Argthtjtr

Water is a substance characterised by properties such as high boiling point and its ability to act as a universal solvent. So why do we say that “the smallest unit of water is a water molecule”? Single molecules cannot possess such properties. Am I missing something here?

No, you aren't missing anything. Indeed, one molecule doesn't have any boiling point, neither high nor low. In fact, you've just stumbled upon one of the holes deliberately left in the early definitions. It is a very common thing in the textbooks on natural sciences: first we give the kids a simplified definition, so they don't have to read a ton of prerequisites before they start reading the book, and then they kinda already know what a molecule is, so why bother returning to it.

If we were to invent a more-or-less realistic definition of a molecule in simple terms, it would go like this: "the smallest unit of matter such that the matter retains its properties when split to these units and then allowed to settle down".

Indeed, say we have a glass of water, and we magically split it to individual molecules and then step aside. The molecules will assemble back into liquid water; probably it will be all over the place, but who cares, it is liquid water all the same, with unchanged boiling point and stuff.

Now what if we magically split a sample of some matter to smaller units, like atoms? Well, as soon as we step aside, those will assemble back to molecules, but not necessarily the same molecules. They may well be different, and so will be the physical properties of the sample.

This definition is not without its flaws either, but that's another story.

The word "water" can be used to mean different things. In everyday language we usually use "water" to mean a large collection of water molecules, which we associate with such phenomena as boiling, freezing, solubilization of salts, etc. We can conjure a different definition of "water", namely, a single water molecule, with molecular formula $ce{H2O}$. These are not the same thing. In a way, one is a subset of the other.

The solvation capabilities and boiling point of water are thermodynamic properties, usually (but not only) defined for macroscopic ("bulk") quantities of water under equilibrium conditions. The boiling point defines a temperature at which a transition occurs between the liquid and the gas states of a substance. The boiling point is a property of the ensemble, the entire collection of molecules. It is important to emphasize that when chemists discuss properties such as boiling points they are pretty strict. Such properties depend on the pressure, amongst other things. Even the geometry of the water volume can influence the experimentally observed boiling point. Chemical thermodynamic properties belong by definition to a collection of molecules under well defined equilibrium (constant) conditions. Thermodynamicists observed that properties like solubility and phase transition temperatures reach limiting values provided you have sufficient molecules, that is, above a limit dealing with bulk matter. In fact, a thermodynamic limit can be defined by observing how properties change with the amount of a substance.

It doesn't make much sense to attribute a bulk property such as a boiling point to a single water molecule, but you can say that a single molecule of water has intrinsic molecular properties that lead reproducibly, when the molecule aggregates with others of its kind, to specific macroscopic properties.

On a historical note, properties such as the boiling point were defined quantitatively as the foundations of thermodynamics were layed down and a formal molecular theory of matter began to be developed, the latter involving amongst other things statement of Avogadro's hypothesis and, later, advances in spectroscopy.

the smallest unit of water is a water molecule

To say that a molecule is the smallest unit of a substance that shares its properties is not a good definition, and has the same problems as defining an atom as the smallest unit that has all the properties of a given element.

For the definition of an atom, you can salvage that definition by specifying exactly what properties are retained. For example, the electronic transitions involving inner electrons will be the same for an isolate atom and for different allotropes of the element (and you can use that to identify atoms from their spectrum even if they are extraterrestrial).

Similarly, you can specify a small set of properties that a bulk sample of a pure molecular substance has in common with a single one of the molecules it contains: Composition, bond lengths and angles (with some minor variations), electronic spectra (more or less).

Of course, if your bulk sample is in the gas phase, there will be more properties that are the same, so pure water in the gas phase or water in air will share most properties with a single isolated water molecule.