The pH of a solution is 5.0 To this solution sufficient acid is added to decreases the pH to 2.0. The no. of times the concentration of `H^(+)` increased is

Answer

To solve the problem, we need to determine how many times the concentration of hydrogen ions \([H^+]\) increased when the pH of a solution changed from 5.0 to 2.0.

### Step-by-Step Solution:

1. **Understanding pH and Hydrogen Ion Concentration**:
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
This means that the concentration of hydrogen ions can be calculated using the formula:
\[ [H^+] = 10^{-\text{pH}} \]

2. **Calculating Initial Hydrogen Ion Concentration**:
When the pH is 5.0:
\[ [H^+] = 10^{-5} \, \text{M} \]

3. **Calculating Final Hydrogen Ion Concentration**:
When the pH is decreased to 2.0:
\[ [H^+] = 10^{-2} \, \text{M} \]

4. **Finding the Increase in Concentration**:
To find out how many times the concentration of \([H^+]\) increased, we will divide the final concentration by the initial concentration:
\[ \text{Increase Factor} = \frac{[H^+] \text{ (at pH 2.0)}}{[H^+] \text{ (at pH 5.0)}} = \frac{10^{-2}}{10^{-5}} \]

5. **Calculating the Increase Factor**:
Simplifying the fraction:
\[ \text{Increase Factor} = 10^{-2 + 5} = 10^{3} = 1000 \]

6. **Conclusion**:
Therefore, the concentration of \([H^+]\) increased by **1000 times**.

### Final Answer:
The number of times the concentration of \(H^+\) increased is **1000**.

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