Dipole moment of `CO_2` is zero which implies that

Options

A. Carbon and oxygen have equal electronegativities
B. Carbon has no polar bond
C. `CO_2` is a linear molecule
D. Carbon has bond moments of zero value.

Explanation

To determine why the dipole moment of carbon dioxide (CO₂) is zero, we need to analyze the structure and properties of the molecule step by step.

### Step 1: Understanding Dipole Moment
The dipole moment is a vector quantity that measures the separation of positive and negative charges in a molecule. It is influenced by the electronegativity of the atoms involved and the geometry of the molecule.

**Hint:** Remember that a dipole moment arises from polar bonds, which occur when there is a difference in electronegativity between bonded atoms.

### Step 2: Analyzing Electronegativity
In CO₂, carbon (C) is bonded to two oxygen (O) atoms. Oxygen is more electronegative than carbon, which means that the electrons in the C=O bonds are pulled closer to the oxygen atoms. This creates a partial negative charge (δ-) on the oxygen atoms and a partial positive charge (δ+) on the carbon atom.

**Hint:** Identify the electronegativity values of the elements involved. Oxygen is more electronegative than carbon.

### Step 3: Structure of CO₂
The molecular structure of CO₂ is linear, with the carbon atom in the center and the two oxygen atoms on either side. The bond angle between the oxygen-carbon-oxygen atoms is 180 degrees.

**Hint:** Visualize the molecular geometry. A linear structure can lead to cancellation of dipole moments.

### Step 4: Symmetry and Cancellation of Dipole Moments
Since CO₂ is a linear molecule, the dipole moments of the two C=O bonds are equal in magnitude but opposite in direction. This symmetry allows the dipole moments to cancel each other out, resulting in a net dipole moment of zero.

**Hint:** Consider how the symmetry of the molecule affects the overall dipole moment. If the molecule is symmetrical, the dipole moments can cancel.

### Step 5: Conclusion
Thus, the dipole moment of CO₂ is zero because the molecule is linear and symmetrical, leading to the cancellation of the individual dipole moments from the polar C=O bonds.

**Final Answer:** The correct implication of the zero dipole moment of CO₂ is that it is a linear molecule (Option 3).

### Summary of Options:
1. Carbon and oxygen are equally electronegative - **Incorrect**
2. Carbon has no polar bond - **Incorrect**
3. Carbon and CO₂ is a linear molecule - **Correct**
4. Carbon has bond moments of zero value - **Incorrect**