Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH 6. if ionization constant of HA is `10^(-5)`, the ratio of salt to acid concentration in the buffer solution will be:

Options

A. `10:1`
B. `4:5`
C. `5:4`
D. `1:10`

Answer

To solve the problem step by step, we will use the information provided and the relevant equations for buffer solutions.

### Step 1: Understand the given information
We have a weak acid (HA) with an ionization constant \( K_a = 10^{-5} \) and the pH of the buffer solution is given as 6.

### Step 2: Calculate the pKa
The pKa can be calculated using the formula:
\[ pK_a = -\log(K_a) \]
Substituting the value of \( K_a \):
\[ pK_a = -\log(10^{-5}) = 5 \]

### Step 3: Use the Henderson-Hasselbalch equation
The Henderson-Hasselbalch equation for a buffer solution is given by:
\[ pH = pK_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
We know:
- \( pH = 6 \)
- \( pK_a = 5 \)

### Step 4: Substitute the values into the equation
Substituting the known values into the equation:
\[ 6 = 5 + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]

### Step 5: Rearranging the equation
Rearranging the equation to isolate the logarithmic term:
\[ \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) = 6 - 5 = 1 \]

### Step 6: Exponentiate to remove the logarithm
To remove the logarithm, we exponentiate both sides:
\[ \frac{[\text{Salt}]}{[\text{Acid}]} = 10^1 = 10 \]

### Step 7: Conclusion
Thus, the ratio of salt to acid concentration in the buffer solution is:
\[ \frac{[\text{Salt}]}{[\text{Acid}]} = 10:1 \]

### Final Answer
The ratio of salt to acid concentration in the buffer solution is **10:1**.

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