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Part A
Use the drawing of the MO energy diagram to predict the bond order of Li_{2}^{+}.
Express the bond order as an integer or fraction.
Part B
Use the drawing of the MO energy diagram to predict the bond order of Li_{2}?.
Express the bond order as an integer or fraction.
Part C
Which molecules are predicted to exist in the gas phase?
Check all that apply
Li_{2}? | |
Li_{2}^{+} |
The theory of molecular orbits tells us the fact that, when two molecules create molecular bonds, molecular orbitals with bonding properties and antibonding molecular orbitals are present which both contribute an extra layer of stability to the molecular bond , and the latter affecting the bond’s strength. The measure or test for the stability that is gained from forming the molecular bond is bond order. A bond that is positive indicates the reduction of energy of the bond and the molecule relative to the energies of the atoms individually while a zero bond order means there is no improvement in stability, and consequently there is no bond formed with the two molecules involved.
This problem can be solved using the MO diagram.
The difference in the number of electrons in anti-bonding molecular orals and in bonding molecular orbitals is equal to one-half of the bond order in a molecule.
The importance of bond orders is as follows:
1.Stability in molecules or ions
If the bond order of a molecule is positive, it will be stable. However, if the bond order value is negative or zero, the molecule/ion will not be stable.
2.Bond dissociation energy:
Bond order and Bond dissociation are directly proportional. Therefore, if bond order is high, then bond dissociation will be greater.
3.Bond length:
Inversely proportional is the relationship between bond length and order
The bond length will therefore be smaller if the bond order is higher.
4. Number of bonds
The number of covalent bonds within a molecule is equal to its bond order value. If bond order is 2 then there are 2 covalent bonds.
If all electrons are paired, the species will be diamagnetic. Para-magnetism needs unpaired electrons.
Part a
This is how the general molecular orbital looks like:
The line that passes through the two nuclei is the center of the sigma (σ), bonding molecular orbitals.
The sigma (σ), bonding molecular orbital
Constructive interference occurs when the parallel and p orbitals are combined with the matching positive and negative phases. This results in a bonding orbital p. The electron probability lies between the nuclei.
Bonding p orbital
The anti-bonding MO sigma (σ ^{*}) has a greater electron probability than either side of the nuclei.
The sigma (σ^{*}) antibonding molecular orbitals
The π ^{*} antibonding MO is formed when the parallel and p orbitals have opposite phases.
The orbital π ^{*} antibonding MO orbital
The atomic number for lithium is 3. There are 6 electrons in lithium molecular, while 5 electrons in ion.
The following Molecular orbital s are occupied in and:
Here’s how to calculate the bond order:
Part b
These Molecular orbital positions are found in and .
Here’s how to calculate the bond order:
Part c
The bond order for , and Li_{2}^{–} is 0.5. This is a positive value.
Ans:
Part a The bond order in 0.5
Part b The bond order in 0.5
Part c In gas phase, ion and are respectively.