Problem 129 - Introductory Chemistry Atoms First

Question

An aqueous solution has an \(\mathrm{H}_{3} \mathrm{O}\) ' concentration of \(1.0 \mathrm{M}\). What is the OH concentration? Is this solution acidic or basic? Justify your answer.

Step-by-Step Solution

Answer

The OH⁻ concentration is \(1.0 \times 10^{-14}\) M, and since the H₃O⁺ concentration (1.0 M) is greater than the OH⁻ concentration, the solution is acidic.

Step 1: Determine the H₃O⁺ concentration

The problem states that the hydronium ion concentration is 1.0 M. So, we have: \[ [\mathrm{H}_{3} \mathrm{O}^{+}] = 1.0\,M \]

Step 2: Calculate the OH⁻ concentration using the ion product of water

The ion product of water, Kw, is given by: \[K_w = [\mathrm{H}_{3} \mathrm{O}^{+}] [\mathrm{OH}^{-}] \] At 25°C, the ion product of water is: \[K_w = 1.0 \times 10^{-14}\] To find the OH⁻ concentration, rearrange the equation: \[[\mathrm{OH}^{-}] = \frac{K_w}{[\mathrm{H}_{3} \mathrm{O}^{+}]}\] Substitute the values of Kw and H₃O⁺ concentration: \[[\mathrm{OH}^{-}] = \frac{1.0 \times 10^{-14}}{1.0\,M}\]

Step 3: Calculate the OH⁻ concentration

Now, divide the value of Kw by the given H₃O⁺ concentration: \[[\mathrm{OH}^{-}] = 1.0 \times 10^{-14}\]

Step 4: Determine if the solution is acidic or basic

To determine if the solution is acidic or basic, compare the H₃O⁺ and OH⁻ concentrations: - If H₃O⁺ > OH⁻, the solution is acidic - If H₃O⁺ < OH⁻, the solution is basic - If H₃O⁺ = OH⁻, the solution is neutral Since [\(\mathrm{H}_{3} \mathrm{O}^{+}\)] = 1.0 M and [\(\mathrm{OH}^{-}\)] = \(1.0 \times 10^{-14}\) M, \[ [\mathrm{H}_{3} \mathrm{O}^{+}] > [\mathrm{OH}^{-}] \] Hence, the given solution is acidic.

Key Concepts

Hydronium Ion Concentration

In any aqueous solution, hydronium ions (H₃O⁺) are a central indicator of acidity. An acid releases hydrogen ions in water which form hydronium ions. The concentration of these ions is directly related to the solution's acidity. For example, a solution with a hydronium ion concentration of 1.0 M is quite acidic, as it shows a significant presence of H₃O⁺ ions. This concentration is crucial not only for determining how acidic a solution is but also for calculating other properties, such as the concentration of hydroxide ions (OH⁻). Knowing the hydronium ion concentration helps in understanding the balance of ions in the solution, thereby informing whether a solution is acidic, basic, or neutral.

Ion Product of Water

Water is a very interesting compound because it can dissociate into ions. In pure water, the concentration of hydronium ions and hydroxide ions is equal, resulting in a neutral solution. The ion product of water, denoted as Kw, is a constant value representing the product of the concentrations of these ions. At around 25°C, this constant Kw is always approximately \(1.0 \times 10^{-14}\). To determine the concentration of hydroxide ions in a solution, you can rearrange the ion product formula:

• \([\mathrm{OH}^{-}] = \frac{K_w}{[\mathrm{H}_3 \mathrm{O}^{+}]}\)

This formula shows a direct inverse relationship between the concentrations of H₃O⁺ and OH⁻; when one increases, the other decreases. Understanding Kw is essential for chemists to determine the nature of the solution they are dealing with.

Acidic and Basic Solutions

Determining whether a solution is acidic or basic involves comparing the concentrations of hydronium and hydroxide ions. A solution is acidic when it contains more hydronium ions than hydroxide ions. Conversely, a solution is basic when it has more hydroxide ions. Neutral solutions have equal concentrations of both ions. One way to determine this is to look at the numerical values: if \([\mathrm{H}_3 \mathrm{O}^{+}] > [\mathrm{OH}^{-}]\), the solution is acidic; and if \([\mathrm{H}_3 \mathrm{O}^{+}] < [\mathrm{OH}^{-}]\), it is basic. Finally, when both concentrations are equal, the solution is neutral. This basic comparison helps in various fields such as biology, chemistry, and medicine, where the acidity or basicity of a solution can influence reactions, biological processes, or medication effectiveness.