When the hydrogen ion concentration `[H^(+)]` changes by a factor of `1000`,the value of `pH` of the solution____.

Options

A. decreases by `3` units
B. decreases by `2` units
C. increases by `3` units
D. increases by `1000` units

Answer

To solve the problem of how the pH changes when the hydrogen ion concentration \([H^+]\) changes by a factor of 1000, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding pH**:
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
This means that pH is the negative logarithm of the hydrogen ion concentration.

2. **Initial Concentration**:
Let’s assume the initial concentration of hydrogen ions is \([H^+] = x\).

3. **Change in Concentration**:
If the concentration changes by a factor of 1000, the new concentration will be:
\[ [H^+] = 1000x = 10^3 x \]

4. **Calculating Initial pH**:
The initial pH can be calculated as:
\[ \text{pH}_{\text{initial}} = -\log(x) \]

5. **Calculating New pH**:
The new pH after the concentration change will be:
\[ \text{pH}_{\text{new}} = -\log(10^3 x) \]
Using the properties of logarithms, we can expand this:
\[ \text{pH}_{\text{new}} = -\log(10^3) - \log(x) = -3 - \log(x) \]
Thus, we can express the new pH in terms of the initial pH:
\[ \text{pH}_{\text{new}} = -3 + \text{pH}_{\text{initial}} \]

6. **Change in pH**:
The change in pH (\(\Delta \text{pH}\)) can be calculated as:
\[ \Delta \text{pH} = \text{pH}_{\text{new}} - \text{pH}_{\text{initial}} = (-3 + \text{pH}_{\text{initial}}) - \text{pH}_{\text{initial}} = -3 \]

7. **Conclusion**:
This indicates that the pH decreases by 3 units when the hydrogen ion concentration increases by a factor of 1000.

### Final Answer:
The value of pH of the solution decreases by 3 units.

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