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The difference between bond orders of CO...

The difference between bond orders of `CO` and `NO^(o+)` is `(x)/(2)` where x = _________ .
(Round off to the Nearest Integer)

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To solve the problem, we need to find the bond orders of carbon monoxide (CO) and the nitric oxide ion (NO^+), and then calculate the difference between these bond orders. ### Step-by-Step Solution: 1. **Determine the Total Number of Electrons:** - CO consists of Carbon (C) and Oxygen (O). - Carbon (C) has 6 electrons. - Oxygen (O) has 8 electrons. - Total electrons in CO = 6 + 8 = **14 electrons**. - NO^+ consists of Nitrogen (N) and Oxygen (O). - Nitrogen (N) has 7 electrons. - Oxygen (O) has 8 electrons. - Since NO^+ has a positive charge, it loses one electron. - Total electrons in NO^+ = 7 + 8 - 1 = **14 electrons**. 2. **Molecular Orbital Configuration:** - Both CO and NO^+ have 14 electrons, so their molecular orbital configurations will be similar. - The filling of molecular orbitals follows this order: - σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p_z)², π(2p_x)², π(2p_y)² - For both CO and NO^+, the configuration will be: - σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p_z)², π(2p_x)², π(2p_y)² - This accounts for 10 bonding electrons and 4 antibonding electrons. 3. **Calculate Bond Order:** - The bond order (BO) is calculated using the formula: \[ \text{Bond Order} = \frac{\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs}}{2} \] - For both CO and NO^+: - Number of bonding electrons = 10 - Number of antibonding electrons = 4 - Bond Order = \(\frac{10 - 4}{2} = \frac{6}{2} = 3\) 4. **Calculate the Difference in Bond Orders:** - Bond Order of CO = 3 - Bond Order of NO^+ = 3 - Difference in bond orders = \(3 - 3 = 0\) 5. **Relate the Difference to x:** - According to the problem, the difference in bond orders is given as \(\frac{x}{2}\). - We have found that the difference is 0, so: \[ 0 = \frac{x}{2} \] - Solving for x gives: \[ x = 0 \times 2 = 0 \] ### Final Answer: The value of x is **0**.
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