Problem 20 - Chemistry The Molecular Science

Question

Consider these four solutions: $$ \begin{array}{lcc} \hline \text { Solution } & {\left[\mathrm{H}_{3} \mathrm{O}^{+}\right](\mathrm{M})} & {\left[\mathrm{OH}^{-}\right](\mathrm{M})} \\ \hline \mathrm{W} & 5 \times 10^{-6} & \\ \mathrm{X} & & 2 \times 10^{-4} \\ \mathrm{Y} & 4 \times 10^{-2} & \\ \mathrm{Z} & & 5 \times 10^{-11} \\ \hline \end{array} $$ (a) Which solution has the highest \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration? (b) One solution's \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration is equal to the \(\mathrm{OH}^{-}\) concentration of a different solution. Identify the two solutions and their concentrations. (c) Which solution is closest to being a neutral solution?

Step-by-Step Solution

Answer

(a) Solution Y has the highest \([\mathrm{H}_3\mathrm{O}^+]\). (b) Solutions W and Z have equal concentrations: \(5 \times 10^{-6}\) M. (c) Solution X is closest to neutral.

Step 1: Understanding the Table

The table presents four solutions: W, X, Y, and Z, along with their respective concentrations of \(\mathrm{H}_3\mathrm{O}^+\) and \(\mathrm{OH}^-\). Some concentrations are missing for certain solutions.

Step 1: Identify Solution with Highest \(\mathrm{H}_3\mathrm{O}^+\) Concentration

From the given data, compare the \([\mathrm{H}_3\mathrm{O}^+]\) values:- Solution W: \(5 \times 10^{-6}\) M- Solution Y: \(4 \times 10^{-2}\) MSolution Y has the highest \([\mathrm{H}_3\mathrm{O}^+]\) concentration.

Step 2: Match Equal \(\mathrm{H}_3\mathrm{O}^+\) and \(\mathrm{OH}^-\) Concentrations

Check the concentrations for equality between \(\mathrm{H}_3\mathrm{O}^+\) and \(\mathrm{OH}^-\):- Solution W: \([\mathrm{H}_3\mathrm{O}^+] = 5 \times 10^{-6}\) M- Solution Z: \([\mathrm{OH}^-] = 5 \times 10^{-11}\) MThe \(\mathrm{H}_3\mathrm{O}^+\) concentration of Solution W equals the \(\mathrm{OH}^-\) concentration of Solution Z.

Step 3: Determine Closest to Neutral Solution

A neutral solution at 25°C has \([\mathrm{H}_3\mathrm{O}^+] = [\mathrm{OH}^-] = 1 \times 10^{-7}\) M. Calculate the hydronium ion concentration for solutions X and Z:- Solution X: \([\mathrm{OH}^-] = 2 \times 10^{-4}\), use \( [\mathrm{H}_3\mathrm{O}^+] = \frac{1 \times 10^{-14}}{[\mathrm{OH}^-]} = 5 \times 10^{-11}\) M- Solution Z: \([\mathrm{OH}^-] = 5 \times 10^{-11}\), use \( [\mathrm{H}_3\mathrm{O}^+] = \frac{1 \times 10^{-14}}{[\mathrm{OH}^-]} = 2 \times 10^{-4}\) M- Compare \([\mathrm{H}_3\mathrm{O}^+]\) to \(1 \times 10^{-7}\) M, Solution X is closest with \(5 \times 10^{-11}\) M.

Key Concepts

Hydronium Ion Concentration

The hydronium ion concentration, denoted as \([\mathrm{H}_3\mathrm{O}^+]\), is central to understanding how acidic a solution is. Hydronium ions are produced when an acid dissolves in water, transferring a proton \((\mathrm{H}^+)\) to a water molecule. The concentration of these ions dictates the solution's acidity level.

In the given exercise, four solutions reveal different hydronium ion concentrations. To determine which solution is the most acidic, we compare their \([\mathrm{H}_3\mathrm{O}^+]\) values. Solution Y, with a hydronium ion concentration of \(4 \times 10^{-2}\) M, stands out. This shows it's significantly more acidic compared to others, like solution W, which has a concentration of \(5 \times 10^{-6}\) M. An important aspect here is understanding that higher \([\mathrm{H}_3\mathrm{O}^+]\) values indicate stronger acidity.

Recognizing these concentrations helps classify solutions into acidic, neutral, or basic. Such comparisons are essential in chemistry for predicting reactions and behaviors of solutions under various conditions.

Neutral Solution

A neutral solution is one where the concentrations of hydronium ions \([\mathrm{H}_3\mathrm{O}^+]\) and hydroxide ions \([\mathrm{OH}^-]\) are equal, typically both equal to \(1 \times 10^{-7}\) M at 25°C. This balance means the solution neither favors acid nor base, maintaining a perfect equilibrium.

In the context of the exercise, identifying the solution closest to neutral involves comparing the given concentrations to this standard. As we calculated, Solution X with a calculated \([\mathrm{H}_3\mathrm{O}^+]\) of \(5 \times 10^{-11}\) M approaches the value for neutral water. This finding suggests that solution X is nearly neutral, whereas the other solutions are markedly different, leaning towards more acidic or basic conditions due to their higher ion concentrations. Understanding this concept is critical as it influences how we approach and handle chemical reactions in various environments.

pH and pOH

The concepts of pH and pOH are crucial tools for quantifying the acidity or basicity of a solution. The pH scale ranges from 0 to 14, where lower values signify more acidic conditions, and higher values indicate more basic ones. The formula for pH is given by \(\text{pH} = -\log [\mathrm{H}_3\mathrm{O}^+]\).

For our solutions, computing pH helps in understanding their acid-base nature accurately. For example, Solution Y, with a high \([\mathrm{H}_3\mathrm{O}^+]\) of \(4 \times 10^{-2}\) M, translates to a low pH, showing strong acidity. Similarly, pOH provides insight into basicity, derived from \([\mathrm{OH}^-]\) using \(\text{pOH} = -\log [\mathrm{OH}^-]\). The relationship is such that \(\text{pH} + \text{pOH} = 14\).

In practical terms, these measures are used to gauge corrosive potential, biochemical compatibility, and the nature of reactions in solutions. Broken down into daily applications, such understanding is vital for environmental monitoring, biological systems, and industrial processes.