The ionization constant of a certain weak acid is `10^(-4)`. What should be the [salt] to [acid] ratio if we have to prepare a buffer with `pH = 5` using this acid and one of the salts

Options

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

Answer

To solve the problem of determining the [salt] to [acid] ratio for preparing a buffer with a pH of 5 using a weak acid with an ionization constant (Ka) of \(10^{-4}\), we can use the Henderson-Hasselbalch equation. Here’s the step-by-step solution:

### Step 1: Identify the given values
- The ionization constant of the weak acid (Ka) = \(10^{-4}\)
- The desired pH of the buffer = 5

### Step 2: Calculate pKa
The relationship between Ka and pKa is given by:
\[ pKa = -\log(Ka) \]
Substituting the given value of Ka:
\[ pKa = -\log(10^{-4}) = 4 \]

### Step 3: Use the Henderson-Hasselbalch equation
The Henderson-Hasselbalch equation is:
\[ pH = pKa + \log\left(\frac{[salt]}{[acid]}\right) \]
Substituting the known values:
\[ 5 = 4 + \log\left(\frac{[salt]}{[acid]}\right) \]

### Step 4: Rearrange the equation to find the ratio
Subtract 4 from both sides:
\[ 5 - 4 = \log\left(\frac{[salt]}{[acid]}\right) \]
This simplifies to:
\[ 1 = \log\left(\frac{[salt]}{[acid]}\right) \]

### Step 5: Convert the logarithmic equation to its exponential form
Using the property of logarithms, we can convert this to:
\[ \frac{[salt]}{[acid]} = 10^1 \]
Thus:
\[ \frac{[salt]}{[acid]} = 10 \]

### Step 6: State the final ratio
The ratio of [salt] to [acid] is:
\[ [salt] : [acid] = 10 : 1 \]

### Summary of the Solution
To prepare a buffer with a pH of 5 using the weak acid with an ionization constant of \(10^{-4}\), the ratio of salt to acid should be \(10:1\).

---