# Why are ions in water not paired?

This question is about ions in water, both in reality and as handled by MD (explicit solvent) and QM methods (eg AIMD). Basically the question is this: why are ions not always paired?

For a back of the envelope calculation take K+ with radius 0.14nm and Cl- with radius 0.18nm or so. The electrostatic energy to separate the ion pair to infinity is 138/(0.14+0.18) = 430kJ/mol. Water (eg TIP3P model) has diameter around 0.3nm and partial charges around -0.8 on oxygen and +0.4 on hydrogen; the energy to separate a water-water pair is 20-30kJ/mol (lower in vacuum, higher if surrounded by water). If we think of inserting a water between an ion pair as breaking two water-water pairs (+50kJ/mol), separating the ions by the diameter of a water (+200kJ/mol or so) and adding two favorable ion-water interactions - I’m really having a hard time seeing how the ion-water interactions would add up to more than the energy needed to separate the ions. And that’s just for adding one water directly in between; separating the ions all the way (until they’re fully hydrated and almost fully screened so they can float around independently) would be even less favorable.

Can anyone explain intuitively what drives the separation of ion pairs? (hydration by multiple waters, overpolarization of the waters, small diameter of the hydrogen atoms allowing them to get closer to negative ion, etc). Is there a simple MD model that would show how that works?

Have there been any studies (either MD or QM) that specifically compare the potential energy (or free energy) of an ion pair in water vs two separate ions in water?

There actually is ion pairing in aqueous solutions, but the concentration of paired ions is usually much lower than fully dissociated ions. You should also take into account that typical concentrations of dissolved salt is much lower than the concentration of bulk water (55.5 M). The water molecules tend to also form tight hydration shells around the ions which act to screen the ionic charge. In some cases, water interacts chemically with the ions, which further stabilizes the ion in solution by forming a “complex ion”, which is chemically distinct from a bare ion.

You already talked about screening effects, but it’s pretty important for stabilizing concentrated salt solutions. The screening effect is captured by the dielectric constant (~78 for bulk water) in the coulomb potential. The dielectric constant is usually lower around ions due to dielectric saturation (where the waters are rigidly oriented around the ion because of the electric field), but larger in bulk water where waters are randomly oriented. The dielectric screening weakens the effective long range interaction of ions, so neighboring ions can’t really “feel” each other as much as if they were at the same distance in vacuum. Hence, the potential energy of ions embedded in a dielectric medium is lower compared to the same arrangement in vacuum.

And finally, there is a large entropic driving force to homogeneously disperse ions into the solution. You can do a back of the envelope calculation treating this as an ideal mixture (obviously it’s far from ideal). This is probably the most important effect for stabilizing the solution. If you read up on this, you’ll see for example that the concentration where salts precipitate are highly temperature-dependent, and that the temperature dependence is related to the entropy of solution.

It's the entropy – suggested reading, ET Jaynes: Information theory and statistical mechanics.

For the same reason, water vapour exists already at room temperatur (~1 mol/m³, TU Wien: Vapor Pressure Calculator), where the heat of vaporization of 44 kJ/mol (Moore et al.: ChemPRIME) is ~18RT.