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According to Molecular Orbital Theory,...

According to Molecular Orbital Theory,

A

`C_(2)^(2-)` is expected to be diamagnetic

B

`O_(2)^(2+)` is expected to have a longer bond length than `O_(2)`

C

`N_(2)^(+) and N_(2)^(-)` have the same bond order

D

`He_(2)^(+)` has the same energy as two isolated He atoms

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To solve the question regarding the molecular orbital theory and the properties of the species mentioned, we will follow a systematic approach. ### Step-by-Step Solution: 1. **Identify the Species and Their Electrons**: - For \( C_2^{2-} \): It has 14 electrons. - For \( O_2^{2+} \): It has 14 electrons. - For \( N_2^{-} \): It has 15 electrons. - For \( N_2^{+} \): It has 13 electrons. - For \( He_2^{+} \): It has 3 electrons. 2. **Molecular Orbital Filling**: - **For \( C_2^{2-} \)**: - Fill the molecular orbitals in the order: - \( \sigma 1s^2 \) - \( \sigma 1s^* \) - \( \sigma 2s^2 \) - \( \sigma 2s^* \) - \( \sigma 2p_z^2 \) - \( \pi 2p_x^2 = \pi 2p_y^2 \) - \( \pi 2p_x^* = \pi 2p_y^* \) - \( \sigma 2p_z^* \) - Total filling: \( 2 + 2 + 2 + 2 + 2 + 2 = 14 \) electrons. - All electrons are paired, hence \( C_2^{2-} \) is **diamagnetic**. 3. **Bond Order Calculation for \( C_2^{2-} \)**: - Bond order = \( \frac{(Number \, of \, bonding \, electrons - Number \, of \, anti-bonding \, electrons)}{2} \) - Bonding electrons = 10, Anti-bonding electrons = 4. - Bond order = \( \frac{10 - 4}{2} = 3 \). 4. **For \( O_2^{2+} \)**: - Fill the molecular orbitals similarly: - Total electrons = 14. - Bonding electrons = 10, Anti-bonding electrons = 4. - Bond order = \( \frac{10 - 4}{2} = 3 \). 5. **Bond Length Comparison**: - Bond length is inversely proportional to bond order. Since \( O_2^{2+} \) has a higher bond order than \( O_2 \), it has a shorter bond length, making the statement "O2 2+ is expected to have a longer bond length than O2" **incorrect**. 6. **For \( N_2^{-} \)** and \( N_2^{+} \)**: - \( N_2^{-} \): 15 electrons. - Bonding electrons = 10, Anti-bonding electrons = 5. - Bond order = \( \frac{10 - 5}{2} = 2.5 \). - \( N_2^{+} \): 13 electrons. - Bonding electrons = 9, Anti-bonding electrons = 4. - Bond order = \( \frac{9 - 4}{2} = 2.5 \). - Both have the same bond order, hence the statement is **correct**. 7. **For \( He_2^{+} \)**: - Total electrons = 3. - Bonding electrons = 2, Anti-bonding electrons = 1. - Bond order = \( \frac{2 - 1}{2} = 0.5 \). - Isolated He atoms have a bond order of 0, thus \( He_2^{+} \) is more stable than isolated He atoms, making the statement **incorrect**. ### Conclusion: - The correct statements based on the analysis are: - \( C_2^{2-} \) is diamagnetic. - \( N_2^{-} \) and \( N_2^{+} \) have the same bond order.
To solve the question regarding the molecular orbital theory and the properties of the species mentioned, we will follow a systematic approach. ### Step-by-Step Solution: 1. **Identify the Species and Their Electrons**: - For \( C_2^{2-} \): It has 14 electrons. - For \( O_2^{2+} \): It has 14 electrons. - For \( N_2^{-} \): It has 15 electrons. ...
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Knowledge Check

  • According to molecular arbital theory,

    A
    `C_(2)^(2+)` is expected to be diamagnetic
    B
    `O_(2)^(2+)`os expected to have a bond length than `O_(2)`
    C
    `N_(2)^(2+) and N_(2)^(-)` have the same bond order.
    D
    `He_(2)^(+)` has the same energy as two isolated He atoms.

