To determine the concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex], we can follow a systematic approach involving the relationship between pH and pOH, and the formula for calculating the hydronium ion concentration from pH.
1. Given Data:
- pOH of the solution is 8.20.
2. Determine the pH:
- The relationship between pH and pOH is given by the equation:
[tex]\[
\text{pH} + \text{pOH} = 14
\][/tex]
- Therefore, we can find pH as:
[tex]\[
\text{pH} = 14 - \text{pOH}
\][/tex]
- Substituting the given pOH:
[tex]\[
\text{pH} = 14 - 8.20 = 5.80
\][/tex]
3. Calculate the concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex]:
- The concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex] ions can be found using the formula:
[tex]\[
[\text{H}_3\text{O}^+] = 10^{-\text{pH}}
\][/tex]
- Substituting the calculated pH:
[tex]\[
[\text{H}_3\text{O}^+] = 10^{-5.80}
\][/tex]
- Evaluating this expression gives:
[tex]\[
[\text{H}_3\text{O}^+] \approx 1.6 \times 10^{-6}
\][/tex]
So, the correct concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex] is:
[tex]\[
1.6 \times 10^{-6}
\][/tex]
Therefore, the correct answer is:
B. [tex]\( 1.6 \times 10^{-6} \)[/tex]
