The correct order of value of pk_b the following amines is (i)`C_2H_5NH_2`(ii)`(C_2H_5)_2NH`(iii)`(C_2H_5)_3N`

Options

A. (i)gt(ii)gt(iii)
B. (iii)gt(ii)gt(i)
C. (ii)gt(i)gt(iii)
D. (i)gt(iii)gt(ii)

Answer

To determine the correct order of the values of \( pK_b \) for the given amines \( C_2H_5NH_2 \) (ethylamine), \( (C_2H_5)_2NH \) (diethylamine), and \( (C_2H_5)_3N \) (triethylamine), we need to analyze their basicity and how it relates to \( pK_b \).

### Step 1: Understand Basicity and \( pK_b \)
- Basicity refers to the ability of a compound to accept protons (H⁺ ions).
- The \( K_b \) value is the equilibrium constant for the base dissociation reaction, and a higher \( K_b \) indicates a stronger base.
- The \( pK_b \) is calculated as \( pK_b = -\log K_b \). Thus, a higher basicity (higher \( K_b \)) corresponds to a lower \( pK_b \) value, and vice versa.

### Step 2: Analyze the Given Amines
1. **Ethylamine \( (C_2H_5NH_2) \)**: This is a primary amine. It has one ethyl group attached to the nitrogen, which can donate electron density to nitrogen, enhancing its basicity.
2. **Diethylamine \( ((C_2H_5)_2NH) \)**: This is a secondary amine. It has two ethyl groups attached to the nitrogen, which increases the electron density on nitrogen more than in ethylamine, making it more basic.
3. **Triethylamine \( ((C_2H_5)_3N) \)**: This is a tertiary amine. It has three ethyl groups attached to nitrogen, providing maximum electron density to nitrogen, making it the most basic among the three.

### Step 3: Order of Basicity
- The order of basicity based on the number of alkyl groups is:
- \( (C_2H_5)_3N \) (triethylamine) > \( (C_2H_5)_2NH \) (diethylamine) > \( C_2H_5NH_2 \) (ethylamine)

### Step 4: Order of \( pK_b \)
- Since \( pK_b \) is inversely related to basicity:
- The order of \( pK_b \) will be the reverse of the order of basicity:
- \( pK_b((C_2H_5)_3N) < pK_b((C_2H_5)_2NH) < pK_b(C_2H_5NH_2) \)

### Step 5: Final Order of \( pK_b \)
- Thus, the correct order of \( pK_b \) values for the amines is:
- \( pK_b(C_2H_5NH_2) > pK_b((C_2H_5)_2NH) > pK_b((C_2H_5)_3N) \)

### Answer
The correct order of the values of \( pK_b \) for the amines is:
1. \( pK_b(C_2H_5NH_2) \) (highest)
2. \( pK_b((C_2H_5)_2NH) \) (middle)
3. \( pK_b((C_2H_5)_3N) \) (lowest)