Question

Determine if each solution is acidic, basic, or neutral. (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-9} \mathrm{M} ;\left[\mathrm{OH}^{-}\right]=1 \times 10^{-5} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-10} \mathrm{M} ;\left[\mathrm{OH}^{-}\right]=1 \times 10^{-4} \mathrm{M}\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-2} \mathrm{M}\); [ \(\left.\mathrm{OH}^{-}\right]=1 \times 10^{-12} \mathrm{M}\) (d) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-13} \mathrm{M} ;\left[\mathrm{OH}^{-}\right]=1 \times 10^{-1} \mathrm{M}\)

Short answer

Each solution is as follows: (a) basic, (b) basic, (c) acidic, (d) basic.

Step-by-step solution

Understanding the Concept

To determine whether each solution is acidic, basic, or neutral, we must look at the concentrations of hydronium ions \(\mathrm{H}_3\mathrm{O}^{+}\) and hydroxide ions \(\mathrm{OH}^{-}\). A neutral solution has \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = \left[\mathrm{OH}^{-}\right] = 1 \times 10^{-7} \mathrm{M}\) due to the autoionization of water. A solution is acidic if \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] > \left[\mathrm{OH}^{-}\right]\) and basic if \(\left[\mathrm{OH}^{-}\right] > \left[\mathrm{H}_3\mathrm{O}^{+}\right]\).

Solution for Part (a)

In part (a), \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = 1 \times 10^{-9} \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right] = 1 \times 10^{-5} \mathrm{M}\). Since \(\left[\mathrm{OH}^{-}\right]\) is greater than \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\), the solution is basic.

Solution for Part (b)

For part (b), \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = 1 \times 10^{-10} \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right] = 1 \times 10^{-4} \mathrm{M}\). Since \(\left[\mathrm{OH}^{-}\right]\) is greater, the solution is basic.

Solution for Part (c)

In part (c), \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = 1 \times 10^{-2} \mathrm{M}\) while \(\left[\mathrm{OH}^{-}\right] = 1 \times 10^{-12} \mathrm{M}\). Since \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\) is greater, the solution is acidic.

Solution for Part (d)

For part (d), \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = 1 \times 10^{-13} \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right] = 1 \times 10^{-1} \mathrm{M}\). Since \(\left[\mathrm{OH}^{-}\right]\) is greater, the solution is basic.

Key concepts

pH level

The pH level is a measure of the acidity or basicity of an aqueous solution. It's a scale that ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are considered basic or alkaline. The pH value is inversely related to the concentration of hydronium ions \(\mathrm{H}_3\mathrm{O}^{+}\); as the concentration of hydronium ions increases, the pH value decreases, indicating an increase in acidity.
This concept explains why in the exercise, when hydronium ion concentration is higher than 1 x 10^-7 M, the solution is acidic. Conversely, when the hydroxide ion concentration is higher, leading to a hydronium ion concentration lower than 1 x 10^-7 M, the solution is basic. The student can further translate the ion concentrations into pH values to deduce the solution's nature without memorizing the greater than or less than relationships.

hydronium ion concentration

Hydronium ion concentration, represented as \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\), determines the acidity of a solution. Acidity is directly proportional to the hydronium ion concentration; higher concentrations indicate stronger acidic properties. To make this easier to understand, consider the concentration as the number of hydronium ions present. More ions result in more acidic solutions because hydronium ions are positively charged and represent free hydrogen ions in water, which lead to acidity.
In the textbook solutions, the concentration of hydronium ions was analyzed to determine the nature of each solution. For example, the high hydronium ion concentration in part (c) of the exercise \(1 \times 10^{-2} \mathrm{M}\) indicates a very acidic solution.

hydroxide ion concentration

In contrast, hydroxide ion concentration \(\left[\mathrm{OH}^{-}\right]\) reflects the basicity of a solution. When the hydroxide ion concentration is high, the solution is basic. The ions are negatively charged and counterbalance the positive charge of hydronium ions. When teaching this concept, it's helpful to analogize hydroxide ions to a cleaner neutralizing dirt—the more cleaner you have (hydroxide ions), the less dirt (acidity) remains.
Looking back at the original exercise, parts (a), (b), and (d) showed that when the hydroxide ion concentration exceeded the hydronium ion concentration, the solutions were deemed basic, stressing the importance of the ions' balance in classifying the solution's nature.

autoionization of water

The autoionization of water is the self-ionization where water acts as both an acid and a base, producing equal concentrations of hydronium \(\mathrm{H}_3\mathrm{O}^{+}\) and hydroxide \(\mathrm{OH}^{-}\) ions. At 25°C, this equilibrium leads to a constant product \(Kw\), which is approximately \(1 \times 10^{-14}\). The concentrations of hydronium and hydroxide ions in pure water are both \(1 \times 10^{-7} \mathrm{M}\), resulting in a neutral pH of 7.
When explaining this to students, a relatable analogy is a tug-of-war between acidity and basicity, with autoionization representing a perfectly balanced rope. This concept is important in the exercise context to elaborate why a neutral solution isn't simply devoid of ions but rather contains an equal number of \(\mathrm{H}_3\mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) ions.