What amount of solid acetate should be added into 1 litre of the `0.1 M CH_(3)COOH` solution so that the resulting solution has pH almost equal to `pK_(a) (CH_(3)COOH) = 4.74`.

Options

A. `12 gm`
B. `5 gm`
C. `10 gm `
D. `14.924 gm`

Explanation

To solve the problem of how much solid acetate should be added to 1 liter of a 0.1 M CH₃COOH solution to achieve a pH of approximately 4.74, we can follow these steps:

### Step 1: Understand the Buffer System
We are dealing with a buffer solution made from a weak acid (acetic acid, CH₃COOH) and its conjugate base (acetate, CH₃COO⁻). The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
where \([\text{A}^-]\) is the concentration of the conjugate base (acetate) and \([\text{HA}]\) is the concentration of the weak acid (acetic acid).

### Step 2: Set Up the Equation
Given:
- pKₐ (CH₃COOH) = 4.74
- pH = 4.74
- \([\text{HA}] = 0.1 \, \text{M}\)

We can substitute these values into the Henderson-Hasselbalch equation:
\[ 4.74 = 4.74 + \log\left(\frac{[\text{A}^-]}{0.1}\right) \]

### Step 3: Simplify the Equation
Since both sides of the equation have 4.74, we can simplify:
\[ 0 = \log\left(\frac{[\text{A}^-]}{0.1}\right) \]

### Step 4: Solve for the Concentration of Acetate
The logarithm equals zero when the argument is 1:
\[ \frac{[\text{A}^-]}{0.1} = 1 \]
This implies:
\[ [\text{A}^-] = 0.1 \, \text{M} \]

### Step 5: Calculate the Number of Moles of Acetate Required
Since we are preparing 1 liter of solution:
\[ \text{Number of moles of acetate (n)} = [\text{A}^-] \times \text{Volume} = 0.1 \, \text{M} \times 1 \, \text{L} = 0.1 \, \text{moles} \]

### Step 6: Calculate the Mass of Sodium Acetate Needed
The molar mass of sodium acetate (CH₃COONa) is approximately 82 g/mol. Therefore, the mass of sodium acetate required is:
\[ \text{Mass} = n \times \text{Molar mass} = 0.1 \, \text{moles} \times 82 \, \text{g/mol} = 8.2 \, \text{g} \]

### Final Answer
To achieve a pH of approximately 4.74, you should add **8.2 grams** of solid sodium acetate to the 1 liter of 0.1 M CH₃COOH solution.

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