The concentration of hydrogen ion in a sample of soft drink is `3.8xx10^(-3) M`. What is its `pH`?

Options

A. a. 3.8
B. b. 5.04
C. c. 2.42
D. d.9.2

Explanation

To find the pH of a solution given the concentration of hydrogen ions, we can use the formula:

\[ \text{pH} = -\log[\text{H}^+] \]

where \([\text{H}^+]\) is the concentration of hydrogen ions in moles per liter (M).

### Step-by-Step Solution:

1. **Identify the concentration of hydrogen ions**:
The concentration of hydrogen ions in the soft drink is given as:
\[ [\text{H}^+] = 3.8 \times 10^{-3} \, \text{M} \]

2. **Apply the pH formula**:
Substitute the concentration into the pH formula:
\[ \text{pH} = -\log(3.8 \times 10^{-3}) \]

3. **Break down the logarithm**:
Using the properties of logarithms, we can separate the terms:
\[ \text{pH} = -\log(3.8) - \log(10^{-3}) \]
Since \(\log(10^{-3}) = -3\), we can rewrite it as:
\[ \text{pH} = -\log(3.8) + 3 \]

4. **Calculate \(-\log(3.8)\)**:
Using a calculator or logarithm table, we find:
\[ \log(3.8) \approx 0.5797 \]
Therefore:
\[ -\log(3.8) \approx -0.5797 \]

5. **Combine the results**:
Now substitute back into the pH equation:
\[ \text{pH} = -0.5797 + 3 \]
\[ \text{pH} \approx 2.4203 \]

6. **Round the pH value**:
We can round the pH value to two decimal places:
\[ \text{pH} \approx 2.42 \]

### Final Answer:
The pH of the soft drink is approximately **2.42**.