The `P^(H)` of `HCl` is `5`, its is diluted by `1000` times Its `P^(H)` will be

Options

A. `5`
B. `8`
C. `2`
D. `7`

Explanation

To solve the problem, we need to determine the new pH of a diluted solution of HCl after it has been diluted 1000 times. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the initial pH
The initial pH of the HCl solution is given as 5. The pH is related to the concentration of hydrogen ions \([H^+]\) in the solution by the formula:
\[ \text{pH} = -\log[H^+] \]

### Step 2: Calculate the initial concentration of hydrogen ions
Using the initial pH, we can find the concentration of hydrogen ions:
\[ \text{pH} = 5 \implies [H^+] = 10^{-\text{pH}} = 10^{-5} \text{ M} \]

### Step 3: Dilute the solution
The solution is diluted 1000 times. When a solution is diluted, the concentration of the solute decreases. Therefore, the new concentration of hydrogen ions after dilution can be calculated as follows:
\[ [H^+]_{\text{new}} = \frac{[H^+]_{\text{initial}}}{1000} = \frac{10^{-5}}{1000} = 10^{-8} \text{ M} \]

### Step 4: Calculate the new pH
Now that we have the new concentration of hydrogen ions, we can calculate the new pH:
\[ \text{pH}_{\text{new}} = -\log[H^+]_{\text{new}} = -\log(10^{-8}) = 8 \]

### Conclusion
Thus, after diluting the HCl solution 1000 times, the new pH will be:
\[ \text{pH} = 8 \]

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