`200ml` of `1 M CH_(3)COOH(K_(a)=10^(-6))` is mixed with `200ml` of `0.1M HCOOH(K_(a)=10^(-5))`. The `pH` of the resulting mixture is

Explanation

To find the pH of the resulting mixture of acetic acid (CH₃COOH) and formic acid (HCOOH), we will follow these steps:

### Step 1: Calculate the concentration of CH₃COOH in the mixture.
- We have 200 mL of 1 M CH₃COOH.
- When mixed with 200 mL of another solution, the total volume becomes 400 mL.
- The concentration of CH₃COOH in the mixture can be calculated as follows:

\[ \text{Concentration of CH₃COOH} = \frac{200 \, \text{mL} \times 1 \, \text{M}}{400 \, \text{mL}} = 0.5 \, \text{M} \]

### Step 2: Calculate the concentration of HCOOH in the mixture.
- We have 200 mL of 0.1 M HCOOH.
- The concentration of HCOOH in the mixture is calculated as:

\[ \text{Concentration of HCOOH} = \frac{200 \, \text{mL} \times 0.1 \, \text{M}}{400 \, \text{mL}} = 0.05 \, \text{M} \]

### Step 3: Calculate the H⁺ ion concentration from both acids.
- The dissociation of weak acids can be approximated using their \( K_a \) values.
- For CH₃COOH, \( K_a = 10^{-6} \) and for HCOOH, \( K_a = 10^{-5} \).

Using the formula for the concentration of H⁺ ions from weak acids:

\[ [H^+] = \sqrt{K_a \cdot [HA]} \]

For CH₃COOH:

\[ [H^+]_{CH₃COOH} = \sqrt{10^{-6} \cdot 0.5} = \sqrt{5 \times 10^{-7}} \approx 7.07 \times 10^{-4} \, \text{M} \]

For HCOOH:

\[ [H^+]_{HCOOH} = \sqrt{10^{-5} \cdot 0.05} = \sqrt{5 \times 10^{-7}} \approx 7.07 \times 10^{-4} \, \text{M} \]

### Step 4: Calculate the total H⁺ concentration.
Since both acids contribute to the H⁺ concentration, we can add the contributions:

\[ [H^+]_{total} = [H^+]_{CH₃COOH} + [H^+]_{HCOOH} \approx 7.07 \times 10^{-4} + 7.07 \times 10^{-4} = 1.414 \times 10^{-3} \, \text{M} \]

### Step 5: Calculate the pH of the mixture.
Using the formula for pH:

\[ pH = -\log[H^+] \]

Substituting the total H⁺ concentration:

\[ pH = -\log(1.414 \times 10^{-3}) \approx 2.85 \]

### Final Answer:
The pH of the resulting mixture is approximately **2.85**.

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