The maximum number of hydrogen bonds that a molecule of water can have is

The correct option is 4.

To understand why a single water molecule ($H_{2}O$) can form a maximum of 4 hydrogen bonds, we need to look at its chemical structure and bonding capacity:
1. Two Hydrogen Atoms (Donors): Each water molecule has two hydrogen atoms covalently bonded to a highly electronegative oxygen atom. This polarization leaves a partial positive charge (${\delta }^{+}$) on each hydrogen atom, allowing each of them to act as a hydrogen bond donor to the lone pairs of neighboring oxygen atoms.
2. One Oxygen Atom (Acceptors): The central oxygen atom in a water molecule has two lone pairs of electrons. Each lone pair has a partial negative charge (${\delta }^{-}$) and can accept a hydrogen bond from a hydrogen atom of a neighboring water molecule.

Combining these two capabilities:
$\text{Total Hydrogen Bonds}=\text{2 (donated by hydrogens)}+\text{2 (accepted by oxygen's lone pairs)}=4$
Therefore, in a fully hydrogen-bonded network (such as in ice), each water molecule is tetrahedrally coordinated, participating in a maximum of 4 hydrogen bonds.