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To complete the table, we need to use the relationship between the concentration of hydronium ions \([H_3O^+]\) and pH. The formula connecting these two is:

\[
\text{pH} = -\log[H_3O^+]
\]

Conversely, if the pH is known, we can find \([H_3O^+]\) using:

\[
[H_3O^+] = 10^{-\text{pH}}
\]

Let's go row by row:

### Solution A:
- Given: \([H_3O^+] = 3.8 \times 10^{-11} \, \text{mol/L}\)
- To find pH:
  
  \[
  \text{pH} = -\log(3.8 \times 10^{-11}) \approx 10.42
  \]

### Solution B:
- Given: pH = 6.92
- To find \([H_3O^+]\):

  \[
  [H_3O^+] = 10^{-6.92} \approx 1.20 \times 10^{-7} \, \text{mol/L}
  \]

### Solution C:
- Given: \([H_3O^+] = 5.9 \times 10^{-6} \, \text{mol/L}\)
- To find pH:

  \[
  \text{pH} = -\log(5.9 \times 10^{-6}) \approx 5.23
  \]

### Final Table:
| Solution | \([H_3O^+]\) (mol/L)      | pH     |
|----------|---------------------------|--------|
| A        | \(3.8 \times 10^{-11}\)    | 10.42  |
| B        | \(1.20 \times 10^{-7}\)    | 6.92   |
| C        | \(5.9 \times 10^{-6}\)     | 5.23   |

Let me know if you'd like further details!

Here are some follow-up questions:
1. How does temperature affect the \([H_3O^+]\) and pH relationship?
2. Can we have a neutral pH at temperatures other than 25°C?
3. Why does pH decrease as the \([H_3O^+]\) increases?
4. How would adding a strong base affect the values in this table?
5. What are some common applications where precise pH measurements are essential?

**Tip**: The pH scale is logarithmic, so small changes in pH represent significant changes in \([H_3O^+]\).

Complete the table. Each row of the table describes an aqueous solution at about 25°C. The missing entries are to be filled in using the relationship between [H3O+] and pH.

Learn how to complete a table of pH values and [H3O+] concentrations for various solutions at 25°C using logarithmic relationships. This solution demonstrates how to use the formulas pH = -log([H3O+]) and [H3O+] = 10^(-pH) to find missing values.

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