Problem 89 - Chemistry Principles and Practice

Question

Write the molecular orbital electron configuration and determine the bond order and number of unpaired electrons for the following ions. (a) \(\mathrm{C}_{2}^{+}\) (b) \(\mathrm{N}_{2}^{-}\) (c) \(\mathrm{Be}_{2}^{-}\)

Step-by-Step Solution

Answer

C2+: Bond order = 2.5, 1 unpaired electron; N2-: Bond order = 2.5, 1 unpaired electron; Be2-: Bond order = 0.5, 1 unpaired electron.

Step 1: Write Molecular Orbital Electron Configuration for C2+

For the C atom, the electron configuration is 1s² 2s² 2p². Thus, for the C2 molecule, the general molecular orbital filling up to C2 is:\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p}^4 \sigma_{2p}^2 \] Removing one electron for C2+, the configuration becomes:\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p}^4 \sigma_{2p}^1 \]

Step 2: Determine Bond Order for C2+

Bond order is calculated using the formula: \( \text{Bond Order} = \frac{1}{2} [ \text{(number of bonding electrons)} - \text{(number of antibonding electrons)}] \).For \( C_2^+ \), calculate:\[ \text{Bond Order} = \frac{1}{2} [ (2 + 2 + 4 + 1) - (2 + 2)] = \frac{1}{2} [9 - 4] = 2.5 \]

Step 3: Identify Unpaired Electrons in C2+

Molecular orbital configuration for \( C_2^+ \) ends with \( \sigma_{2p}^1 \), which means there is 1 unpaired electron.

Step 4: Write Molecular Orbital Electron Configuration for N2-

For the N atom, the electron configuration is 1s² 2s² 2p³. Thus, for the N2 molecule, the general molecular orbital is:\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p}^4 \sigma_{2p}^2 \pi^*_{2p}^0 \] Adding one electron for \(N_2^-\), configuration becomes:\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p}^4 \sigma_{2p}^2 \pi^*_{2p}^1 \]

Step 5: Determine Bond Order for N2-

Calculate bond order for \( N_2^- \):\[ \text{Bond Order} = \frac{1}{2} [(2 + 2 + 4 + 2) - (2 + 2 + 1)] = \frac{1}{2} [10 - 5] = 2.5 \]

Step 6: Identify Unpaired Electrons in N2-

There is 1 electron in the \( \pi^*_{2p} \) orbital, leading to 1 unpaired electron.

Step 7: Write Molecular Orbital Electron Configuration for Be2-

For the Be atom, the electron configuration is 1s² 2s². Thus, for the \( Be_2 \) molecule, the general molecular orbital is:\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^0 \]Adding an electron for \(Be_2^-\), configuration becomes:\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^1 \]

Step 8: Determine Bond Order for Be2-

Calculate bond order for \( Be_2^- \):\[ \text{Bond Order} = \frac{1}{2} [(2 + 2) - (2 + 1)] = \frac{1}{2} [4 - 3] = 0.5 \]

Step 9: Identify Unpaired Electrons in Be2-

There is 1 electron in the \( \sigma^*_{2s} \) orbital, leading to 1 unpaired electron.

Key Concepts

Bond Order

When it comes to understanding molecular stability and bonding, bond order is a key concept in Molecular Orbital Theory. It indicates the strength and stability of a bond between two atoms. Bond order is calculated using the formula:\[ \text{Bond Order} = \frac{1}{2} \left( \text{Number of bonding electrons} - \text{Number of antibonding electrons} \right) \]Here's a breakdown of how bond order influences bond properties:

• A higher bond order implies a stronger, more stable bond.
• A bond order of 1 signifies a single bond.
• A bond order of 2 indicates a double bond, and so on.
• If bond order is zero or negative, the bond is unstable, and the molecule is unlikely to exist.

For example, in the case of \(C_2^+\), the calculated bond order is 2.5. This indicates strong bonding but highlights that it is less stable than a molecule like \(N_2\), which has a bond order of 3. Understanding bond order helps in predicting not just bond strength but also molecular geometry and reactivity.

Unpaired Electrons

Unpaired electrons are electrons that do not have a partner with opposite spin in a given molecular orbital. This concept is crucial for predicting magnetic properties of a molecule.In Molecular Orbital Theory, the presence of unpaired electrons affects:

• The magnetic property: Molecules with unpaired electrons are paramagnetic and attracted to magnetic fields.
• The reactivity: Unpaired electrons usually imply higher reactivity due to their tendency to pair up.

For example, \(C_2^+\) has one unpaired electron in its molecular orbital configuration, making it paramagnetic. Similarly, \(N_2^-\) and \(Be_2^-\) each have one unpaired electron, contributing to their paramagnetism as well. Identifying unpaired electrons is essential in understanding and predicting how a molecule will behave in chemical reactions and in the presence of a magnetic field.

Electron Configuration

Electron configuration in molecules represents how electrons are distributed among various orbitals. In Molecular Orbital Theory, we deal with combining atomic orbitals to form new orbitals that encompass the entire molecule.Key points about molecular electron configuration include:

• Electrons fill the lower energy orbitals first, following Aufbau principle.
• Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule: Electrons fill degenerate orbitals, one electron per orbital, before pairing up.

For instance, the electron configuration for \(C_2^+\) is \(\sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \pi_{2p}^4 \sigma_{2p}^1\), reflecting the removal of one electron from its neutral state. These configurations provide valuable insights into the chemical properties and behavior of molecules, guiding predictions on molecular bonding patterns and stability.