`6ml` of `0.1M CH_(3)COOH` when mixed with `x` ml of `0.1 M NaOH` the `pH` of the resulting buffer solution was found to be `5.04`. The value of `x` is `(log2=0.3)pK_(a(CH_(3)COOH))=4.74`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the moles of acetic acid (CH₃COOH)
Given:
- Volume of acetic acid (CH₃COOH) = 6 mL
- Molarity of acetic acid = 0.1 M

To find the number of moles:
\[ \text{Number of moles of CH₃COOH} = \text{Volume (L)} \times \text{Molarity} = \frac{6 \, \text{mL}}{1000} \times 0.1 \, \text{M} = 0.0006 \, \text{mol} = 0.6 \, \text{mmol} \]

### Step 2: Set up the number of moles of NaOH
Let the volume of NaOH be \( x \) mL. The molarity of NaOH is also 0.1 M.

To find the number of moles of NaOH:
\[ \text{Number of moles of NaOH} = \frac{x \, \text{mL}}{1000} \times 0.1 \, \text{M} = \frac{x}{10} \, \text{mol} \]

### Step 3: Write the pH equation for the buffer solution
The pH of the buffer solution is given by the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
Where:
- pKa of acetic acid = 4.74
- pH = 5.04

### Step 4: Substitute values into the equation
We know that:
- The concentration of the salt (CH₃COO⁻) formed = \(\frac{x}{10}\)
- The concentration of acetic acid remaining = \(0.6 - \frac{x}{10}\)

Substituting into the Henderson-Hasselbalch equation:
\[ 5.04 = 4.74 + \log\left(\frac{\frac{x}{10}}{0.6 - \frac{x}{10}}\right) \]

### Step 5: Simplify the equation
Subtract 4.74 from both sides:
\[ 5.04 - 4.74 = \log\left(\frac{x/10}{0.6 - x/10}\right) \]
\[ 0.3 = \log\left(\frac{x/10}{0.6 - x/10}\right) \]

### Step 6: Convert the logarithmic equation to exponential form
Using the property of logarithms:
\[ \frac{x/10}{0.6 - x/10} = 2 \]

### Step 7: Solve for \( x \)
Cross-multiplying gives:
\[ x = 2(0.6 - \frac{x}{10}) \]
\[ x = 1.2 - \frac{2x}{10} \]
\[ x + \frac{2x}{10} = 1.2 \]
\[ \frac{10x + 2x}{10} = 1.2 \]
\[ \frac{12x}{10} = 1.2 \]
\[ 12x = 12 \quad \Rightarrow \quad x = 1 \]

### Step 8: Final answer
The value of \( x \) is 4 mL.