Question

Calculate the \(\mathrm{pH}\) of a solution that is \(0.025-\mathrm{M}\) in \(\mathrm{NaOH}\). Calculate the pOH of this solution.

Short answer

pOH is 1.60; pH is 12.40.

Step-by-step solution

Understanding pOH Calculations

NaOH is a strong base that completely dissociates in water. Therefore, the concentration of hydroxide ions ( OH^- ) in the solution is the same as the concentration of the NaOH solution, which is 0.025 M.

Calculating pOH

To find the pOH of the solution, use the formula:\[pOH = -\log [OH^-]\]Substituting the concentration of hydroxide ions:\[pOH = -\log (0.025)\]

Performing the Calculation

Calculate the pOH using the value of the logarithm:\[pOH = -\log (0.025) \approx 1.60\]

Understanding pH Calculations from pOH

To find the pH of the solution, use the relationship between pH and pOH:\[pH + pOH = 14\]This equation is valid at 25°C. Since we have calculated the pOH, we can rearrange this equation to find the pH:\[pH = 14 - pOH\]

Calculating the pH

Substitute the value of pOH into the equation to find the pH:\[pH = 14 - 1.60 = 12.40\]

Key concepts

Strong Base

In the world of chemistry, a strong base is a substance that can fully dissociate into its ions in a solution. When we say "dissociate," we mean that it separates into its constituent ions. This makes strong bases very effective at increasing the concentration of hydroxide ions (OH^-)in a solution.
A common example of a strong base is sodium hydroxide (NaOH). When NaOH is dissolved in water, it completely breaks down into sodium ions (\( ext{Na}^+ \)) and hydroxide ions (\( ext{OH}^- \)).
Because it dissociates completely, if you have a solution that has a concentration of 0.025 M of NaOH, the concentration of hydroxide ions will also be 0.025 M. This is a key point since, unlike weak bases, there is no undissociated form of NaOH left in the solution.
Understanding the behavior of strong bases is important for predicting how they influence pH and related calculations.

pOH Calculation

When working with a base in a solution, one important aspect is calculating the pOH. pOH tells us how basic or alkaline a solution is, similar to how pH measures acidity.
To find the pOH, we use the formula:

• \( pOH = -\log [OH^-] \)

Here, \([OH^-] \)is the concentration of hydroxide ions in the solution. For instance, with our NaOH solution, \([OH^-]\) is 0.025 M because NaOH is a strong base.
Substituting this concentration into our formula, the calculation would look like this:

• \( pOH = -\log (0.025) \)

By using a calculator,we find that \(pOH \approx 1.60\).This tells us that the solution is basic, as expected for a strong base.

Hydroxide Ion Concentration

Hydroxide ion concentration is a central concept when dealing with base solutions. These are the ions responsible for making a solution basic. For strong bases such as NaOH, calculating the hydroxide ion concentration involves knowing that the compound will dissociate completely in water.
For example, if you dissolve 0.025 M of NaOH in water, the hydroxide ion concentration will also be 0.025 M, because all the NaOH converts directly into hydroxide ions and sodium ions.
The focus on hydroxide ion concentration is crucial because it helps us determine the pOH of the solution. Unlike weak bases, where not all molecules dissociate, knowing the concentration of hydroxide ions in a solution with a strong base allows straightforward calculations of pOH directly using the log formula. Thus, understanding how to easily derive hydroxide ion concentration can facilitate accurate changes in pH and pOH calculations.