Problem 120 - A Complete Resource Book in Chemistry for JEE Main

Question

For the complex \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (a) Shape is tetrahedral (b) Hybridization state of central ion is \(\mathrm{sp}^{3}\) (c) Effective atomic number of central ion is 35 (d) Number of unpaired electrons present in the central ion is 1

Step-by-Step Solution

Answer

Only statements (c) and (d) are consistent with the characteristics of the complex.

Step 1: Understanding the Complex

The given complex is \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\), where copper is the central metal ion and ammonia acts as a ligand. The structure of this complex will depend on the electronic configuration and coordination environment of the copper ion.

Step 2: Analyzing the Statements

We need to analyze each statement to determine its validity:(a) The shape of a copper(II) complex with four ligands is usually square planar, not tetrahedral, contradicting the statement.(b) Square planar complexes typically have \(dsp^2\) hybridization rather than \(sp^3\), which contradicts the statement.(c) Calculate the effective atomic number (EAN) of the central copper ion to verify statement (c).(d) Determine the electron configuration to find the number of unpaired electrons and check statement (d).

Step 3: Calculate Effective Atomic Number (EAN)

The Effective Atomic Number (EAN) is calculated using the formula: \[ \text{EAN} = Z - x + 2n \] where \(Z\) is the atomic number of Cu (29), \(x\) is the oxidation state (2 for Cu in \([\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+}\)), and \(n\) is the number of electrons donated by ligands (4 ammonia ligands each donating 2 electrons). Thus, \[ \text{EAN} = 29 - 2 + (4 \times 2) = 35 \] Statement (c) is correct.

Step 4: Determine Unpaired Electrons

The electronic configuration of \(\mathrm{Cu}^{2+}\) is \([\mathrm{Ar}]\ 3d^9\). This means in its molecular orbitals, one of the d orbitals will have an unpaired electron. Therefore, statement (d) which asserts one unpaired electron is correct.

Key Concepts

Complex Formation

In coordination chemistry, complex formation refers to the bonding of molecules or ions, known as ligands, to a central metal ion. This interaction forms a structure called a coordination complex. For instance, in the complex \( [\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+} \), copper is the central metal ion, and the ammonia molecules are ligands.
The ligands donate electron pairs to the central metal ion, forming coordinate covalent bonds. This process influences the shape and stability of the complex.

• The number of ligands attached to the metal ion is known as the coordination number.
• This particular complex involves four NH₃ ligands, giving a coordination number of four.
• The shape and electronic properties of such complexes are crucial for understanding their behavior and applications in fields like catalysis and medicinal chemistry.

Hybridization

Hybridization is a concept that helps explain the bonding and geometry of coordination complexes. It involves mixing atomic orbitals to form new hybrid orbitals suitable for pairing with ligands' electron pairs. Typically, the type of hybridization in a complex influences its shape.
For the copper complex \( [\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+} \), a common scenario for four-coordinate copper(II) complexes is square planar geometry, which would involve \( dsp^2 \) hybridization.

• In \( dsp^2 \) hybridization, one \( d \), one \( s \), and two \( p \) orbitals combine.
• This contrasts with \( sp^3 \) hybridization suggested by statement (b), which is incorrect for square planar structures.
• The choice of hybridization affects not just the molecular geometry but also the magnetic and electronic properties of the complex.

Effective Atomic Number

The effective atomic number (EAN) is a useful tool for understanding the stability and electronic configuration of coordination complexes. It represents the total number of electrons surrounding the central metal ion, both from the metal itself and from the ligands.
The formula for calculating the EAN is \( \text{EAN} = Z - x + 2n \). Here, \( Z \) is the atomic number, \( x \) is the oxidation state of the metal, and \( n \) is the number of electron pairs donated by the ligands.

• For \( [\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+} \), \( Z = 29 \) for copper.
• The oxidation state \( x = 2 \), as ammonia is neutral and the overall charge is \( +2 \).
• Each of the four ligands donates two electrons, so \( n = 4 \).
• Substituting these into the equation gives \( \text{EAN} = 29 - 2 + 8 = 35 \), confirming statement (c).

Unpaired Electrons

Unpaired electrons in a coordination complex play a significant role in its magnetic properties. Copper(II), in the complex \( [\mathrm{Cu}(\mathrm{NH}_3)_4]^{2+} \), has one unpaired electron, which contributes to its paramagnetic behavior.
To understand this, we need to look at the electronic configuration of \( \text{Cu}^{2+} \) ions. Transition metal copper normally has an electronic configuration of \([\mathrm{Ar}]3d^{10}4s^1\).

• When copper is in the \( +2 \) oxidation state, it loses two electrons: one from \( 4s \) and one from \( 3d \).
• This leaves the \( \text{Cu}^{2+} \) ion with a \( 3d^9 \) configuration.
• In this configuration, there is one electron unpaired in the \( 3d \) orbitals.
• Thus, the presence of an unpaired electron confirms statement (d), indicating paramagnetic properties.