The correct order of decreasing `C-O` bond length of (1) `CO,(II)CO_(3)^(2-) (III)CO_(2)` is .

Options

A. `CO gt CO_(2) gt CO_(3)^(2-)`
B. `CO_(3)^(2-) gt CO_(2) gt CO`
C. `CO_(2) gt CO gt CO_(3)^(2-)`
D. `CO_(2) gt CO_(3)^(2-) gt CO`

Explanation

To determine the correct order of decreasing C-O bond length for the compounds CO (carbon monoxide), CO3^(2-) (carbonate ion), and CO2 (carbon dioxide), we need to analyze the types of bonds present in each molecule and their corresponding bond lengths.

### Step 1: Analyze the bond in Carbon Monoxide (CO)
- Carbon monoxide (CO) has a triple bond between carbon and oxygen.
- Triple bonds consist of one sigma bond and two pi bonds, which are very strong and short.
- Therefore, CO has the shortest bond length among the three compounds.

**Hint:** Remember that the more bonds between two atoms (single, double, triple), the shorter the bond length.

### Step 2: Analyze the bond in Carbon Dioxide (CO2)
- Carbon dioxide (CO2) has a double bond between carbon and each oxygen atom (C=O).
- A double bond consists of one sigma bond and one pi bond, which is longer than a triple bond but shorter than a single bond.
- Thus, CO2 has a bond length that is longer than CO but shorter than that of carbonate.

**Hint:** Compare the bond types: double bonds are longer than triple bonds but shorter than single bonds.

### Step 3: Analyze the bond in Carbonate Ion (CO3^(2-))
- The carbonate ion (CO3^(2-)) has resonance structures, where the C-O bonds are not purely single or double.
- The bonds in carbonate are considered to be equivalent to a bond order of 1.33 (due to resonance), which is longer than a double bond but shorter than a single bond.
- Therefore, the bond length in carbonate is longer than that in CO2.

**Hint:** Remember that resonance can affect bond lengths, making them longer than a pure double bond.

### Step 4: Order the bond lengths
- Based on the analysis:
1. CO (triple bond) - shortest bond length
2. CO2 (double bond) - shorter than carbonate
3. CO3^(2-) (resonance with bond order of 1.33) - longest bond length

### Conclusion
The correct order of decreasing C-O bond length is:
**CO > CO2 > CO3^(2-)**

### Final Answer
The correct order of decreasing C-O bond length is: **CO > CO2 > CO3^(2-)**.