Question

Which one of the following forms, with an excess of \(\mathrm{CN}^{-}\), a complex having coordination number two? (a) \(\mathrm{Ni}^{2+}\) (b) \(\mathrm{Cu}^{+}\) (c) \(\mathrm{Ag}^{+}\) (d) \(\mathrm{Fe}^{2+}\)

Short answer

Ag^{+} forms a complex with coordination number two, specifically \([Ag(CN)_2]^{-}\).

Step-by-step solution

Understand the Coordination Number

The coordination number is the number of ligand atoms that are bonded to the central metal ion in a coordination complex. In this problem, we're looking for a complex with a coordination number of two.

Consider the Influence of Geometry

Coordination number two often leads to a linear geometry. Therefore, we're identifying which metal ion can form a linear complex with cyanide ions, \(cm{-}\).

Examine Metal Ion Tendencies

Analyze the tendency for each metal ion to form a two-coordinated complex with \(cm{-}\). Generally, \(cm{-}\) is a strong field ligand that prefers stable, low coordination geometries.

Evaluate 2c^{+} with 2\\)(-}\\

\(\mathrm{Ni}^{2+}\) usually forms complexes of coordination number 4 or 6, such as \([\mathrm{Ni(CN)_4)]^{2-}\).

Evaluate \({Cu^{+}}\)

\({Cu^{+}}\) typically forms complexes with coordination numbers greater than 2, as it does not commonly exist in linear geometries with only two ligands.

Evaluate \({Ag^{+}}\)

\({Ag^{+}}\) can form a stable linear complex with two cyanide ions, \({[Ag(CN)_2]^{-}}\). This complex confirms a coordination number of two.

Evaluate \({Fe^{2+}}\)

\({Fe^{2+}}\) usually forms complexes having coordination number 6 with cyanide ions, such as \({[Fe(CN)_6]^{4-}}\).

Determine the Correct Answer

The only metal ion that forms a linear complex with \(cm{-}\) and has a coordination number of two is \({Ag^{+}}\).

Key concepts

Coordination Number

In coordination chemistry, the concept of coordination number is crucial. It refers to the number of ligand atoms that are bonded directly to the central metal ion in a coordination complex. This number provides insight into the structure and geometry of the complex. A coordination number of two is relatively rare and usually results in a specific linear geometry. When examining metal ions and their possible coordination complexes, it's essential to identify which ions can bind with ligands to form simpler complexes. Knowing the coordination number helps us predict how the complex will look and how it might behave chemically. For example, in this exercise, Ag⁺ has a coordination number of two when forming a complex with two cyanide ions, CN^-.

Complex Formation

Complex formation is a process where a central metal ion binds with surrounding ligands to create a coordination complex. This process is influenced by the nature of the metal ion and the ligands involved. In our context, we're focusing on metal ions that form complexes with cyanide ions, CN^-. Each metal ion has a preference for specific coordination numbers based on factors such as electronic configuration and the nature of the ligands. Some complexes are more stable with certain geometrical arrangements and coordination numbers. Here, Ag⁺ forms a stable linear complex with cyanide ions, [Ag(CN)₂]^-, due to its tendency to prefer lower coordination numbers and stable linear geometry.

Linear Geometry

Linear geometry in coordination complexes typically arises when the coordination number is two. This shape minimizes repulsion between the two bonded atom pairs. The metal ion sits between the ligands, forming a straight line. Linear geometry is significant because it characterizes the spatial arrangement of the bonds, impacting the overall properties and stability of the complex. Certain metal ions naturally favor forming linear geometry due to their electron configurations. For example, Ag⁺, when interacted with cyano groups, prefers this arrangement, resulting in the complex [Ag(CN)₂]^-.

Ligand Field Theory

Ligand field theory describes how ligands affect the distribution of electrons in transition metal complexes. It provides insight into the strength and geometric preferences of various complexes. Strong field ligands, like CN^-, generally promote low coordination numbers and unique geometries, like linear shapes. They can alter the energy levels of d-orbitals in the metal ion, affecting the complex's magnetism and color. In this context, CN^- as a ligand forms a linear complex with Ag⁺, demonstrating its strong field behavior, favoring a coordination number of two and stabilizing the linear configuration.