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The central atom in a molecule has a bent molecular geometry. Determine the hybridization of the orbitals in the atom. Sp Sp^2 Sp^3 Cannot be determined B. Which type of orbitals overlap to form the sigma bond between C and O in H^2C=O?
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Step 1:

The hybridization of the orbitals in an atom can be determined by considering the number of electron-donating atoms or groups (also known as ligands) attached to the central atom and the molecular geometry.

Step 2:

For a molecule with a bent molecular geometry, the central atom typically has two ligands arranged linearly and one lone pair of electrons. This configuration corresponds to a hybridization of sp³.

Step 3:

To better understand this, recall that sp³ hybridization results from the combination of one s orbital and three p orbitals to form four equivalent hybrid orbitals. These hybrid orbitals are arranged tetrahedrally around the central atom, with two of them used to form σ bonds with the ligands and the other two containing the lone pairs.

Step 4:

Therefore, the hybridization of the central atom in a bent molecular geometry is sp³. For the second part of the question:

Step 5:

Sigma (σ) bonds are formed by the end-to-end overlapping of atomic orbitals. In the case of the C-O bond in H^2C=O, the sigma bond is formed by the overlap of a sp² hybrid orbital from the carbon atom and a sp hybrid orbital from the oxygen atom.

Step 6:

In sp² hybridization, one s orbital and two p orbitals combine to form three equivalent hybrid orbitals, leaving one p orbital unhybridized. The sp² hybrid orbitals are arranged trigonally around the central atom, with the unhybridized p orbital perpendicular to the plane formed by the sp² orbitals.

Step 7:

Similarly, in sp hybridization, one s orbital and one p orbital combine to form two equivalent hybrid orbitals, leaving two p orbitals unhybridized. The sp hybrid orbitals are arranged linearly around the central atom, with the unhybridized p orbitals perpendicular to the plane formed by the sp orbitals.

Step 8:

In H^2C=O, the sp² hybrid orbital from the carbon atom overlaps with the sp hybrid orbital from the oxygen atom to form the σ bond.

Final Answer

1. The hybridization of the central atom in a bent molecular geometry is sp³. 2. The sigma bond between C and O in H^2C=O is formed by the overlap of a sp² hybrid orbital from the carbon atom and a sp hybrid orbital from the oxygen atom.