The coordination number of the Eu III ion in the complex [Eu NO3 3 H2O 9] is 9. This is because there are 9 ligands 6 water molecules and 3 nitrate ions surrounding the central europium ion, each forming a coordinate covalent bond with it.The coordination number of lanthanide ions in coordination complexes is determined by several factors:1. Size of the lanthanide ion: Lanthanide ions have relatively large ionic radii, which allows them to accommodate a higher number of ligands around them. As you move across the lanthanide series from La III to Lu III , the ionic radii decrease due to the lanthanide contraction, which may affect the coordination number.2. Charge of the lanthanide ion: Lanthanide ions typically have a +3 charge, which creates a strong electrostatic attraction between the positively charged metal ion and the negatively charged ligands. This strong attraction allows for a higher coordination number.3. Nature of the ligands: The size, charge, and shape of the ligands play a crucial role in determining the coordination number. Small, negatively charged ligands like water and nitrate can easily fit around the lanthanide ion, leading to a higher coordination number. Bulky or neutral ligands may result in a lower coordination number.4. Steric factors: The spatial arrangement of the ligands around the lanthanide ion can also influence the coordination number. If the ligands are too large or have a specific geometry that prevents them from fitting around the metal ion, the coordination number may be lower.In summary, the coordination number of lanthanide ions in coordination complexes is influenced by the size and charge of the lanthanide ion, the nature of the ligands, and steric factors. In the case of [Eu NO3 3 H2O 9], the coordination number is 9 due to the presence of 9 ligands 6 water molecules and 3 nitrate ions surrounding the central Eu III ion.