Final answer:
Given the hydroxide ion concentration of 4.0x10⁻² M, and using the water ion-product constant, we find the hydronium ion concentration to be below 1x10⁻⁷ M. Therefore, the solution is basic.
Step-by-step explanation:
When determining whether a solution is acidic, basic, or neutral, it's essential to consider the hydroxide ion concentration ([OH-]) and relate it to the hydronium ion concentration ([H3O+]). Since the given hydroxide ion concentration is 4.0x10-2 M, we can use the water ion-product constant (Kw = 1x10-14 at 25°C) to find the corresponding hydronium ion concentration by the formula [H3O+] = Kw / [OH-]. Doing this calculation: [H3O+] = 10-14 / 4.0x10-2 = 2.5x10-13 M. Since this concentration of H3O+ is considerably less than 1x10-7 M, the solution is basic.
Remember, a neutral solution has equal concentrations of H3O+ and OH-, each at 1x10-7 M. If [H3O+] were greater than 1x10-7 M, the solution would be acidic. Conversely, because the given [OH-] concentration corresponds to a much lower [H3O+], the solution has basic characteristics. Hence, based on the hydroxide ion concentration provided, we can conclude that the solution is indeed basic.