The total number of coordination sites in ethylenediaminetetraacetate ($$\text{EDTA}^{4-}$$) is..................

First, we recall the basic idea of coordination sites. A coordination site (also called a donor site) on a ligand is an atom that possesses at least one lone pair of electrons and is able to donate that pair to a metal ion, thereby forming a coordinate (dative) bond. The total number of such donor atoms present in one molecule or one ion of a ligand gives us the coordination number of that ligand, also called its denticity.

Now we focus on the ligand in the question, namely ethylenediaminetetraacetate in its quadruply deprotonated form, written as $$\text{EDTA}^{4-}$$. The neutral acid before deprotonation is ethylenediaminetetraacetic acid, abbreviated $$\text{H}_4\text{Y}$$ in many texts; after losing four protons it becomes $$\text{Y}^{4-}$$, which is exactly $$\text{EDTA}^{4-}$$.

To locate every potential donor atom, we write out or imagine the full structural formula. EDTA contains:

1. Two nitrogen atoms that come from an ethylenediamine fragment, written $$-NH-CH_2-CH_2-NH-$$. Each nitrogen has a lone pair of electrons.

2. Four carboxylate groups $$(-COO^-)$$, each of which offers one oxygen atom with a lone pair suitable for donation. Remember that in a carboxylate ion, although there are two oxygens, only one oxygen from each $$-COO^-$$ group normally binds to the metal in a simple chelate structure because the two oxygens are in resonance; they effectively behave as a single donor site per carboxylate group.

We therefore list the donor atoms explicitly:

$$$\begin{aligned} \text{Donor atoms} &= \text{2 nitrogen atoms} \; + \; \text{4 oxygen atoms (one from each } -COO^- \text{ group)} \\ &= 2 + 4 \\ &= 6. \end{aligned}$$$

Each of those six atoms can donate one lone pair to the same central metal ion, wrapping the ligand around the metal in a hexadentate (six-toothed) fashion. In coordination‐chemistry terminology we therefore say “EDTA is a hexadentate ligand.” The phrase “hexadentate” literally means “having six teeth,” i.e. having six coordination sites.

So, the answer is $$6$$.