Question

What is the hydroxide ion concentration in an aqueous solution having a pH of 5 ?

Short answer

The hydroxide ion concentration is \(1.0 \times 10^{-9}\, \text{M}\).

Step-by-step solution

Understand the pH and pOH Relationship

The pH of a solution is related to its pOH by the equation: \[\text{pH} + \text{pOH} = 14\]This relationship holds true at 25°C for aqueous solutions. To find the hydroxide ion concentration, we first need the pOH.

Calculate the pOH from the Given pH

Given that the pH is 5, use the relationship from Step 1:\[\text{pOH} = 14 - \text{pH} = 14 - 5 = 9\]

Use pOH to Find \\[OH^-\\]

The pOH is related to the hydroxide ion concentration \[OH^-\] by the equation:\[\text{pOH} = -\log[OH^-]\]To find \[OH^-\], rearrange the equation as follows:\[[OH^-] = 10^{-\text{pOH}} = 10^{-9}\]

Calculate the Hydroxide Ion Concentration

Substitute the value of pOH into the equation from Step 3:\[[OH^-] = 10^{-9} = 1.0 \times 10^{-9}\, \text{M}\]

Key concepts

Hydroxide Ion Concentration

The hydroxide ion concentration, represented often as \[OH^-\], is a measure of how much hydroxide is present in a solution. This is important because it helps determine the basicity of the solution. In general, when you have a higher \[OH^-\] concentration, the solution is more basic. Conversely, a lower concentration implies a more acidic solution.

To determine the hydroxide ion concentration from a known pH, one must first understand the relationship between pH and pOH. These two factors put together give insight into the overall acidity or basicity of a solution.

Because \[OH^-\] deals with the basic aspect of a solution, knowing how to calculate it can be essential in various chemical processes, whether you're titrating in a lab or adjusting the chemistry of a pool.

pH Calculation

The pH of a solution is a measure of its acidity and is defined as the negative logarithm of the hydrogen ion concentration \[H^+\]. The equation to calculate pH is:

\[ ext{pH} = - ext{log}[H^+] \]

This equation means that if you know the concentration of \[H^+\] in a solution, you can easily determine its pH. Keep in mind that a lower pH value corresponds to a higher acidity, while a higher pH indicates a more basic or alkaline solution.

In the case of a solution with a known pH, like a pH of 5, this means the concentration of hydrogen ions is \([H^+] = 10^{-5} \, ext{M}\). Then, by knowing the pH, it allows you to use additional relationships, such as the one between pH and pOH, to find the \[OH^-\] concentration.

pOH Calculation

The concept of pOH is similar to pH, but instead focuses on the basicity of a solution by looking at the concentration of hydroxide ions. The equation to find pOH is:

\[ ext{pOH} = - ext{log}[OH^-] \]

This means if you know the hydroxide ion concentration, you can determine the pOH of the solution. However, even if the concentration is unknown initially, it can be deduced from the pH using the relationship:

\[ ext{pH} + ext{pOH} = 14 \]

This relationship is valid at 25°C for aqueous solutions.

For a solution with a pH of 5, the calculation would result in a pOH of 9, since: \[ ext{pOH} = 14 - 5 = 9 \]. Once you have the pOH, the hydroxide ion concentration, \[OH^-\], can be calculated as \[10^{- ext{pOH}} = 10^{-9} \, ext{M}\], a pivotal step in understanding the solution's basic properties.