Answer and Explanation:
When methanol (CH₃OH) dissolves in water, the following equilibrium takes place:
CH₃OH + H₂O ⇄ CH₃O⁻ + H₃O⁺
The dissociation constant is about 10⁻¹⁶ (very very small), so methanol practically does not dissociate in its ions in water, thus the solution does not conduct electricity (because there is a very small quantity of ions).
By other hand, acetic acid (CH₃COOH) dissociates in water as follows:
CH₃COOH + H₂O ⇄ CH₃COO⁻ + H₃O⁺
and its dissociation constant is about 10⁻⁵, which is not negligible. So, there is a considerable quantity of ions in solution and they can conduct electricity.
