Question

Give the formula of a complex constructed from one \(\mathrm{Cr}^{3+}\) ion, two ethylenediamine ligands, and two ammonia molecules. Is the complex neutral or is it charged? If charged, give the charge.

Short answer

The complex is \([\mathrm{Cr(en)_2(NH_3)_2}]^{3+}\) and it is positively charged with a charge of +3.

Step-by-step solution

Identify the Components

The complex is to be constructed from one \( \mathrm{Cr}^{3+} \) ion, ethylenediamine ligands, and ammonia molecules. Ethylenediamine is a bidentate ligand, which means it can attach to the central metal at two points. Ammonia acts as a monodentate ligand, meaning it coordinates through one atom.

Determine the Oxidation States

The central ion \( \mathrm{Cr}^{3+} \) has a charge of \( +3 \). Ethylenediamine (en) is a neutral ligand, so it does not carry any charge. Ammonia (NH₃) is also a neutral ligand.

Count the Total Charges and Formulate the Complex

The formula of the complex will be \([\mathrm{Cr(en)_2(NH_3)_2}]^{3+}\). The \( \mathrm{Cr}^{3+} \) ion provides the charge for the complex. Two ethylenediamine ligands do not add or remove any charge because they are neutral. Similarly, two ammonia molecules also do not add or remove any charge.

Evaluate the Charge of the Complex

Since all the ligands are neutral and the central ion \( \mathrm{Cr}^{3+} \) has a charge of \( +3 \), the entire complex will carry a charge of \( +3 \). Therefore, the complex is charged and its charge is \( +3 \).

Key concepts

Ethylenediamine

Ethylenediamine, often abbreviated as 'en', is a common type of ligand used in coordination chemistry. Ligands are molecules or ions that bond to a central metal atom to form a coordination complex. Ethylenediamine is particularly interesting because it is a bidentate ligand. This means it can form two bonds with the central metal atom.

Ethylenediamine includes two nitrogen atoms available for coordination. These nitrogen atoms have lone pairs of electrons that can be donated to the metal atom's empty orbitals, forming a stable chelate ring. By attaching to the metal in two places, ethylenediamine increases the stability of a coordination complex compared to ligands that only coordinate in one place (monodentate ligands).

Moreover, ethylenediamine is a neutral ligand, which implies it doesn't carry any charge. Therefore, when forming a coordination complex, it does not contribute to the overall charge of the complex. Its primary role is to stabilize the metal ion within the complex. In the example problem, because ethylenediamine is neutral, the total charge on the complex reflects only the charge from the central metal ion and any other charged ligands.

Ammonia Ligands

Ammonia (NH₃) is another essential ligand that plays a significant role in coordination complexes. Unlike ethylenediamine, ammonia is a monodentate ligand. This means that it uses only one atom to coordinate with the metal center.

In the structure of ammonia, the nitrogen atom has a lone pair of electrons. This lone pair is donated to the central metal atom's orbital to form a coordinate covalent bond. Because it only provides one pair of electrons in the bonding process, it's considered a simple, single-point attachment ligand.

Similar to ethylenediamine, ammonia is a neutral ligand. This neutrality means that, when ammonia binds to the metal center, it doesn't alter the overall charge of the complex. It merely helps stabilize the coordination sphere by forming bonds with the central metal ion without introducing additional charges.

In coordination complexes, ammonia's simplicity and neutrality make it a versatile ligand, useful in various combinations and configurations with a wide range of metal ions.

Oxidation States

The concept of oxidation states is crucial for understanding coordination complexes and the formula derivation. An oxidation state is a number that represents the total number of electrons an atom either loses, gains, or appears to have when forming a chemical bond with another atom.

In coordination chemistry, the central metal ion's oxidation state determines the overall charge of the complex. For instance, in the problem provided, the central chromium ion has an oxidation state of +3, denoted as \( \mathrm{Cr}^{3+} \). This means the chromium ion carries a positive charge of three.

Both ethylenediamine and ammonia are neutral ligands. As such, they do not contribute to the charge of the overall complex. Neutral ligands like these play a supportive role, bonding to the central metal without altering its charge.

Therefore, in the formula \([\mathrm{Cr(en)_2(NH_3)_2}]\) with the central metal ion \( \mathrm{Cr}^{3+} \), the complex will have a charge of +3, the same as the oxidation state of the chromium ion. Understanding oxidation states helps predict the chemical behavior and properties of the complex ion formed.