The dissociation constant of a weak acid is `1 xx 10^(-4)`. In order of prepare a buffer solution with a pH =5 the [Salt]/[Acid] ratio should be

Options

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

Answer

To solve the problem of finding the [Salt]/[Acid] ratio for a buffer solution with a pH of 5, given the dissociation constant (Ka) of a weak acid as \(1 \times 10^{-4}\), we can follow these steps:

### Step 1: Calculate pKa
The dissociation constant \(K_a\) is given as \(1 \times 10^{-4}\). To find \(pK_a\), we use the formula:

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

Substituting the value of \(K_a\):

\[ pK_a = -\log(1 \times 10^{-4}) = -(-4) = 4 \]

### Step 2: Use the Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation relates pH, pKa, and the ratio of the concentrations of salt and acid:

\[ pH = pK_a + \log\left(\frac{[Salt]}{[Acid]}\right) \]

We know \(pH = 5\) and \(pK_a = 4\). Substituting these values into the equation gives:

\[ 5 = 4 + \log\left(\frac{[Salt]}{[Acid]}\right) \]

### Step 3: Rearrange the Equation
To isolate the log term, we can rearrange the equation:

\[ \log\left(\frac{[Salt]}{[Acid]}\right) = 5 - 4 = 1 \]

### Step 4: Exponentiate to Remove the Logarithm
To find the ratio of salt to acid, we exponentiate both sides:

\[ \frac{[Salt]}{[Acid]} = 10^1 = 10 \]

### Conclusion
Thus, the ratio of salt to acid is:

\[ \frac{[Salt]}{[Acid]} = 10:1 \]

### Final Answer
The ratio of [Salt]/[Acid] should be \(10:1\).

---