Final answer:
The theoretical van't Hoff factor is 3 for Ca(OH)2, as it dissociates into three ions, and 1 for CH3OH, which does not dissociate into ions.
Step-by-step explanation:
The theoretical van't Hoff factor (i) for a compound represents the number of particles into which a compound dissociates when it dissolves. For Ca(OH)₂, it dissociates into three ions: one Ca²⁺ and two OH⁻ ions, so its theoretical van't Hoff factor is 3.
The compound CH₃OH (methanol) does not dissociate into ions in solution; therefore, its theoretical van't Hoff factor is 1. Note that these are ideal values and real measurements can differ.