The pH of an aqueous solution containing `[H^(+)] = 3 xx 10^(-3) M` is

Options

A. 2.471
B. 2.523
C. 3
D. `-3`

Explanation

To find the pH of an aqueous solution with a hydrogen ion concentration of \([H^+] = 3 \times 10^{-3} \, M\), we can follow these steps:

### Step 1: Understand the pH formula
The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]

### Step 2: Substitute the given concentration into the formula
Given that \([H^+] = 3 \times 10^{-3} \, M\), we can substitute this value into the pH formula:
\[ \text{pH} = -\log(3 \times 10^{-3}) \]

### Step 3: Apply logarithmic properties
Using the properties of logarithms, we can separate the logarithm of the product:
\[ \text{pH} = -\log(3) - \log(10^{-3}) \]
Since \(\log(10^{-3}) = -3\), we can rewrite the equation as:
\[ \text{pH} = -\log(3) + 3 \]

### Step 4: Calculate \(-\log(3)\)
Using a calculator or logarithm table, we find:
\[ \log(3) \approx 0.477 \]
Thus,
\[ -\log(3) \approx -0.477 \]

### Step 5: Final calculation
Now, we can substitute this value back into the pH equation:
\[ \text{pH} = -0.477 + 3 = 2.523 \]

### Conclusion
Therefore, the pH of the solution is approximately:
\[ \text{pH} \approx 2.523 \]