Question

For a given aqueous solution, if \(\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-9} \mathrm{M},\) what is \(\left[\mathrm{OH}^{-}\right] ?\)

Short answer

The \\([\mathrm{OH}^-]\\) concentration is \\(1.0 \times 10^{-5} \, \mathrm{M}\\).

Step-by-step solution

Understanding the Relation

In an aqueous solution, the product of the hydrogen ion concentration \([\mathrm{H}^+]\) and the hydroxide ion concentration \([\mathrm{OH}^-]\) is equal to the ion product constant of water, \(K_w\), which at 25 °C is \(1.0 \times 10^{-14}\). This can be expressed by the equation: \[ \left[\mathrm{H}^+\right] \cdot \left[\mathrm{OH}^-\right] = K_w \]

Substitute the Known Values

We substitute the given value of \([\mathrm{H}^+] = 1.0 \times 10^{-9} \, \mathrm{M}\) into the equation: \[ 1.0 \times 10^{-9} \cdot \left[\mathrm{OH}^-\right] = 1.0 \times 10^{-14} \]

Solve for Hydroxide Ion Concentration

To find \([\mathrm{OH}^-]\), we rearrange the equation to isolate \([\mathrm{OH}^-]\): \([\mathrm{OH}^-] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-9}}\).

Perform the Calculation

Perform the division: \[ \left[\mathrm{OH}^-\right] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-9}} = 1.0 \times 10^{-5} \, \mathrm{M} \]

Conclude the Result

Thus, the concentration of hydroxide ions in the solution is \([\mathrm{OH}^-] = 1.0 \times 10^{-5} \, \mathrm{M}\).

Key concepts

Aqueous Solutions

Aqueous solutions are simply solutions where water is the solvent. Water is an excellent solvent due to its polarity, allowing it to dissolve a wide range of substances. When ionic compounds dissolve in water, they dissociate into ions, which are uniformly distributed throughout the solution. This process makes water an essential medium for many chemical reactions.

An interesting property of water is its ability to ionize slightly. This means that a small fraction of water molecules naturally dissociate into hydrogen ions \([\mathrm{H}^+]\) and hydroxide ions \([\mathrm{OH}^-]\).
Although this ionization is minimal, it is crucial in dictating the acidity or basicity of the solution.

• When a substance is dissolved, it can change the concentration of \([\mathrm{H}^+]\) and \([\mathrm{OH}^-]\).
• This leads to either acidic, basic, or neutral solutions depending on the balance of the ions.

Understanding the behavior of aqueous solutions is vital in fields like chemistry and biology, where water-based reactions are common.

Hydrogen Ion Concentration

The hydrogen ion concentration in a solution is a measure of its acidity. The concentration is expressed in molarity (M), which tells us the number of moles of hydrogen ions per liter of solution. In water, and in aqueous solutions, the hydrogen ions originate from the self-ionization of water and any acidic substances that may be added.

As per the ion product constant of water, \(K_w\), at 25 °C, the relationship can be expressed as follows:

• The product of \[\mathrm{H}^+\] and \[\mathrm{OH}^-\] concentrations is \[1.0 \times 10^{-14}\].
• In pure water, these concentrations are equal, each being about \[1.0 \times 10^{-7} \, M\].

Some key points include:
- \[\mathrm{H}^+\] indirectly determines the pH of the solution, a scale to assess acidity or alkalinity.
- Low \[\mathrm{H}^+\] concentration indicates a basic solution, while a high one indicates an acidic solution.

Balancing \[\mathrm{H}^+\] is crucial in industrial and laboratory settings for controlling solution properties.

Hydroxide Ion Concentration

Hydroxide ion concentration is a measure of a solution's basicity. Similar to hydrogen ion concentration, it too is expressed in terms of molarity. The hydroxide ions \(\mathrm{OH}^-\) in an aqueous solution come from the dissociation of water and any basic substances dissolved in water.

The basic unit of relationship is the ion product constant of water, \(K_w\).

• The equilibrium equation states: \[ [\mathrm{H}^+] \cdot [\mathrm{OH}^-] = 1.0 \times 10^{-14}\].
• This means if \[\mathrm{H}^+\] concentration increases, \[\mathrm{OH}^-\] must decrease, and vice versa, at constant temperature.

Calculating hydroxide ion concentration often involves rearranging the equilibrium equation to focus on \[\mathrm{OH}^-\]. This is essential for:
- Determining the pOH, which indicates the level of basicity.
- Adjusting conditions in chemical reactions where specific pH is required, like in biochemistry experiments or industrial processes.

Being fluent in calculating and interpreting \[\mathrm{OH}^-\] is essential for anyone dealing with chemical solutions.