The concentration of hydrogen ion in a sample of soft drink is `3.8 xx 10^(-3)M`. What is its `pH`?

Explanation

To find the pH of a soft drink with a hydrogen ion concentration of \(3.8 \times 10^{-3} \, M\), we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify the Given Concentration**:
From the problem, we know that:
\[ [H^+] = 3.8 \times 10^{-3} \, M \]

3. **Substitute the Concentration into the pH Formula**:
Plug the value of \([H^+]\) into the pH formula:
\[ \text{pH} = -\log(3.8 \times 10^{-3}) \]

4. **Break Down the Logarithm**:
We can separate the logarithm into two parts:
\[ \text{pH} = -\log(3.8) - \log(10^{-3}) \]
Since \(\log(10^{-3}) = -3\), we have:
\[ \text{pH} = -\log(3.8) + 3 \]

5. **Calculate \(-\log(3.8)\)**:
Using a calculator or logarithm table, we find:
\[ \log(3.8) \approx 0.58 \]
Therefore:
\[ -\log(3.8) \approx -0.58 \]

6. **Combine the Results**:
Now substitute back into the pH equation:
\[ \text{pH} = -0.58 + 3 = 2.42 \]

7. **Final Answer**:
The pH of the soft drink is:
\[ \text{pH} \approx 2.42 \]