pH of 0.005 M calcium acetate `(pK_a" of " CH_3COOH= 4.74) ` is

Options

A. ` 7.04`
B. ` 9.37`
C. ` 9.26`
D. ` 8.37 `

Explanation

To find the pH of a 0.005 M calcium acetate solution, we can follow these steps:

### Step 1: Understand the Dissociation of Calcium Acetate
Calcium acetate (Ca(CH₃COO)₂) dissociates in water to give calcium ions (Ca²⁺) and acetate ions (CH₃COO⁻):
\[ \text{Ca(CH}_3\text{COO)}_2 \rightarrow \text{Ca}^{2+} + 2 \text{CH}_3\text{COO}^- \]

### Step 2: Calculate the Concentration of Acetate Ions
Since one mole of calcium acetate produces two moles of acetate ions, the concentration of acetate ions will be:
\[ [\text{CH}_3\text{COO}^-] = 2 \times 0.005 \, \text{M} = 0.01 \, \text{M} \]

### Step 3: Use the Henderson-Hasselbalch Equation
To find the pH of the solution, we can use the Henderson-Hasselbalch equation for a weak acid and its conjugate base:
\[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \]

Here, \(\text{A}^-\) is the acetate ion (the conjugate base) and \(\text{HA}\) is acetic acid (the weak acid).

### Step 4: Determine the pK_a and Concentrations
We are given:
- \( \text{pK}_a \) of acetic acid (CH₃COOH) = 4.74
- Concentration of acetate ions, \( [\text{A}^-] = 0.01 \, \text{M} \)
- Since we are considering the acetate ions in a solution of calcium acetate, we can assume that the concentration of acetic acid is negligible compared to the acetate ions.

### Step 5: Substitute Values into the Equation
Since the concentration of acetic acid is negligible, we can approximate it as:
\[ \text{pH} = 7 + \frac{\text{pK}_a}{2} + \log \left( \frac{C}{2} \right) \]
Where \( C \) is the concentration of acetate ions.

Substituting the values:
\[ \text{pH} = 7 + \frac{4.74}{2} + \log(0.01) \]

### Step 6: Calculate Each Component
1. Calculate \( \frac{4.74}{2} = 2.37 \)
2. Calculate \( \log(0.01) = -2 \)

### Step 7: Combine the Results
Now substitute back into the pH equation:
\[ \text{pH} = 7 + 2.37 - 1 \]
\[ \text{pH} = 8.37 \]

### Final Answer
The pH of the 0.005 M calcium acetate solution is **8.37**.

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