Correct order of bond length is

Options

A. `CO_(3)^(2-) gt CO_(2) gt CO`
B. `CO_(2) gt CO gt CO_(3)^(2-)`
C. `CO gt CO_(2) gt CO_(3)^(2-)`
D. None of these

Explanation

To determine the correct order of bond lengths for the species CO3²⁻ (carbonate ion), CO2 (carbon dioxide), and CO (carbon monoxide), we can follow these steps:

### Step 1: Understand the Relationship Between Bond Order and Bond Length
Bond length is inversely proportional to bond order. This means that as the bond order increases, the bond length decreases.

### Step 2: Calculate the Bond Order for Each Species
We will use the formula for bond order:
\[ \text{Bond Order} = \frac{\text{Total Number of Bonds}}{\text{Total Number of Resonating Structures}} \]

#### a) For CO (Carbon Monoxide)
- Total number of bonds: 3 (one triple bond)
- Total number of resonating structures: 1
- Bond Order = \( \frac{3}{1} = 3 \)

#### b) For CO2 (Carbon Dioxide)
- Total number of bonds: 4 (two double bonds)
- Total number of resonating structures: 2
- Bond Order = \( \frac{4}{2} = 2 \)

#### c) For CO3²⁻ (Carbonate Ion)
- Total number of bonds: 3 (one double bond and two single bonds)
- Total number of resonating structures: 3
- Bond Order = \( \frac{3}{3} = 1 \)

### Step 3: Summarize the Bond Orders
- CO: Bond Order = 3
- CO2: Bond Order = 2
- CO3²⁻: Bond Order = 1

### Step 4: Determine the Order of Bond Lengths
Since bond length is inversely proportional to bond order, we can now determine the order of bond lengths:
- Highest bond order (shortest bond length): CO (3)
- Next bond order: CO2 (2)
- Lowest bond order (longest bond length): CO3²⁻ (1)

### Step 5: Write the Correct Order of Bond Lengths
The correct order of bond lengths from shortest to longest is:
1. CO (shortest)
2. CO2
3. CO3²⁻ (longest)

### Final Answer
The correct order of bond length is:
**CO < CO2 < CO3²⁻**

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