The number of water molecules not coordinated to copper ion directly in CuSO$$_4$$ . 5H$$_2$$O, is:

We need to find the number of water molecules NOT directly coordinated to the copper ion in $$CuSO_4 \cdot 5H_2O$$.

The crystal structure of copper(II) sulfate pentahydrate ($$CuSO_4 \cdot 5H_2O$$) has been well established by X-ray crystallography.

In this compound, the $$Cu^{2+}$$ ion has a coordination number of 6, forming an octahedral geometry.

The coordination sphere of $$Cu^{2+}$$ consists of:

- Four water molecules ($$H_2O$$) coordinated directly to $$Cu^{2+}$$, occupying the equatorial positions.

- Two oxygen atoms from two different sulfate ($$SO_4^{2-}$$) ions, occupying the axial positions.

This gives the structural formula: $$[Cu(H_2O)_4]SO_4 \cdot H_2O$$.

Out of the 5 water molecules in the formula:

- 4 water molecules are directly coordinated to $$Cu^{2+}$$ (in the inner coordination sphere).

- 1 water molecule is NOT directly coordinated to $$Cu^{2+}$$. This fifth water molecule is held in the crystal lattice through hydrogen bonds — it forms hydrogen bonds with the coordinated water molecules and the sulfate ion.

Therefore, the number of water molecules not coordinated to the copper ion directly is $$1$$.

The correct answer is Option C: 1.