Question

In a complex ion, a central \(\mathrm{Cr}^{3+}\) ion is bonded to two ammonia molecules, three water molecules, and a hydroxide ion. (a) Give the formula and charge of the complex ion. (b) Identify a single counter ion that could be used with the complex ion to form an uncharged compound.

Short answer

Complex ion formula: \([\text{Cr}(\text{NH}_3)_2(\text{H}_2\text{O})_3(\text{OH})]^2+\); counter ion: \(\text{SO}_4^{2-}\).

Step-by-step solution

Identify the components

Identify the central metal ion and its ligands. The center is a chromium ion: \(\text{Cr}^{3+}\). It is bonded to two ammonia molecules (\(\text{NH}_3\)), three water molecules (\(\text{H}_2\text{O}\)), and one hydroxide ion (\(\text{OH}^-\)).

Assign charges to the ligands

Determine the charge of each ligand in the complex. \(\text{NH}_3\) and \(\text{H}_2\text{O}\) are neutral ligands with a charge of 0. The \(\text{OH}^-\) ligand has a charge of -1.

Determine the total charge of the complex ion

Calculate the total charge of the complex ion by combining the charges of the central ion and the ligands. The formula for the complex is \([\text{Cr}(\text{NH}_3)_2(\text{H}_2\text{O})_3(\text{OH})]\), with charges being \(+3 -1 = +2\). Thus, the complex ion has a charge of \(+2\).

Find a suitable counter ion

Identify a counter ion that will balance the charge of the complex to form a neutral compound. Since the complex ion has a charge of \(+2\), we need an anion with a charge of \(-2\). An example of such an ion is \(\text{SO}_4^{2-}\), the sulfate ion.

Key concepts

Complex Ion Formation

In coordination chemistry, a complex ion forms when a central metal ion binds with surrounding molecules or ions, called ligands. These ions or molecules donate electron pairs to the central metal ion, creating a stable structure known as a coordination complex. In our example, the chromium ion (\(\text{Cr}^{3+}\)) serves as the metal center. It is surrounded by and bonded to ligands like ammonia (\(\text{NH}_3\)), water (\(\text{H}_2\text{O}\)), and hydroxide (\(\text{OH}^-\)). This coordination around the central metal ion forms the complex ion:

• The central metal ion provides coordination sites for ligands to bond.
• Bonds between the metal ion and ligands can be partially ionic or covalent, reflecting shared electron pairs.
• The formation of the complex ion is driven by the stabilization provided by electron pairing and coordination bonds.

The charge of a complex ion is calculated by summing the charges of the central ion and each ligand. Here, the chromium ion has a +3 charge, while the ligands are mostly neutral except for the hydroxide ion, which has a -1 charge. Therefore, the overall charge of the complex ion in this example is +2.

Ligands in Coordination Compounds

Ligands are the molecules or ions that surround and bind to the central metal ion in a coordination compound. They play a crucial role in determining the properties of the complex ion. In our case, the chromium ion \(\text{Cr}^{3+}\) is bound by the following ligands:

• Ammonia (\(\text{NH}_3\)): A neutral ligand that binds to the metal ion via its lone pair of electrons. Despite its neutrality, it significantly contributes to the stabilization of the complex through coordination bonding.


• Water (\(\text{H}_2\text{O}\)): Another neutral ligand, water also acts as a donor of electron pairs through the oxygen atom. It is commonly found in coordination complexes.


• Hydroxide (\(\text{OH}^-\)): A negatively charged ligand. The presence of a charge significantly influences the overall charge of the complex ion, contributing to its specific coordination chemistry.

Different types of ligands can have differing effects on the properties and stability of the coordination complex, such as electron donation strength, which can lead to color changes or variations in the complex's chemistry and reactivity.

Counter Ions

Counter ions are ions that balance the charge of the complex ion to create a neutral compound. They are not directly bonded to the central metal ion but are critical for maintaining charge balance in the entire compound. In the case of our coordination complex, which possesses a charge of +2, the role of a counter ion is to neutralize this charge. This allows the compound to be balanced and often precipitates if appropriate:

• Counter ions might be negatively charged ions (anions) that are found in the vicinity of the complex ion.


• The key function of these ions is to make sure that the overall charge of the entire coordination complex is zero.


• An example of a suitable counter ion for a complex ion with a charge of +2 is the sulfate ion (\(\text{SO}_4^{2-}\)), which has a charge of -2.

Once paired with \(\text{SO}_4^{2-}\), the resulting compound becomes electrically neutral and could then potentially exist as a solid salt, assuming other precipitation conditions are met.