Step 1: Understanding the Question:
The octet rule states that atoms tend to combine such that they each have eight electrons in their valence shell, giving them the same electronic configuration as a noble gas.
Step 2: Detailed Explanation:
1. \( CO_2 \): Carbon forms two double bonds with two Oxygen atoms. Carbon has 8 electrons (4 pairs), and each Oxygen has 8 electrons (2 bonding pairs + 2 lone pairs). Obeys.
2. \( CHCl_3 \): Carbon forms 4 single bonds (one with H, three with Cl). Carbon has 8 electrons in its valence shell. Obeys.
3. \( ClF_3 \): Chlorine is the central atom. It has 7 valence electrons. It forms 3 single bonds with Fluorine atoms and retains 2 lone pairs. Total electrons around \( Cl = (3 \times 2) + (2 \times 2) = 10 \). This is an expanded octet. Does not obey.
4. \( NH_3 \): Nitrogen forms 3 single bonds and has 1 lone pair. Total electrons = \( (3 \times 2) + 2 = 8 \). Obeys.
Step 4: Final Answer:
\( ClF_3 \) has 10 electrons in the valence shell of the central atom, thus violating the octet rule.