`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`

Explanation

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

### Step 1: Identify the given concentration of hydronium ions
The concentration of hydronium ions \([H^+]\) is given as:
\[ [H^+] = 6.2 \times 10^{-9} \, \text{mol/L} \]

### Step 2: Use the pH formula
The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]

### Step 3: Substitute the concentration into the pH formula
Now we will substitute the given concentration into the pH formula:
\[ \text{pH} = -\log(6.2 \times 10^{-9}) \]

### Step 4: Break down the logarithm
Using the property of logarithms, we can separate the logarithm of the product:
\[ \text{pH} = -\log(6.2) - \log(10^{-9}) \]
Since \(\log(10^{-9}) = -9\), we have:
\[ \text{pH} = -\log(6.2) + 9 \]

### Step 5: Calculate \(\log(6.2)\)
Using a calculator or logarithm table, we find:
\[ \log(6.2) \approx 0.792 \]

### Step 6: Substitute \(\log(6.2)\) back into the pH equation
Now substituting back:
\[ \text{pH} = -0.792 + 9 \]
\[ \text{pH} = 8.208 \]

### Step 7: Round the pH value
Rounding to two decimal places, we get:
\[ \text{pH} \approx 8.21 \]

### Final Answer
The pH value of the solution is approximately **8.21**.

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