Among the following which has lowest `pK_a` value?

Options

A. `HCOOH`
B. `CH_3COOH `
C. `(CH_3)_2 -CH -COOH `
D. `CH_3-CH_2 -COOH`

Explanation

To determine which of the given compounds has the lowest pK_a value, we need to analyze the acidity of each compound. The pK_a value is a measure of the strength of an acid; the lower the pK_a value, the stronger the acid.

### Step-by-Step Solution:

1. **Understanding pK_a and Acid Strength**:
- pK_a is defined as the negative logarithm of the acid dissociation constant (K_a).
- A lower pK_a value indicates a stronger acid, meaning it dissociates more completely in solution to release H⁺ ions.

2. **Identifying the Compounds**:
- Let's assume the compounds in question are:
1. HCOOH (Formic acid)
2. CH₃COOH (Acetic acid)
3. CH₃CH₂COOH (Propanoic acid)
4. CH₃(CH₂)₃COOH (Butanoic acid)

3. **Comparing Acid Strength**:
- The strength of an acid can be influenced by the stability of its conjugate base (A⁻).
- For example, the more stable the conjugate base, the stronger the acid.

4. **Analyzing the Conjugate Bases**:
- **Formic acid (HCOOH)**: Conjugate base is HCOO⁻. The negative charge is stabilized by resonance.
- **Acetic acid (CH₃COOH)**: Conjugate base is CH₃COO⁻. The negative charge is also stabilized by resonance, but the methyl group is an electron-donating group, which slightly destabilizes the conjugate base.
- **Propanoic acid (CH₃CH₂COOH)**: Conjugate base is CH₃CH₂COO⁻. Similar to acetic acid, but with an additional ethyl group, which further destabilizes the conjugate base.
- **Butanoic acid (CH₃(CH₂)₃COOH)**: Conjugate base is CH₃(CH₂)₃COO⁻. The longer carbon chain further destabilizes the conjugate base.

5. **Conclusion**:
- Among the acids listed, **formic acid (HCOOH)** is the strongest acid due to the stability of its conjugate base (HCOO⁻) from resonance stabilization.
- Therefore, **formic acid has the lowest pK_a value** compared to the other acids listed.

### Final Answer:
Formic acid (HCOOH) has the lowest pK_a value among the given compounds.