Total number of covalent bonds in `C_(3)O_(2)` is x and y is the number of sp - hybridised atom. Find the sum of `x+y`?

Answer

To solve the problem regarding the compound \( C_3O_2 \), we need to determine two values: the total number of covalent bonds (denoted as \( x \)) and the number of sp-hybridized atoms (denoted as \( y \)). Finally, we will find the sum \( x + y \).

### Step 1: Determine the Structure of \( C_3O_2 \)

1. **Count the Valence Electrons**:
- Carbon (C) has 4 valence electrons, and there are 3 carbon atoms: \( 3 \times 4 = 12 \) electrons.
- Oxygen (O) has 6 valence electrons, and there are 2 oxygen atoms: \( 2 \times 6 = 12 \) electrons.
- Total valence electrons = \( 12 + 12 = 24 \) electrons.

2. **Draw the Lewis Structure**:
- Arrange the atoms: The structure can be represented as \( O=C=C=C=O \) with double bonds between the carbon atoms and between the carbon and oxygen atoms.
- Each double bond consists of one sigma bond and one pi bond.

### Step 2: Count the Total Number of Covalent Bonds (x)

1. **Identify the Bonds**:
- Between the three carbon atoms, there are 2 double bonds (each contributing 1 sigma and 1 pi bond).
- Between each carbon and oxygen, there are 2 double bonds (each contributing 1 sigma and 1 pi bond).

2. **Count the Bonds**:
- Total bonds between carbon atoms: 2 double bonds = \( 2 \times 2 = 4 \) (2 sigma + 2 pi).
- Total bonds between carbon and oxygen: 2 double bonds = \( 2 \times 2 = 4 \) (2 sigma + 2 pi).
- Total covalent bonds \( x = 4 + 4 = 8 \).

### Step 3: Determine the Number of sp-Hybridized Atoms (y)

1. **Identify Hybridization**:
- For each carbon atom:
- Each carbon in the chain has 2 sigma bonds (with adjacent carbon atoms) and no lone pairs, giving a steric number of 2. Thus, the hybridization is \( sp \).
- For each oxygen atom:
- Each oxygen has 1 sigma bond (with carbon) and 2 lone pairs, giving a steric number of 3. Thus, the hybridization is \( sp^2 \).

2. **Count the Hybridized Atoms**:
- Number of sp-hybridized carbon atoms = 3 (all three carbons).
- Number of sp-hybridized oxygen atoms = 0.
- Total sp-hybridized atoms \( y = 3 \).

### Step 4: Calculate the Sum \( x + y \)

1. **Add the Values**:
- \( x = 8 \) (total covalent bonds).
- \( y = 3 \) (number of sp-hybridized atoms).
- Therefore, \( x + y = 8 + 3 = 11 \).

### Final Answer
The sum \( x + y = 11 \).

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