Certainly! Let's go through a step-by-step solution to find the hydroxide ion concentration [tex]\([\text{OH}^-]\)[/tex] in a solution with a pH of 8.45 at [tex]\(25^{\circ} \text{C}\)[/tex].
Step 1: Understanding the relationship between pH and pOH.
The pH and pOH of a solution are related through the following equation:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Step 2: Calculate the pOH from the given pH.
Given the pH of the solution is 8.45, we can calculate the pOH as follows:
[tex]\[ \text{pOH} = 14 - \text{pH} \][/tex]
Substituting the given pH value:
[tex]\[ \text{pOH} = 14 - 8.45 \][/tex]
[tex]\[ \text{pOH} = 5.55 \][/tex]
Step 3: Convert the pOH to the hydroxide ion concentration.
The hydroxide ion concentration [tex]\([\text{OH}^-]\)[/tex] can be calculated using the pOH value. The formula to convert pOH to [tex]\([\text{OH}^-]\)[/tex] is:
[tex]\[ [\text{OH}^-] = 10^{-\text{pOH}} \][/tex]
Substituting the pOH value:
[tex]\[ [\text{OH}^-] = 10^{-5.55} \][/tex]
Step 4: Interpret the results.
From these calculations, the hydroxide ion concentration [tex]\([\text{OH}^-]\)[/tex] is found to be:
[tex]\[ [\text{OH}^-] \approx 2.82 \times 10^{-6} \, \text{M} \][/tex]
Thus, the hydroxide ion concentration in this solution is approximately [tex]\( 2.82 \times 10^{-6} \, \text{M} \)[/tex].
