The dissociation constant of a substituted benzoic acid at `25^@C` is `1.0 xx 10^(-4)`, Calculate pH of a 0.01 M solution of its sodium salt.

Answer

To calculate the pH of a 0.01 M solution of the sodium salt of a substituted benzoic acid, we can follow these steps:

### Step 1: Determine the pKa of the substituted benzoic acid
The dissociation constant (Ka) of the substituted benzoic acid is given as \(1.0 \times 10^{-4}\).

To find pKa, we use the formula:
\[ \text{pKa} = -\log(\text{Ka}) \]

Substituting the value of Ka:
\[ \text{pKa} = -\log(1.0 \times 10^{-4}) = 4 \]

### Step 2: Use the formula for pH of the sodium salt solution
Since the sodium salt of the substituted benzoic acid is a weak acid and strong base salt, we can use the following formula to calculate the pH:
\[ \text{pH} = 7 + \frac{1}{2} \text{pKa} + \frac{1}{2} \log C \]
where \(C\) is the concentration of the sodium salt solution.

Given that the concentration \(C = 0.01 \, \text{M}\), we can substitute the values into the formula.

### Step 3: Calculate the log of the concentration
First, calculate \(\log C\):
\[ \log(0.01) = \log(10^{-2}) = -2 \]

### Step 4: Substitute values into the pH formula
Now substituting the values into the pH formula:
\[ \text{pH} = 7 + \frac{1}{2} \times 4 + \frac{1}{2} \times (-2) \]
\[ \text{pH} = 7 + 2 - 1 = 8 \]

### Final Answer
The pH of a 0.01 M solution of the sodium salt of the substituted benzoic acid is **8**.

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