Calculate the `H_(3)O^(+)` ion concentration of a solution having a pH of 10.6

Answer

To calculate the \( H_3O^+ \) ion concentration of a solution with a pH of 10.6, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between pH and \( H_3O^+ \) concentration**:
The pH of a solution is defined as:
\[ \text{pH} = -\log_{10} [H_3O^+] \]
where \( [H_3O^+] \) is the concentration of hydronium ions in moles per liter (M).

2. **Rearrange the formula to find \( [H_3O^+] \)**:
To find the concentration of \( H_3O^+ \), we can rearrange the formula:
\[ [H_3O^+] = 10^{-\text{pH}} \]

3. **Substitute the given pH value**:
We are given that the pH is 10.6. Substitute this value into the equation:
\[ [H_3O^+] = 10^{-10.6} \]

4. **Calculate \( 10^{-10.6} \)**:
Using a calculator or logarithmic tables:
\[ [H_3O^+] \approx 2.5119 \times 10^{-11} \text{ M} \]

5. **Round the answer**:
For simplicity, we can round this to three significant figures:
\[ [H_3O^+] \approx 2.512 \times 10^{-11} \text{ M} \]

### Final Answer:
The concentration of \( H_3O^+ \) ions in the solution is approximately \( 2.512 \times 10^{-11} \text{ M} \).

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