Which of the following solutions when added to 1L of a 0.1 M `CH_3COOH` will cause no change in the pH of the solution `K_a=1.8xx10^(-5)` for `CH_3COOH`?

Options

A. `3 mM HCOOH (K_a=6xx10^(-4))`
B. `0.1 M CH_3COONa`
C. `1.34 mM HCl`
D. `0.1 M CH_3COOH`

Explanation

To solve the problem, we need to determine which of the given solutions, when added to 1L of a 0.1 M CH₃COOH solution, will not change the pH of the solution. The dissociation constant (Kₐ) for acetic acid (CH₃COOH) is given as 1.8 x 10^(-5).

### Step-by-Step Solution:

1. **Calculate the concentration of hydrogen ions in the 0.1 M CH₃COOH solution**:
The concentration of hydrogen ions can be calculated using the formula:
\[ [H^+] = \sqrt{K_a \times C} \]
where \( K_a = 1.8 \times 10^{-5} \) and \( C = 0.1 \, \text{M} \).

\[ [H^+] = \sqrt{1.8 \times 10^{-5} \times 0.1} = \sqrt{1.8 \times 10^{-6}} \approx 1.34 \times 10^{-3} \, \text{M} \]

2. **Determine the conditions for no change in pH**:
For the pH to remain unchanged, any solution added must not increase the hydrogen ion concentration above \( 1.34 \times 10^{-3} \, \text{M} \).

3. **Analyze each solution option**:
- **Option 1: 3 millimolar HCOOH**:
- Calculate the \( [H^+] \):
\[ [H^+] = \sqrt{K_a \times C} = \sqrt{6 \times 10^{-4} \times 3 \times 10^{-3}} = \sqrt{1.8 \times 10^{-6}} \approx 1.34 \times 10^{-3} \, \text{M} \]
- This is equal to the original \( [H^+] \), hence **no change in pH**.

- **Option 2: 0.1 M CH₃COONa**:
- This will create a buffer solution. The pH will be calculated using the Henderson-Hasselbalch equation:
\[ pH = pK_a + \log\left(\frac{[Salt]}{[Acid]}\right) \]
- Since both salt and acid are 0.1 M, the pH will change from the original pH of the acetic acid solution. Thus, **change in pH** occurs.

- **Option 3: 1.34 millimolar HCl**:
- Since HCl is a strong acid, it will dissociate completely:
\[ [H^+] = 1.34 \times 10^{-3} \, \text{M} \]
- This is equal to the original \( [H^+] \), hence **no change in pH**.

- **Option 4: 0.1 M CH₃COOH**:
- Adding more of the same weak acid does not change the concentration of \( [H^+] \):
\[ [H^+] = 1.34 \times 10^{-3} \, \text{M} \]
- Thus, **no change in pH**.

4. **Conclusion**:
The solutions that cause no change in pH are:
- Option 1: 3 millimolar HCOOH
- Option 3: 1.34 millimolar HCl
- Option 4: 0.1 M CH₃COOH

### Final Answer:
The correct options are 1, 3, and 4.

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