When acetic acid [tex]\((CH_3COOH)\)[/tex] dissolves in water, it partially dissociates into its ions. The correct representation of this equilibrium reaction is:
[tex]\[ CH_3COOH (aq) + H_2O (l) \rightleftharpoons H_3O^+ (aq) + CH_3COO^- (aq) \][/tex]
This equation shows that acetic acid donates a proton [tex]\((H^+)\)[/tex] to a water molecule, forming hydronium ion [tex]\((H_3O^+)\)[/tex] and acetate ion [tex]\((CH_3COO^-)\)[/tex]. This reaction is reversible and establishes an equilibrium between the reactants and the products in aqueous solution. Therefore, the first option is the correct one.