The composition of an acidic buffer mixture made up of HA and NaA of total molarity `0.29` having `pH=4.4` and `K_(a)=1.8xx10^(-5)` in terms of concentration of salt and acid respectively is:

Options

A. `0.09M and 0.20M`
B. `0.20M and 0.09M`
C. `0.1M and 0.19M`
D. `0.19M and 0.10M`

Explanation

To solve the problem of finding the composition of an acidic buffer mixture made up of HA (acid) and NaA (salt) with a total molarity of 0.29, pH of 4.4, and \( K_a = 1.8 \times 10^{-5} \), we can follow these steps:

### Step 1: Calculate \( pK_a \)
The first step is to calculate \( pK_a \) from the given \( K_a \):
\[ pK_a = -\log(K_a) = -\log(1.8 \times 10^{-5}) \]
Calculating this gives:
\[ pK_a \approx 4.74 \]

### Step 2: Use the Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation for an acidic buffer is given by:
\[ pH = pK_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
Substituting the known values:
\[ 4.4 = 4.74 + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]

### Step 3: Rearranging the Equation
Rearranging the equation to isolate the log term:
\[ \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) = 4.4 - 4.74 = -0.34 \]

### Step 4: Exponentiating to Remove the Logarithm
Exponentiating both sides to eliminate the logarithm:
\[ \frac{[\text{A}^-]}{[\text{HA}]} = 10^{-0.34} \approx 0.46 \]

### Step 5: Set Up the Concentration Relationships
Let the concentration of the salt (NaA) be \( [\text{A}^-] = A \) and the concentration of the acid (HA) be \( [\text{HA}] = 0.29 - A \). Thus, we can write:
\[ \frac{A}{0.29 - A} = 0.46 \]

### Step 6: Solve for A
Cross-multiplying gives:
\[ A = 0.46(0.29 - A) \]
Expanding this:
\[ A = 0.1334 - 0.46A \]
Combining like terms:
\[ A + 0.46A = 0.1334 \]
\[ 1.46A = 0.1334 \]
\[ A \approx \frac{0.1334}{1.46} \approx 0.0913 \]

### Step 7: Calculate Concentration of Acid
Now, substituting back to find the concentration of the acid:
\[ [\text{HA}] = 0.29 - A \approx 0.29 - 0.0913 \approx 0.1987 \]

### Final Answer
Thus, the concentrations of the salt and acid in the buffer mixture are approximately:
- Concentration of salt (NaA): \( 0.0913 \, \text{M} \)
- Concentration of acid (HA): \( 0.1987 \, \text{M} \)

### Summary
The composition of the acidic buffer mixture is:
- Salt (NaA): \( 0.0913 \, \text{M} \)
- Acid (HA): \( 0.1987 \, \text{M} \)