Q11.36 P - Chemistry: Molecular Nature Of Matter And Change

Question

Question: Use MO diagrams to place  ${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}$, ${\mathbf{C}}_{\mathbf{2}}$ , ${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}$and  in order of 

(a) Increasing bond energy; 

(b) Increasing bond length.        

Step-by-Step Solution

Answer

Electrons in bonding orbitals stabilize they are between the nuclei. 

1. Increasing bond energy: ${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{>}{\mathbf{C}}_{\mathbf{2}}\mathbf{>}{{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}$
2. Increasing bond length:  ${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}\mathbf{>}{\mathbf{C}}_{\mathbf{2}}\mathbf{>}{{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}$

Step 1: Bonding

Bonding may be defined as the force of attraction between two or more atoms to form a compound. The molecule can have the same atom and a different atom.

 

Bond energy is the energy that is released or required during the formation of a bond.

 

The bond length is the length between the two atoms in a molecule, which can be the same or different atoms, showing the force of attraction to form a bond.

Step 2: Stability

Bond order of the following molecule:

$$\begin{gathered} \mathbf{BondOrderof}{{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\mathbf{\left(}\mathbf{ElectroninBMO}\mathbf{\right)}\mathbf{-}\mathbf{\left(}\mathbf{ElectroninABMO}\mathbf{\right)}\right] \\ \mathbf{BondOrder}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\mathbf{(}\mathbf{7}\mathbf{-}\mathbf{2}\mathbf{)}\right] \\ \mathbf{BondOrder}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{5} \end{gathered}$$

$$\begin{gathered} \mathbf{BondOrderofC}\mathbf{2}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\mathbf{\left(}\mathbf{ElectroninBMO}\mathbf{\right)}\mathbf{-}\mathbf{\left(}\mathbf{ElectroninABMO}\mathbf{\right)}\right] \\ \mathbf{BondOrder}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\mathbf{(}\mathbf{6}\mathbf{-}\mathbf{2}\mathbf{)}\right] \\ \mathbf{BondOrder}\mathbf{=}\mathbf{2} \end{gathered}$$

$$\begin{gathered} \mathbf{BondOrderof}{{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\mathbf{\left(}\mathbf{ElectroninBMO}\mathbf{\right)}\mathbf{-}\mathbf{\left(}\mathbf{ElectroninABMO}\mathbf{\right)}\right] \\ \mathbf{BondOrder}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left[\mathbf{(}\mathbf{5}\mathbf{-}\mathbf{2}\mathbf{)}\right] \\ \mathbf{BondOrder}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5} \end{gathered}$$

$\mathbf{BMO}\mathbf{=}\mathbf{Bonding}\mathbf{ }\mathbf{Molecular}\mathbf{ }\mathbf{Orbital}$

$\mathbf{ABMO}\mathbf{=}\mathbf{Anti}\mathbf{-}\mathbf{Bonding}\mathbf{ }\mathbf{Molecular}\mathbf{ }\mathbf{Orbital}$

The bond energy depends upon the bond order. The bond energy is proportional to the bond order, as the bond order increases, the bond energy tends to increase

${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}\mathbf{>}{\mathbf{C}}_{\mathbf{2}}\mathbf{>}{{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}$

Step 3: Bond length

The bond order is inversely proportional to the bond length. The bond length of the molecule depend upon the bond order, lower the bond order then higher is the bond length.      

 

Increasing order of the Bond length:

${{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{+}}\mathbf{>}{\mathbf{C}}_{\mathbf{2}}\mathbf{>}{{\mathbf{C}}_{\mathbf{2}}}^{\mathbf{-}}$