Step 1: VSEPR Theory.
The VSEPR (Valence Shell Electron Pair Repulsion) model helps predict the geometry of molecules based on the repulsion between electron pairs. The shape of a molecule depends on the number of bonding pairs and lone pairs around the central atom.
Step 2: Analyzing \( \text{PCl}_4^+ \).
For the \( \text{PCl}_4^+ \) ion:
- The central atom is phosphorus (P).
- It is surrounded by 4 chlorine atoms, forming 4 bonding pairs of electrons.
- The charge on the ion is \( +1 \), which means there is one fewer electron than the neutral molecule, so there are no lone pairs on the phosphorus atom.
Therefore, with 4 bonding pairs and no lone pairs, the shape is tetrahedral according to VSEPR theory.
Step 3: Conclusion.
Thus, the correct shape of the \( \text{PCl}_4^+ \) ion is tetrahedral, corresponding to option (1).