  • According to MOT (Molecular Orbital Theory), the molecular orbitals are formed by mixing of atomic orbitals through LCAO (linear combination of atomic orbitals). The correct statement(s) about molecular orbitals is/are Statement (A) : Bonding molecular orbitals are formed by addition of wave-functions of atomic orbitals of same phase Statement (B) : Anti-bonding molecular orbitals are formed by subtraction of wave-functions of atomic orbitals of same phase Statement (C) : Non-bonding molecular orbitals do not take part in bond formation because they belong to inner shells Statement (D) : Anti-bonding molecular orbitals provide stability to molecules while bonding molecular orbitals make the molecules unstable.

    A
    Statement a, d
    B
    Statement a, b, c
    C
    Statement a, b, d
    D
    Statement a, b

  • L.C.A.O. Principle is involved in the formationof the molecular orbitals according ot molecular orbital theory. The energy of the bonding molecular orbital is less than that of thecombining atomic orbitals while that of the antibonding molecular orbitals while that of the order (B.O.)=1/2(N_(b)-N_(a)) helps in predicting (i) formation of molecules/molecular ions, bond dossociation energy, stability and bond length. Only the molecules or ions with positive B.O. can be formed. These will be diamagnetic if all molecular orbitals are dilled and paramagnetic if one of more are half filled. The atomic prbitals at the time of overlap must have the same symmetry as well. Bond arder is :

    A
    directly related to bond length
    B
    inversely related to bond length
    C
    incersely related to bond strength
    D
    never fractional.

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    L.C.A.O. Principle is involved in the formationof the molecular orbitals according ot molecular orbital theory. The energy of the bonding molecular orbital is less than that of thecombining atomic orbitals while that of the antibonding molecular orbitals while that of the order (B.O.)=1/2(N_(b)-N_(a)) helps in predicting (i) formation of molecules/molecular ions, bond dossociation energy, stability and bond length. Only the molecules or ions with positive B.O. can be formed. These will be diamagnetic if all molecular orbitals are dilled and paramagnetic if one of more are half filled. The atomic prbitals at the time of overlap must have the same symmetry as well. The bond order (B.O.) in B_(2) molecule is:

    L.C.A.O. Principle is involved in the formationof the molecular orbitals according ot molecular orbital theory. The energy of the bonding molecular orbital is less than that of thecombining atomic orbitals while that of the antibonding molecular orbitals while that of the order (B.O.)=1/2(N_(b)-N_(a)) helps in predicting (i) formation of molecules/molecular ions, bond dossociation energy, stability and bond length. Only the molecules or ions with positive B.O. can be formed. These will be diamagnetic if all molecular orbitals are dilled and paramagnetic if one of more are half filled. The atomic prbitals at the time of overlap must have the same symmetry as well. In the homonuclear molecule3 which of the following sets of M.O. orbitals are degenerate ?

    L.C.A.O. Principle is involved in the formationof the molecular orbitals according ot molecular orbital theory. The energy of the bonding molecular orbital is less than that of thecombining atomic orbitals while that of the antibonding molecular orbitals while that of the order (B.O.)=1/2(N_(b)-N_(a)) helps in predicting (i) formation of molecules/molecular ions, bond dossociation energy, stability and bond length. Only the molecules or ions with positive B.O. can be formed. These will be diamagnetic if all molecular orbitals are dilled and paramagnetic if one of more are half filled. The atomic prbitals at the time of overlap must have the same symmetry as well. Which of the followijng combinatinos is not allowed (assume z axis as the internuclear azis) ?

    L.C.A.O. Principle is involved in the formationof the molecular orbitals according ot molecular orbital theory. The energy of the bonding molecular orbital is less than that of thecombining atomic orbitals while that of the antibonding molecular orbitals while that of the order (B.O.)=1/2(N_(b)-N_(a)) helps in predicting (i) formation of molecules/molecular ions, bond dossociation energy, stability and bond length. Only the molecules or ions with positive B.O. can be formed. These will be diamagnetic if all molecular orbitals are dilled and paramagnetic if one of more are half filled. The atomic prbitals at the time of overlap must have the same symmetry as well. In the formation of N_(2)^(+) from N_(2), the electron is removed from a

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