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In chemistry, bond order refers to the number of chemical bonds between a pair of atoms. It's an important concept in molecular orbital theory, which is used to understand how electrons are distributed in a molecule. The bond order can tell us how strong or stable a bond might be.
To find the bond order of \({\mathrm{CN}}^{-}\), you use the formula: \[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \] In the case of \({\mathrm{CN}}^{-}\), there are 10 bonding electrons and 4 antibonding electrons. This brings us to:

• 10 bonding electrons - 4 antibonding electrons = 6
• \[\frac{6}{2} = 3\] This means that the bond order for \({\mathrm{CN}}^{-}\) is 3, indicating a strong triple bond. A higher bond order generally means a stronger and shorter bond, making the molecule more stable.

Electron configuration is like a map that shows where electrons reside in an atom or molecule. It's crucial to understand electron configurations to predict molecular behavior, such as bond formation and chemical reactivity.
For \({\mathrm{CN}}^{-}\), we first calculate the total number of electrons. \({\mathrm{CN}}^{-}\) is made up of a carbon atom and a nitrogen atom, with a negative charge adding an extra electron:

• Carbon: 6 electrons
• Nitrogen: 7 electrons
• Extra electron due to negative charge: 1 electron
• Total: 14 electrons

Using molecular orbital theory, the electron configuration of \({\mathrm{CN}}^{-}\) is:

• \(\sigma_{1s}^{2}\)
• \(\sigma_{1s}^{*2}\)
• \(\sigma_{2s}^{2}\)
• \(\sigma_{2s}^{*2}\)
• \(\pi_{2p_x}^{2}\)
• \(\pi_{2p_y}^{2}\)
• \(\sigma_{2p_z}^{2}\)
• \(\pi_{2p_x}^{*0}\)

Each of these stands for a molecular orbital where the electrons are arranged. The \(\sigma\) orbitals are in line with the internuclear axis, while the \(\pi\) orbitals lie above and below this axis.

Determining the magnetic characteristics of a molecule is crucial for understanding its behavior in a magnetic field. The molecule can be either diamagnetic or paramagnetic based on electron configuration.
- **Diamagnetic molecules** have all paired electrons and do not get attracted to magnetic fields.- **Paramagnetic molecules** contain unpaired electrons, which causes them to be attracted to magnetic fields.When looking at \({\mathrm{CN}}^{-}\), its electron configuration reveals all electrons are paired. This indicates that \({\mathrm{CN}}^{-}\) is **diamagnetic**.Check the orbitals for paired and unpaired electrons:

• \(\sigma_{1s}^{2}\) – both electrons are paired
• \(\sigma_{1s}^{*2}\) – both electrons are paired
• \(\sigma_{2s}^{2}\) – both electrons are paired
• \(\sigma_{2s}^{*2}\) – both electrons are paired
• \(\pi_{2p_x}^{2}\) – both electrons are paired
• \(\pi_{2p_y}^{2}\) – both electrons are paired
• \(\sigma_{2p_z}^{2}\) – both electrons are paired

Because there are no unpaired electrons, \({\mathrm{CN}}^{-}\) repels magnetic fields, showing that it is diamagnetic.