C_6H_5OH, known as phenol, acts as a weak acid in water, while C_6H_5NH_2, or aniline, functions as a weak base. To derive the equilibrium expressions for their dissociation, one must first write the ionization reactions for both substances in water. The equilibrium constant expressions, K_a for phenol and K_b for aniline, can then be formulated. These expressions will include the concentration of water, which is constant and can be omitted from the final equations. The relationship between K_a and K_b is established through the concentrations of their respective conjugate base and acid. The discussion emphasizes the importance of showing work and understanding the initial steps in deriving these constants, while also providing resources for further clarification on dissociation constants and chemical calculations.