A buffer solution is made by mixing a weak acid HA `(K_(a) =10^(-6))` with its salt NaA in equal amounts. What should be amount of acid or salt that should be added to make 90 mL of buffer solution in which if 0.1 mole of strong acid are added into 1 L of this buffer solution then change in pH is unity ?

Explanation

To solve the problem, we need to determine the amount of weak acid (HA) and its salt (NaA) required to prepare a buffer solution that can withstand the addition of 0.1 moles of strong acid without changing the pH by more than one unit.

### Step-by-Step Solution:

1. **Understanding Buffer Solutions**: A buffer solution consists of a weak acid and its conjugate base. The weak acid (HA) will react with added strong acid (H⁺), while the conjugate base (A⁻) will react with any added strong base (OH⁻).

2. **Given Data**:
- \( K_a \) of the weak acid (HA) = \( 10^{-6} \)
- Volume of buffer solution = 90 mL
- Amount of strong acid added = 0.1 moles
- Change in pH = 1 unit

3. **Using the Henderson-Hasselbalch Equation**: The pH of a buffer solution can be expressed using the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
where \( \text{pK}_a = -\log(K_a) = -\log(10^{-6}) = 6 \).

4. **Calculating Moles of Acid and Base**:
- To maintain a pH change of 1 unit, we need to calculate the moles of HA and A⁻ required.
- For a buffer to resist a pH change of 1 unit upon addition of 0.1 moles of strong acid, we can use the formula:
\[ \Delta \text{pH} = \frac{[\text{HA}] + [\text{A}^-]}{[\text{H}^+]} \]
where \( [\text{H}^+] \) is the concentration of the added strong acid.

5. **Calculating Concentrations**:
- The total volume of the buffer solution is 90 mL or 0.09 L.
- The concentration of the added strong acid in 1 L of buffer solution is \( 0.1 \, \text{moles} \) in \( 1 \, \text{L} \) = \( 0.1 \, \text{M} \).

6. **Setting Up the Equation**:
- For a change in pH of 1 unit, we need:
\[ [\text{HA}] + [\text{A}^-] = 0.1 \, \text{moles} \]

7. **Calculating Moles for 90 mL**:
- The total moles of HA and A⁻ needed for the buffer solution can be calculated as:
\[ \text{Total moles} = 0.1 \, \text{moles} \times \frac{90 \, \text{mL}}{1000 \, \text{mL}} = 0.009 \, \text{moles} \]

8. **Final Calculation**:
- Since we need equal amounts of HA and NaA, we divide the total moles by 2:
\[ \text{Moles of HA} = \text{Moles of NaA} = \frac{0.009}{2} = 0.0045 \, \text{moles} \]

### Conclusion:
To prepare 90 mL of buffer solution, you need to add 0.0045 moles of the weak acid (HA) and 0.0045 moles of its salt (NaA).