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Question: How many of the following species are stabilized by cation formation $C_2, O_2, NO, F_2, B_2, N_2$...

How many of the following species are stabilized by cation formation C2,O2,NO,F2,B2,N2C_2, O_2, NO, F_2, B_2, N_2

Answer

3

Explanation

Solution

A species is stabilized by cation formation if the bond order of its cation is greater than the bond order of the neutral molecule. This occurs when the electron is removed from an antibonding molecular orbital (MO).

The molecular orbital energy level order depends on the atomic number. For diatomic molecules of elements with atomic number Z≤7Z \le 7 (like B, C, N), there is s-p mixing, and the energy order is σ1s<σ1s∗<σ2s<σ2s∗<π2p<σ2p<π2p∗<σ2p∗\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \pi_{2p} < \sigma_{2p} < \pi_{2p}^* < \sigma_{2p}^*. For elements with Z≥8Z \ge 8 (like O, F), s-p mixing is less significant for the 2p2p orbitals, and the order is σ1s<σ1s∗<σ2s<σ2s∗<σ2p<π2p<π2p∗<σ2p∗\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \sigma_{2p} < \pi_{2p} < \pi_{2p}^* < \sigma_{2p}^*.

The bond order is calculated as BO=12(number of bonding electrons−number of antibonding electrons)BO = \frac{1}{2} (\text{number of bonding electrons} - \text{number of antibonding electrons}).

  1. C2C_2: 12 electrons. MO configuration (valence): (σ2s)2(σ2s∗)2(π2p)4(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2p})^4. BO = 12(8−4)=2\frac{1}{2}(8-4) = 2. HOMO is π2p\pi_{2p} (bonding). C2+C_2^+ (11e⁻) has BO = 12(7−4)=1.5\frac{1}{2}(7-4) = 1.5. BO(C2C_2) > BO(C2+C_2^+). Not stabilized.

  2. O2O_2: 16 electrons. MO configuration (valence): (σ2s)2(σ2s∗)2(σ2p)2(π2p)4(π2p∗)2(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p})^2 (\pi_{2p})^4 (\pi_{2p}^*)^2. BO = 12(10−6)=2\frac{1}{2}(10-6) = 2. HOMO is π2p∗\pi_{2p}^* (antibonding). O2+O_2^+ (15e⁻) has BO = 12(10−5)=2.5\frac{1}{2}(10-5) = 2.5. BO(O2+O_2^+) > BO(O2O_2). Stabilized.

  3. NONO: 15 electrons. MO configuration (valence): (σ2s)2(σ2s∗)2(σ2p)2(π2p)4(π2p∗)1(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p})^2 (\pi_{2p})^4 (\pi_{2p}^*)^1. BO = 12(10−5)=2.5\frac{1}{2}(10-5) = 2.5. HOMO is π2p∗\pi_{2p}^* (antibonding). NO+NO^+ (14e⁻) has BO = 12(10−4)=3\frac{1}{2}(10-4) = 3. BO(NO+NO^+) > BO(NONO). Stabilized.

  4. F2F_2: 18 electrons. MO configuration (valence): (σ2s)2(σ2s∗)2(σ2p)2(π2p)4(π2p∗)4(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2p})^2 (\pi_{2p})^4 (\pi_{2p}^*)^4. BO = 12(10−8)=1\frac{1}{2}(10-8) = 1. HOMO is π2p∗\pi_{2p}^* (antibonding). F2+F_2^+ (17e⁻) has BO = 12(10−7)=1.5\frac{1}{2}(10-7) = 1.5. BO(F2+F_2^+) > BO(F2F_2). Stabilized.

  5. B2B_2: 10 electrons. MO configuration (valence): (σ2s)2(σ2s∗)2(π2p)2(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2p})^2. BO = 12(6−4)=1\frac{1}{2}(6-4) = 1. HOMO is π2p\pi_{2p} (bonding). B2+B_2^+ (9e⁻) has BO = 12(5−4)=0.5\frac{1}{2}(5-4) = 0.5. BO(B2B_2) > BO(B2+B_2^+). Not stabilized.

  6. N2N_2: 14 electrons. MO configuration (valence): (σ2s)2(σ2s∗)2(π2p)4(σ2p)2(\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2p})^4 (\sigma_{2p})^2. BO = 12(10−4)=3\frac{1}{2}(10-4) = 3. HOMO is σ2p\sigma_{2p} (bonding). N2+N_2^+ (13e⁻) has BO = 12(9−4)=2.5\frac{1}{2}(9-4) = 2.5. BO(N2N_2) > BO(N2+N_2^+). Not stabilized.

The species stabilized by cation formation are O2O_2, NONO, and F2F_2. Therefore, there are 3 such species.