chloride in water, and perhaps a bit surprisingly, we see that the process is slightly endothermic,
at 4 kilojoules per mole. The amount of energy required to disrupt the lattice is just barely
more than the energy released upon dissolution. So this is not an enthalpically driven process.
But recalling our Gibbs free energy equation, even with a positive delta H,
if the delta S is sufficiently positive, we can still end up with a negative delta G
and a spontaneous process. And it is indeed the case that dissolution is entropically favorable,
as it involves a dispersal of matter. So the dissolution of sodium chloride in water is
an entropically driven process. In fact, the higher the temperature, the more relevant this
second term becomes, because as T delta S gets bigger, delta G becomes more negative, and this
is why most soluble ionic solids have their solubilities increase at higher temperatures.
But the key thing to understand about dissolution is that just as with any other chemical process,
there is a change in enthalpy and a change in entropy, and both must be considered when
examining the spontaneity of the process. While the dissolution of sodium chloride is slightly
endothermic, dissolution can be exothermic for many other salts, it all depends on the
lattice energy of that particular ionic solid, and whether it is exceeded by the hydration energy.
And with that we have a better understanding of the free energy of dissolution.