In a solution of pH = 5, more acid is added in order to reduce the pH = 2. The increase in hydrogen ions concentration is

Options

A. 100 times
B. 1000 times
C. 3 times
D. 5 times.

Explanation

To solve the problem, we need to determine the increase in hydrogen ion concentration when the pH of a solution changes from 5 to 2.

### Step-by-Step Solution:

1. **Understand the pH scale**: The pH scale is a measure of the acidity or basicity of a solution. It is defined as:
\[ \text{pH} = -\log[\text{H}^+] \]
where \([\text{H}^+]\) is the concentration of hydrogen ions in moles per liter.

2. **Calculate the initial hydrogen ion concentration at pH = 5**:
\[ \text{pH} = 5 \implies [\text{H}^+] = 10^{-5} \, \text{mol/L} \]

3. **Calculate the hydrogen ion concentration at pH = 2**:
\[ \text{pH} = 2 \implies [\text{H}^+] = 10^{-2} \, \text{mol/L} \]

4. **Determine the increase in hydrogen ion concentration**:
To find the increase in hydrogen ion concentration, we subtract the initial concentration from the final concentration:
\[ \text{Increase} = [\text{H}^+]_{\text{final}} - [\text{H}^+]_{\text{initial}} = 10^{-2} - 10^{-5} \]
Since \(10^{-2}\) is much larger than \(10^{-5}\), we can approximate:
\[ \text{Increase} \approx 10^{-2} \, \text{mol/L} \]

5. **Calculate the factor of increase**:
To find out how many times the concentration has increased, we can divide the final concentration by the initial concentration:
\[ \text{Factor of increase} = \frac{[\text{H}^+]_{\text{final}}}{[\text{H}^+]_{\text{initial}}} = \frac{10^{-2}}{10^{-5}} = 10^{3} = 1000 \]

Thus, the increase in hydrogen ion concentration is 1000 times.

### Final Answer:
The increase in hydrogen ion concentration is **1000 times**.