I am just reading what a double replacement reaction is and what are the examples.
So I came up with this question : what is a reaction actually?
For example when we add $\ce{Fe(NO3)3}$ and NaOH to water we see $\ce{Fe(OH)3}$ forms as a precipitate. So hay! A reaction has occurred!
But the reaction in the title doesn't form any precipitate depending on solubility rules. So does any reaction really takes place or the substances just dissociate into separate ions?
$\ce{Na2SO4}$ will dissolve and dissociate into separate ions. And there will be some protonation $\ce{H+ + SO4^{2-} -> HSO4-}$.
A reaction occurs when the starting chemicals (molecules, ions) are changed into some different molecules (ions). This involves making and breaking bonds. It can include transferring electrons from one species to another.
Just because a ppt is not formed does not mean that reaction has not occurred. In general chemists use a host of different techniques to determine the outcome of a reaction. Some of these are (in random order) measuring pH, quantitative analysis,titration, nuclear magnetic resonance (NMR), uv, visible, infra red & microwave spectroscopy, chromatography, xray scattering, mass spectrometry, and i've missed quite a few out. After all knowing what you have made, or if you have made it, is a major part of chemistry.
Your question seems more philosophical then chemical in that you are aware of what happens and why, but want to attach semantic labels to various states and process involved. This study is called semantics. In information science, ontologies concern the codifying of semantics. While arguably not classically chemistry per se, ontologies are valuable resources in science, particularly in the era of "big data" and involve a great deal of chemistry to develop and deploy correctly. However, analysis such as the following is definitely in the domain of recreational or pedagogical study, and the best answer is probably you know one when you see one.
Fortunately, to that end IUPAC are greatly concerned with matters of semantics and ontology, and the IUPAC Gold Book provides endless hours of gripping reading on such matters.
If you want to know the IUPAC gold books definition of chemical reaction, chemical species, and molecular entity (important, more fundamental concepts), then you can easily find it online, but ontologies can be confusing and not particularly enlightening, so please accept this user's "reader" on the relevant entries.
A chemical reaction is the result of the conversion of chemical species. So, to answer your question, the first thing we need to do is to work out the chemical species involved (whatever they are) and work out whether they are converted at the end of the reaction compared to the start.
A chemical species is a set of identical molecular entities. Jumping ahead of ourselves a bit, for example, some "ideal" water is a chemical species, but a single $\ce{H2O}$ molecule is a molecular entity. Of course, real water will at least have $\ce{H3O+}$ and $\ce{OH-}$ in it, and so each of those molecules is a different molecular entity, so together they make up other chemical species in water.
But we've just put the cart before the horse. We don't have a definition of molecular entity yet. The precision required, surprisingly, depends a lot on context, ie your theoretical and practical capabilities and purposes. For example, maybe singlet and triplet oxygen are important to you, in which case they are considered different molecular entities, or maybe you don't care and so the oxygen is all considered a single molecular entity. That may disappoint armchair philosophers but might constitute a ray of hope to people who need to just get the job done.
But the actual definition of molecular entity in the gold book is a bit of a damp squib: it merely lists some examples followed by "etc". The definition of chemical species comes to our rescue here, where it describes species as molecular entities which can explore the same set of molecular energy levels.
While IUPAC are quiet on what molecular energy levels are, that's actually quite uncontroversial: they are the energy levels of electrons in atoms, which may have been transformed by adjacent atoms, also known as a chemical bond.
So, putting it back together:
Atoms can associate with each other through chemical bonding to create a new set of energy levels, and these are known as molecular energy levels. Where there exist entities which indistinguishable (for the purposes envisaged), which have available to them (in the context of the experiment) various molecular energy levels then they are the molecular entities of of a chemical species. Should the inventory of such species change in an experiment, then you have a reaction.
Once more, with feeling:
A reaction is a process whereby, as far as the precision of the experiment is concerned, the variety of indistinguishable assemblies of atoms with distinct accessible molecular energy levels changes.
For the situation you asked about: the initial dissolution is a chemical reaction because various molecular bonds are broken, various intermolecular bonds of solvation are formed in the reactions with the solvent, and so on. This changes the inventory of the kinds of entities with distinct molecular energy levels. The precipitation is also the result of a reaction in solution, in that many of these changes in bonding on solvation are reversed. However, the settling action of the precipitation itself is largely a physical, not chemical, process concerning gravity, convection, etc. Should there be no precipitation, only the solvation reaction has taken place.
(Quotes in this answer are for clarity, not of external sources).
