To find the hydronium ion concentration \([H_3O^+]\) of a solution with a given \( \text{pOH} \) of 6.90, we follow these steps:
1. Calculate the pH:
The relationship between pH and pOH is given by:
[tex]\[
\text{pH} + \text{pOH} = 14
\][/tex]
So, we can find the pH by subtracting the pOH from 14:
[tex]\[
\text{pH} = 14 - \text{pOH} = 14 - 6.90 = 7.10
\][/tex]
2. Calculate the hydronium ion concentration \([H_3O^+]\):
The hydronium ion concentration can be found using the formula:
[tex]\[
[H_3O^+] = 10^{-\text{pH}}
\][/tex]
Plugging in the pH value:
[tex]\[
[H_3O^+] = 10^{-7.10} \approx 7.94 \times 10^{-8} \, M
\][/tex]
3. Compare calculated \([H_3O^+]\) with given choices:
We are given the following options:
[tex]\[
\begin{align*}
&6.29 \times 10^{-7} \, M \\
&6.53 \times 10^{-7} \, M \\
&7.18 \times 10^{-8} \, M \\
&7.94 \times 10^{-8} \, M \\
\end{align*}
\][/tex]
The calculated \( [H_3O^+] \) value is \( \approx 7.94 \times 10^{-8} \, M \), which matches most closely with the option \( 7.94 \times 10^{-8} \, M \).
Therefore, the hydronium ion concentration is [tex]\( 7.94 \times 10^{-8} \, M \)[/tex], which matches the fourth option.
