If the `pK_(a)` of a weak and acid HA is 4.80 and the `pK_(b)` of a weak base `BOH` is 4.78. Then, the pH of an aqeuous solution of the corresponding salt, BA will be

Options

A. 8.23
B. 9.41
C. 7.01
D. 5.91

Answer

To find the pH of an aqueous solution of the salt BA formed from the weak acid HA and the weak base BOH, we can use the following steps:

### Step 1: Understand the relationship between pKa and pKb
The pKa of the weak acid HA is given as 4.80, and the pKb of the weak base BOH is given as 4.78. The relationship between pKa and pKb for a conjugate acid-base pair is important for calculating the pH of the resulting salt solution.

### Step 2: Use the formula for pH of a salt solution
For a solution of a salt formed from a weak acid and a weak base, the pH can be calculated using the formula:
\[ \text{pH} = 7 + \frac{1}{2}(\text{pKa} - \text{pKb}) \]

### Step 3: Substitute the values into the formula
Now, we can substitute the given values of pKa and pKb into the formula:
- pKa = 4.80
- pKb = 4.78

Substituting these values:
\[ \text{pH} = 7 + \frac{1}{2}(4.80 - 4.78) \]

### Step 4: Calculate the difference and divide by 2
Calculate the difference:
\[ 4.80 - 4.78 = 0.02 \]
Now, divide this difference by 2:
\[ \frac{0.02}{2} = 0.01 \]

### Step 5: Add the result to 7
Finally, add this value to 7 to find the pH:
\[ \text{pH} = 7 + 0.01 = 7.01 \]

### Final Answer
The pH of the aqueous solution of the salt BA is **7.01**.

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