Question

What is \(\left[\mathrm{OH}^{-}\right]\) in a solution whose \(\left[\mathrm{H}^{+}\right]\) is \(3.23 \times 10^{-6} \mathrm{M} ?\)

Short answer

The \([ ext{OH}^-]\) concentration is \(3.10 \times 10^{-9} \text{ M}\).

Step-by-step solution

Identify the relationship between [H+] and [OH-]

We need to use the relation given by the ion product of water, which is \[ [ ext{H}^+][ ext{OH}^-] = 1.0 \times 10^{-14} \], at 25°C.

Rearrange the equation to find [OH-]

To find \([ ext{OH}^-]\), we rearrange the equation as follows:\[ [ ext{OH}^-] = \frac{1.0 \times 10^{-14}}{[ ext{H}^+]} \]

Substitute the given [H+] into the equation

Substitute the given value of \([ ext{H}^+] = 3.23 \times 10^{-6} \text{ M}\) into the equation:\[ [ ext{OH}^-] = \frac{1.0 \times 10^{-14}}{3.23 \times 10^{-6}} \]

Perform the calculation

Calculate \([ ext{OH}^-]\):\[ [ ext{OH}^-] = \frac{1.0 \times 10^{-14}}{3.23 \times 10^{-6}} = 3.10 \times 10^{-9} \text{ M} \]

Key concepts

Hydrogen Ion Concentration

In chemistry, understanding the concentration of hydrogen ions (\(\left[\mathrm{H}^{+}\right]\)) is crucial for grasping the behavior of acids. This concentration signifies the strength of an acidic solution, measuring how many hydrogen ions are present. The presence of a higher concentration of hydrogen ions indicates a stronger acid. Acids increase the hydrogen ion concentration when dissolved in water, causing the pH to drop.

The pH scale, ranging from 0 to 14, helps us represent this concentration more conveniently. A lower pH value corresponds to a higher hydrogen ion concentration. For example, a solution with \(\left[\mathrm{H}^{+}\right] = 3.23 \times 10^{-6} \, \text{M}\) is slightly acidic, as it has a pH just below 7.

To find the pH, you can use the formula:\[\text{pH} = -\log_{10}(\left[\mathrm{H}^{+}\right])\] Being familiar with how to calculate and interpret hydrogen ion concentration is fundamental for predicting the behavior of acids in various chemical reactions.

Hydroxide Ion Concentration

Hydroxide ion concentration (\(\left[\mathrm{OH}^{-}\right]\)) is a key element of understanding the behavior of basic solutions. Bases release hydroxide ions when dissolved in water, and a higher concentration of these ions indicates a stronger base.

In the example given, we are tasked with finding the\(\left[\mathrm{OH}^{-}\right]\)in a solution where \(\left[\mathrm{H}^{+}\right] = 3.23 \times 10^{-6} \, \text{M}\). Using the relationship identified by the ion product of water (more on that below), we can calculate the hydroxide concentration. This is crucial for understanding the balance between acidic and basic components in neutral, acidic, or alkaline solutions.

By rearranging the ion product formula, the hydroxide concentration can be determined using:\[\left[\mathrm{OH}^{-}\right] = \frac{1.0 \times 10^{-14}}{\left[\mathrm{H}^{+}\right]}\]For this specific solution, substituting the hydrogen ion concentration results in \(\left[\mathrm{OH}^{-}\right] = 3.10 \times 10^{-9} \, \text{M}\). Being able to calculate the hydroxide ion concentration enables you to infer the basicity of a solution.

Ion Product of Water

The ion product of water is a fundamental concept in the study of acid-base equilibrium. It describes the self-ionization process of water and is an essential constant in chemistry. At 25°C, the product of the concentrations of hydrogen ions and hydroxide ions always equals a constant value:\[\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right] = 1.0 \times 10^{-14}\]
This equilibrium is crucial as it forms the basis for understanding neutral, acidic, and basic solutions. In pure water, where neither an acid nor a base is added, the concentrations of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) are both equal to \(1.0 \times 10^{-7} \, \text{M}\).

Because of this relationship, if you know the concentration of either hydrogen or hydroxide ions in a solution, you can always calculate the other. This is shown in the provided exercise; by knowing one ion's concentration, the other can be found using the ion product. This concept is vital for predicting the pH changes and behavior of solutions during chemical reactions or in different environmental conditions.