Question

Calculate \(\left[\mathrm{H}^{+}\right]\) for each of the following solutions, and indicate whether the solution is acidic, basic, or neutral: (a) \(\left[\mathrm{OH}^{-}\right]=0.00045 \mathrm{M} ;\) (b) \(\left[\mathrm{OH}^{-}\right]=8.8 \times 10^{-9} \mathrm{M} ;(\mathrm{c})\) a so- lution in which \(\left[\mathrm{OH}^{-}\right]\) is 100 times greater than \(\left[\mathrm{H}^{+}\right]\).

Short answer

(a) \(\left[\mathrm{H}^{+}\right] \approx 2.2\times10^{-12} \mathrm{M}\) (basic); (b) \(\left[\mathrm{H}^{+}\right] \approx 1.1\times10^{-6} \mathrm{M}\) (acidic); (c) \(\left[\mathrm{H}^{+}\right] \approx 1.0\times10^{-12} \mathrm{M}\) (basic).

Step-by-step solution

Calculate \(\left[\mathrm{H}^{+}\right]\)

Use the ion product constant of water and the given \(\left[\mathrm{OH}^{-}\right]\) to calculate \(\left[\mathrm{H}^{+}\right]\): \[ \left[\mathrm{H}^{+}\right] = \frac{K_w}{\left[\mathrm{OH}^{-}\right]} = \frac{1.0 \times 10^{-14}}{0.00045} \]

Determine whether the solution is acidic, basic, or neutral

If \(\left[\mathrm{H}^{+}\right] > \left[\mathrm{OH}^{-}\right]\), the solution is acidic. If \(\left[\mathrm{H}^{+}\right] < \left[\mathrm{OH}^{-}\right]\), the solution is basic. If \(\left[\mathrm{H}^{+}\right] = \left[\mathrm{OH}^{-}\right]\), the solution is neutral. (b) Solution with \(\left[\mathrm{OH}^{-}\right] = 8.8 \times10^{-9} \mathrm{M}\)

Calculate \(\left[\mathrm{H}^{+}\right]\)

Use the ion product constant of water and the given \(\left[\mathrm{OH}^{-}\right]\) to calculate \(\left[\mathrm{H}^{+}\right]\): \[ \left[\mathrm{H}^{+}\right] = \frac{K_w}{\left[\mathrm{OH}^{-}\right]} = \frac{1.0 \times 10^{-14}}{8.8 \times 10^{-9}} \]

Determine whether the solution is acidic, basic, or neutral

If \(\left[\mathrm{H}^{+}\right] > \left[\mathrm{OH}^{-}\right]\), the solution is acidic. If \(\left[\mathrm{H}^{+}\right] < \left[\mathrm{OH}^{-}\right]\), the solution is basic. If \(\left[\mathrm{H}^{+}\right] = \left[\mathrm{OH}^{-}\right]\), the solution is neutral. (c) Solution with \(\left[\mathrm{OH}^{-}\right] = 100\left[\mathrm{H}^{+}\right]\)

Calculate \(\left[\mathrm{H}^{+}\right]\)

Use the ion product constant of water and the given relationship between \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) to calculate \(\left[\mathrm{H}^{+}\right]\): \[ \left[\mathrm{H}^{+}\right] = \frac{K_w}{\left[\mathrm{OH}^{-}\right]} = \frac{1.0 \times 10^{-14}}{100\left[\mathrm{H}^{+}\right]} \]

Determine whether the solution is acidic, basic, or neutral

If \(\left[\mathrm{H}^{+}\right] > \left[\mathrm{OH}^{-}\right]\), the solution is acidic. If \(\left[\mathrm{H}^{+}\right] < \left[\mathrm{OH}^{-}\right]\), the solution is basic. If \(\left[\mathrm{H}^{+}\right] = \left[\mathrm{OH}^{-}\right]\), the solution is neutral.

Key concepts

Ion Product Constant of Water

Understanding the ion product constant of water, denoted as K_w, is fundamental to calculating pH and determining the acidity or basicity of a solution. K_w represents the equilibrium constant for the self-ionization of water, a process where water molecules dissociate into hydrogen ions (H⁺) and hydroxide ions (OH⁻), and it is a fixed value at a given temperature. For instance, at 25°C, K_w is 1.0 × 10⁻¹⁴.

This constant is used for calculating the concentration of hydrogen ions when the concentration of hydroxide ions is known, and vice versa, as shown in the exercise. The relationship is given by the equation K_w = [H⁺] × [OH⁻]. When working with solutions, understanding how to apply this concept allows us to analyze the solution's characteristics regarding its pH level.

Acidity and Basicity

The concepts of acidity and basicity are integral to chemistry, especially when dealing with aqueous solutions. Acidity refers to the concentration of hydrogen ions (H⁺) in a solution, while basicity refers to the concentration of hydroxide ions (OH⁻). The pH scale is a measure of how acidic or basic a solution is, ranging from 0 (very acidic) to 14 (very basic), with 7 being neutral.

In the context of the exercise, if a solution has more hydrogen ions than hydroxide ions, it's considered acidic. In contrast, if there are more hydroxide ions, the solution is basic. This is determined by comparing the calculated concentrations of H⁺ and OH⁻ to one another. The pH can then be calculated using the equation pH = -log([H⁺]), which gives a direct, numerical representation of a solution's acidity or basicity.

Hydrogen Ion Concentration

Hydrogen ion concentration, expressed as [H⁺], is a crucial parameter for assessing the chemical nature of a solution. It is directly related to pH, where a high concentration of hydrogen ions corresponds to a low pH (acidic), and a low concentration corresponds to a high pH (basic). In the exercises provided, the student is tasked with calculating the [H⁺] from the given hydroxide ion concentration using the ion product constant of water.

The accuracy of calculating the hydrogen ion concentration is pivotal since it dictates whether a solution is acidic, basic, or neutral. Furthermore, the exercise provided explores various scenarios, such as when the hydroxide concentration is given or when it is a certain multiple of the hydrogen ion concentration. By mastering these calculations, students gain a strong foundation for understanding chemical reactions, biological systems, and environmental science, where pH plays a significant role.