Final answer:
VSEPR theory dictates that a carbon with four single bonds exhibits a tetrahedral geometry, as seen in CHCl₃, due to the repulsion of electron pairs. Contrarily, CO₂ has a linear shape as it only has two double bonds around the central carbon. The geometries are a result of sp³ hybridization in the former and sp hybridization in the latter.
Step-by-step explanation:
The VSEPR theory predicts that a carbon atom with four single covalent bonds will have a tetrahedral geometry. When looking at a central carbon atom with four single bonds, each bond is counted as one electron group. In the case of CHCl₃, with four electron pairs around the central carbon, the molecule adopts a tetrahedral shape due to the repulsion between these electron regions. Carbon atoms in molecules with tetrahedral geometry are typically sp³ hybridized, allowing for the formation of four equivalent bonding orbitals.
Consider carbon dioxide (CO₂), which shows us two regions of high electron density around the carbon atom - each double bond is counted as one electron region. Since there are no lone pairs on the carbon atom, VSEPR theory tells us the molecule has a linear geometry with a bond angle of 180°, contrasting the tetrahedral shape when there are four single bonds.