Useful buffer range of weak acid `HA(K_(a)=10^(-5))` is :

Options

A. 5 to 7
B. 4 to 6
C. 3 to 6
D. None of these

Answer

To determine the useful buffer range of the weak acid \( HA \) with a dissociation constant \( K_a = 10^{-5} \), we can follow these steps:

### Step 1: Calculate \( pK_a \)
The first step is to calculate the \( pK_a \) value from the given \( K_a \) value. The formula to find \( pK_a \) is:

\[ pK_a = -\log(K_a) \]

Substituting the given \( K_a \):

\[ pK_a = -\log(10^{-5}) = 5 \]

### Step 2: Understand the Buffer Range
A buffer solution is effective in resisting pH changes when the concentrations of the weak acid and its conjugate base are within a certain ratio. The useful buffer range can be approximated using the Henderson-Hasselbalch equation:

\[ pH = pK_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]

Where:
- \( [\text{A}^-] \) is the concentration of the conjugate base
- \( [\text{HA}] \) is the concentration of the weak acid

### Step 3: Determine the Lower Limit of the Buffer Range
To find the lower limit of the buffer range, we can consider the ratio of the concentrations of the conjugate base to the weak acid as \( \frac{1}{10} \):

\[ pH = pK_a + \log\left(\frac{1}{10}\right) \]

Substituting \( pK_a = 5 \):

\[ pH = 5 + \log(0.1) = 5 - 1 = 4 \]

### Step 4: Determine the Upper Limit of the Buffer Range
For the upper limit, we consider the ratio of the concentrations of the conjugate base to the weak acid as \( 10 \):

\[ pH = pK_a + \log(10) \]

Substituting \( pK_a = 5 \):

\[ pH = 5 + \log(10) = 5 + 1 = 6 \]

### Conclusion
Thus, the useful buffer range for the weak acid \( HA \) is from \( pH = 4 \) to \( pH = 6 \).

### Final Answer
The useful buffer range of weak acid \( HA (K_a = 10^{-5}) \) is **4 to 6**.

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