When one drop of a concentrated `HC1` is added to `1L` of pure water at `25^(@)C`, the `pH` drops suddenly from `7` to `4`. When the second drop of the same acid is added, the `pH` of the solution further drops to about

Options

A. `0`
B. `1.0`
C. `2.0`
D. `3.7`

Explanation

To solve the problem step by step, we will analyze the situation of adding hydrochloric acid (HCl) to pure water and how it affects the pH.

### Step 1: Understand the Initial pH
The initial pH of pure water at 25°C is 7. This means that the concentration of hydrogen ions \([H^+]\) in pure water is:
\[ [H^+] = 10^{-7} \, \text{M} \]

### Step 2: Calculate the Change in pH After Adding the First Drop of HCl
When one drop of concentrated HCl is added, the pH drops to 4. We can calculate the new concentration of hydrogen ions:
\[ [H^+] = 10^{-4} \, \text{M} \]

### Step 3: Determine the Change in Hydrogen Ion Concentration
Now, we need to find out how much hydrogen ion concentration has increased due to the addition of HCl. The increase in \([H^+]\) can be calculated as:
\[ \Delta [H^+] = [H^+]_{\text{new}} - [H^+]_{\text{initial}} = 10^{-4} - 10^{-7} \]
To simplify this, we can factor out \(10^{-4}\):
\[ \Delta [H^+] = 10^{-4} \left(1 - 0.001\right) \approx 10^{-4} \, \text{M} \]

### Step 4: Calculate the Total Hydrogen Ion Concentration After the Second Drop
When the second drop of HCl is added, it will add another \(10^{-4} \, \text{M}\) of hydrogen ions. Therefore, the total concentration of hydrogen ions becomes:
\[ [H^+]_{\text{total}} = [H^+]_{\text{new}} + \Delta [H^+] = 10^{-4} + 10^{-4} = 2 \times 10^{-4} \, \text{M} \]

### Step 5: Calculate the New pH
Now, we can calculate the new pH using the total hydrogen ion concentration:
\[ \text{pH} = -\log[H^+]_{\text{total}} = -\log(2 \times 10^{-4}) \]
Using the logarithmic property:
\[ \text{pH} = -\log(2) - \log(10^{-4}) = -\log(2) + 4 \]
Since \(-\log(2) \approx -0.301\):
\[ \text{pH} \approx 4 - 0.301 = 3.699 \approx 3.7 \]

### Conclusion
After adding the second drop of concentrated HCl, the pH of the solution drops to approximately **3.7**.

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