If the equlibrium constant for the reaction of weak acid HA with strong base is `10^(9)` then calculate the pH of 0.1 M NaA.

Answer

To calculate the pH of a 0.1 M NaA solution, we can follow these steps:

### Step 1: Understand the reaction and equilibrium constant
The weak acid HA dissociates in water as follows:
\[ HA \rightleftharpoons H^+ + A^- \]
When a strong base (like NaOH) is added, it reacts with the weak acid HA, shifting the equilibrium to the right and producing more A^-. The equilibrium constant for this reaction is given as \( K = 10^9 \).

### Step 2: Relate the equilibrium constant to \( K_a \) and \( K_w \)
The equilibrium constant \( K \) for the reaction of the weak acid with the strong base can be expressed as:
\[ K = \frac{K_a}{K_w} \]
where:
- \( K_a \) is the acid dissociation constant of HA,
- \( K_w \) is the ion product of water, which at 25°C is \( 1 \times 10^{-14} \).

Given \( K = 10^9 \), we can rearrange this to find \( K_a \):
\[ K_a = K \times K_w = 10^9 \times 10^{-14} = 10^{-5} \]

### Step 3: Calculate \( pK_a \)
Now, we can find \( pK_a \):
\[ pK_a = -\log(K_a) = -\log(10^{-5}) = 5 \]

### Step 4: Use the Henderson-Hasselbalch equation
For a salt solution like NaA, we can use the Henderson-Hasselbalch equation to find the pH:
\[ pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) \]
In this case, since NaA completely dissociates in solution, we can assume:
- \([A^-] = 0.1 \, M\)
- \([HA] \approx 0\) (since it is a weak acid and is mostly converted to A^-)

Thus, we can simplify the equation:
\[ pH = pK_a + \log(0.1) \]

### Step 5: Substitute values into the equation
Substituting the values we have:
\[ pH = 5 + \log(0.1) \]
Since \(\log(0.1) = -1\):
\[ pH = 5 - 1 = 4 \]

### Step 6: Final calculation
Thus, the pH of the 0.1 M NaA solution is:
\[ pH = 4 \]

### Summary of Steps
1. Identify the reaction and equilibrium constant.
2. Relate the equilibrium constant to \( K_a \) and \( K_w \).
3. Calculate \( pK_a \).
4. Use the Henderson-Hasselbalch equation.
5. Substitute values and simplify.