# What is the proof of complete ionic dissociation in water?

Is there any way to prove that ionic compounds, for instance $\ce{NaCl}$, completely dissociate into singular $\ce{Na+}$ and $\ce{Cl-}$ ions within water by hard experimental evidence?

Besides adhering to the perfect solvation model in theory, I am interested in definitive proof of monoatomic solvation in practice.

How do we know that the ionic crystal lattice isn't only partially dissolved? When the superficial reaction between water and the ionic compound takes place, could it stop at say 10-100 atom microcluster lattices ($\ce{Na/Cl/Na/Cl}$ etc), giving the appearance by standard means that it is completely dissolved?

I am only interested in experimental means of verification, not concepts taken from books.

• Osmotic pressure? – Ivan Neretin Jul 2 '18 at 21:38
• Possibly, but I am not sure if this thoroughly ensures that there aren’t still ultra small lattice clusters emulating ions to a sufficient degree. For example, what if the cluster had only 4 atoms, Na-Cl-Na-Cl? This particle is ridiculously small. How do we know that it doesn’t exist? Or rather, larger ones? – Michael S. Jul 2 '18 at 21:43
• You wanna check out if Earth isn't flat too? Salty water conducts electricity way better and it wouldn't if salt wasn't dissociated. – Mithoron Jul 2 '18 at 21:53
• It strikes me as a statistical probability that there will be one Na+ ion next to a Cl- ion without a water molecule in between for some number of femtoseconds. But real "particles" of NaCl floating around... No. Particles of NaCl could be detected by x-ray diffraction, but it is a S/N problem. One cluster of four NaCl "molecules" floating around in 1 ml of water would be undetectable. – MaxW Jul 2 '18 at 23:16
• @MichaelS. - Yes, using statistical arguments you could calculate the probability of a 4 "molecule" cluster existing. But chemical properties are about "average" behavior not some probability like winning the lottery 5 times in a row. The chemical behavior of ionic solutions isn't determined by the concentration of the ions, but rather their activity. Within experimental error the plot goes through the origin. You have to realize with $6.023\times 10^{23}$ molecules per mole the state of 3 or 4 molecules just isn't important chemically. – MaxW Jul 2 '18 at 23:31

One method is by making electrical conductivity measurements on aqueous solutions of salts. If we take four strong electrolytes:

• Sodium chloride
• Potassium chloride
• Sodium perchlorate
• Potassium perchlorate

We can measure the electrical conductivities at very low concentrations which allows us to obtain the limiting specific conductivties of the salts (extrapolation to zero concentration).

We will then find that the sum of the limiting conductivity of sodium chloride and potassium perchlorate will be the same as that of potassium chloride and sodium perchlorate.

This is because the limiting conductivity of a strong electrolyte salt is the sum of the contributions of the cations and anions. This allows us in an indirect way to show that some salts can totally dissociate when very dilute.

• I think this is a good answer, but I was wondering whether limiting conductivities imply true ionic dissociation in practice even if the measurements are the same for different species. I understand logically the sum of the parts equals the whole, I am still trying to confirm the true nature of the parts. So, far this is a good answer. I am nearly satisfied. (Upvoted) – Michael S. Jul 3 '18 at 15:12

Another method is to look at boiling point elevation (using this to study dissociation is called ebulliscopy). In theory (think ideal liquid), boiling points increase linearly with the molality of dissolved non-volatile components. Thus change in boiling point of water is equal to the ebulliscopic factor times the solution molality. This allows the estimation of a value 'i' that denotes the moles of dissociated ions vs the moles of the dissolved substance.

This would indicate the likely conclusion that NaCl does not completely dissociate with the resulting ions randomly dispersed throughout an completely disordered solution (there is probably some local structure around the ions), but it's close.

(NOTE: Alternatively, you can look at freezing point depression, which for low concentrations of solute is a linear function of molality, also.)

Taking aside modern methods on nanochemistry, many experiences can be used. The mixture will have very different properties depending on which is the final particle size, from entropy changes to conductivity changes.

You can argue in terms of conductivity just by the verification of the law of independent ionic molar conductivities. Salts must dissolve completely for the law verification.

The halfwave potential (polarography) is quite independent of the counterion.

In essence, almost anything that turns to be independent of the counter ion is a good proof (from electric methods above, to ionic chromatography, to selective electrodes etc.)

One of the simpler evidences can be the diffusion speed, which is easily modeled and measured and turns to be compatible which small particle size. Of course you can say that the models are not exact and small differences are hard to predict. Let's consider we just bounded the possible sizes to very few ions clusters. In such case you can measure (for example) frequency dependent dielectric permittivity and confirm that there are not relaxations at frequencies compatibles with molecular rotations.

By the way, thousands of good predictions are made monthly requiring such consideration (dissolution to individual ions), and do not forget nanochemistry.