The dessociation cosntants of acetic acid and propionic acid are `1.0 xx 10^(-5)` and `1.0 xx 10^(-6)` respectively. The value of `P^(K_(a))` (propionic acid) - `P^(K_(a))` (Acetic acid) is

Options

A. 10
B. `10^(-1)`
C. 1
D. `-1.0`

Answer

To solve the problem, we need to calculate the pKa values for both acetic acid and propionic acid using their dissociation constants (Ka) and then find the difference between these two pKa values.

### Step-by-Step Solution:

1. **Identify the given values**:
- Dissociation constant of acetic acid (Ka_acetic) = \(1.0 \times 10^{-5}\)
- Dissociation constant of propionic acid (Ka_propionic) = \(1.0 \times 10^{-6}\)

2. **Calculate pKa of propionic acid**:
- The formula for pKa is given by:
\[ pKa = -\log(Ka) \]
- For propionic acid:
\[ pKa_{\text{propionic}} = -\log(1.0 \times 10^{-6}) \]
- This can be simplified as:
\[ pKa_{\text{propionic}} = -(-6 \log(10)) = 6 \]

3. **Calculate pKa of acetic acid**:
- Using the same formula:
\[ pKa_{\text{acetic}} = -\log(1.0 \times 10^{-5}) \]
- Simplifying this gives:
\[ pKa_{\text{acetic}} = -(-5 \log(10)) = 5 \]

4. **Find the difference between pKa of propionic acid and pKa of acetic acid**:
- Now, we calculate the difference:
\[ pKa_{\text{propionic}} - pKa_{\text{acetic}} = 6 - 5 = 1 \]

5. **Conclusion**:
- The value of \( pKa_{\text{propionic}} - pKa_{\text{acetic}} \) is \(1\).

### Final Answer:
The value of \( pKa_{\text{propionic}} - pKa_{\text{acetic}} \) is \(1\).

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