Record the following sets of compounds according to increasing `pK_(a) ( = - log Ka)`
Propanoic acid, 3-bromopropanoic acid, 2-nitropropanoic acid

Answer

To solve the problem of arranging propanoic acid, 3-bromopropanoic acid, and 2-nitropropanoic acid according to their increasing pKa values, we will follow these steps:

### Step 1: Understand pKa and Ka
- pKa is the negative logarithm of the acid dissociation constant (Ka). A lower pKa value indicates a stronger acid, which means it dissociates more in solution to release H+ ions.

### Step 2: Identify the Structures of the Compounds
- **Propanoic Acid**: CH3CH2COOH
- **3-Bromopropanoic Acid**: CH2BrCH2COOH
- **2-Nitropropanoic Acid**: CH3CH(NO2)COOH

### Step 3: Analyze the Effects of Substituents
- **Propanoic Acid**: This compound has no substituents that affect acidity significantly.
- **3-Bromopropanoic Acid**: The bromine atom is a -I (inductive effect) group, which withdraws electron density and stabilizes the conjugate base (the carboxylate ion) when the acid donates a proton. This increases acidity compared to propanoic acid.
- **2-Nitropropanoic Acid**: The nitro group (-NO2) is a strong -I group and also has resonance effects. It significantly stabilizes the conjugate base, making this acid the strongest among the three.

### Step 4: Determine the Order of Acidity
- Based on the analysis:
1. **2-Nitropropanoic Acid** is the strongest acid due to the strong -I effect and resonance stabilization.
2. **3-Bromopropanoic Acid** is next, as bromine has a weaker -I effect compared to the nitro group.
3. **Propanoic Acid** is the weakest acid as it has no electron-withdrawing substituents.

### Step 5: Convert Acidity Order to pKa Order
- Since pKa is inversely related to acidity:
- 2-Nitropropanoic Acid has the lowest pKa (strongest acid).
- 3-Bromopropanoic Acid has a higher pKa than 2-nitropropanoic acid.
- Propanoic Acid has the highest pKa (weakest acid).

### Final Order of Increasing pKa Values
- **Increasing pKa Order**:
2-Nitropropanoic Acid < 3-Bromopropanoic Acid < Propanoic Acid

### Summary
- The final arrangement according to increasing pKa values is:
2-Nitropropanoic Acid < 3-Bromopropanoic Acid < Propanoic Acid

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