`pH` value of a solution , whose hydronium ion concentration is a `6.2 xx 10^(-9) mol//l` is

Options

A. `6.21`
B. `7.21`
C. `7.75`
D. `8.21`

Answer

To find the pH value of a solution with a hydronium ion concentration of \(6.2 \times 10^{-9} \, \text{mol/L}\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the pH Formula**:
The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
where \([\text{H}^+]\) is the concentration of hydronium ions (H⁺ ions).

2. **Identify the Given Concentration**:
The given hydronium ion concentration is:
\[ [\text{H}^+] = 6.2 \times 10^{-9} \, \text{mol/L} \]

3. **Substitute the Concentration into the pH Formula**:
Plugging the value into the pH formula gives:
\[ \text{pH} = -\log(6.2 \times 10^{-9}) \]

4. **Break Down the Logarithm**:
Using the properties of logarithms, we can separate the terms:
\[ \text{pH} = -\log(6.2) - \log(10^{-9}) \]
This simplifies to:
\[ \text{pH} = -\log(6.2) + 9 \]

5. **Calculate \(-\log(6.2)\)**:
Using a calculator or logarithm table, we find:
\[ \log(6.2) \approx 0.79 \]
Therefore:
\[ -\log(6.2) \approx -0.79 \]

6. **Combine the Results**:
Now, substituting back into the pH equation:
\[ \text{pH} = -0.79 + 9 \]
This results in:
\[ \text{pH} = 8.21 \]

7. **Final Answer**:
The pH value of the solution is:
\[ \text{pH} = 8.21 \]