A sample of sour milk was found to be 0.1 M solution of lactic acid `CH_(3) CH(OH)CO OH`. What is the pH of the sample of milk ? `K_(a)` for lactic acid at `25^(@)C` is `1.37xx10^(-4)`.

Answer

To find the pH of a 0.1 M solution of lactic acid (CH₃CH(OH)COOH), we will follow these steps:

### Step 1: Identify the given values
- Concentration of lactic acid (C) = 0.1 M
- Acid dissociation constant (Kₐ) for lactic acid = 1.37 × 10⁻⁴

### Step 2: Use the formula for weak acids
For weak acids, the concentration of hydrogen ions [H⁺] can be calculated using the formula:
\[ [H^+] = \sqrt{K_a \times C} \]

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ [H^+] = \sqrt{1.37 \times 10^{-4} \times 0.1} \]

### Step 4: Calculate the value inside the square root
Calculating the product:
\[ 1.37 \times 10^{-4} \times 0.1 = 1.37 \times 10^{-5} \]

### Step 5: Take the square root
Now, we take the square root:
\[ [H^+] = \sqrt{1.37 \times 10^{-5}} \]
\[ [H^+] \approx 0.0037 \, \text{M} \]

### Step 6: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Substituting the value of [H⁺]:
\[ \text{pH} = -\log(0.0037) \]

### Step 7: Calculate the logarithm
Using a calculator:
\[ \text{pH} \approx 2.43 \]

### Final Answer
The pH of the sample of sour milk is approximately **2.43**.

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