Question
Calculate the bond order,the molecular configuration,Number of bonding electron,and Number of anti-bonding electron following molecules
i) Carbon monoxide (CO)
ii) Nitrosonium(NO+)
i) Carbon monoxide (CO)
ii) Nitrosonium(NO+)
Answers
GPT-4o mini
To analyze the bond order, molecular configuration, number of bonding electrons, and number of anti-bonding electrons for the molecules Carbon Monoxide (CO) and Nitrosonium (NO\(^+\)), we will follow the principles of molecular orbital (MO) theory.
### i) Carbon Monoxide (CO)
1. **Molecular Configuration:**
For CO, the electronic configuration based on molecular orbital theory is:
\[
\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1 \pi^*(2p_y)^0
\]
This implies:
- 10 bonding electrons (from \(\sigma\) and \(\pi\) orbitals)
- 2 anti-bonding electrons (from \(\sigma^*\) in the 1s)
2. **Bond Order Calculation:**
\[
\text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} = \frac{(10 - 2)}{2} = 4
\]
3. **Number of Bonding Electrons:**
- 10 bonding electrons (including \(\sigma(2p_z)\) and \(\pi(2p_x), \pi(2p_y)\))
4. **Number of Anti-bonding Electrons:**
- 2 anti-bonding electrons (\(\sigma^*(1s)\))
### Summary for CO:
- **Bond Order:** 3
- **Molecular Configuration:** \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- **Number of Bonding Electrons:** 10
- **Number of Anti-Bonding Electrons:** 2
### ii) Nitrosonium (NO\(^+\))
1. **Molecular Configuration:**
For NO\(^+\) (which has one less electron than NO), the electronic configuration based on molecular orbital theory is:
\[
\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1 \pi^*(2p_y)^0
\]
This implies:
- 9 bonding electrons
- 2 anti-bonding electrons (contributing from \(\sigma^*(1s)\))
2. **Bond Order Calculation:**
\[
\text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} = \frac{(9 - 2)}{2} = 3.5
\]
3. **Number of Bonding Electrons:**
- 9 bonding electrons
4. **Number of Anti-bonding Electrons:**
- 2 anti-bonding electrons
### Summary for NO\(^+\):
- **Bond Order:** 3.5
- **Molecular Configuration:** \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- **Number of Bonding Electrons:** 9
- **Number of Anti-Bonding Electrons:** 2
### Final Results:
- **For CO:**
- Bond Order: 3
- Configuration: \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- Bonding Electrons: 10
- Anti-bonding Electrons: 2
- **For NO\(^+\):**
- Bond Order: 3.5
- Configuration: \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- Bonding Electrons: 9
- Anti-bonding Electrons: 2
### i) Carbon Monoxide (CO)
1. **Molecular Configuration:**
For CO, the electronic configuration based on molecular orbital theory is:
\[
\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1 \pi^*(2p_y)^0
\]
This implies:
- 10 bonding electrons (from \(\sigma\) and \(\pi\) orbitals)
- 2 anti-bonding electrons (from \(\sigma^*\) in the 1s)
2. **Bond Order Calculation:**
\[
\text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} = \frac{(10 - 2)}{2} = 4
\]
3. **Number of Bonding Electrons:**
- 10 bonding electrons (including \(\sigma(2p_z)\) and \(\pi(2p_x), \pi(2p_y)\))
4. **Number of Anti-bonding Electrons:**
- 2 anti-bonding electrons (\(\sigma^*(1s)\))
### Summary for CO:
- **Bond Order:** 3
- **Molecular Configuration:** \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- **Number of Bonding Electrons:** 10
- **Number of Anti-Bonding Electrons:** 2
### ii) Nitrosonium (NO\(^+\))
1. **Molecular Configuration:**
For NO\(^+\) (which has one less electron than NO), the electronic configuration based on molecular orbital theory is:
\[
\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1 \pi^*(2p_y)^0
\]
This implies:
- 9 bonding electrons
- 2 anti-bonding electrons (contributing from \(\sigma^*(1s)\))
2. **Bond Order Calculation:**
\[
\text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of anti-bonding electrons})}{2} = \frac{(9 - 2)}{2} = 3.5
\]
3. **Number of Bonding Electrons:**
- 9 bonding electrons
4. **Number of Anti-bonding Electrons:**
- 2 anti-bonding electrons
### Summary for NO\(^+\):
- **Bond Order:** 3.5
- **Molecular Configuration:** \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- **Number of Bonding Electrons:** 9
- **Number of Anti-Bonding Electrons:** 2
### Final Results:
- **For CO:**
- Bond Order: 3
- Configuration: \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- Bonding Electrons: 10
- Anti-bonding Electrons: 2
- **For NO\(^+\):**
- Bond Order: 3.5
- Configuration: \(\sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 \pi(2p_y)^2 \pi^*(2p_x)^1\)
- Bonding Electrons: 9
- Anti-bonding Electrons: 2