Correct order of increasing basicity is

Options

A. `NH_(3)ltC_(6)H_(5)NH_(2)(C_(2)H_(5))_(2)NHltC_(2)H_(5)NH_(2)lt(C_(2)H_(5))_(3)N`
B. `C_(6)H_(5)NH_(2)ltNH_(3)lt(C_(2)H_(5))lt(C_(2)H_(5))_(3)Nlt(C_(2)H_(5))_(2)NHltC_(2)H_(5)NH_(2)`
C. `C_(6)H_(4)NH_(2)ltNH_(3)ltC_(2)H_(5)NH_(2)lt(C_(2)H_(5))_(3)Nlt(C_(2)H_(5))_(2)NH`
D. `C_(6)H_(5)NH_(2)lt(C_(2)H_(5))_(3)NltNH_(3)ltC_(2)H_(5)NH_(2)lt(C_(2)H_(5))_(2)NH`

Explanation

To determine the correct order of increasing basicity among the given compounds (NH3, C6H5NH2, C2H5NH2, and C2H5)3N, we need to analyze the basic strength of each compound systematically.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- We have the following compounds:
- NH3 (Ammonia)
- C6H5NH2 (Aniline)
- C2H5NH2 (Ethylamine)
- (C2H5)3N (Triethylamine)

2. **Understand Basicity**:
- Basicity refers to the ability of a compound to accept protons (H+ ions). The more readily a compound can accept a proton, the stronger the base it is.

3. **Compare Alkyl and Aryl Amines**:
- Alkyl amines (like ethylamine and triethylamine) are generally more basic than aryl amines (like aniline) due to the electron-donating effect of alkyl groups.
- Aryl amines have a delocalized pi system that can stabilize the lone pair on nitrogen, making it less available for protonation.

4. **Rank the Compounds**:
- **Triethylamine (C2H5)3N**: This is a tertiary amine and is very basic due to the three electron-donating ethyl groups.
- **Ethylamine (C2H5NH2)**: This is a primary amine and is more basic than ammonia due to the electron-donating effect of the ethyl group.
- **Ammonia (NH3)**: This is less basic than ethylamine but more basic than aniline.
- **Aniline (C6H5NH2)**: This is the least basic due to the resonance stabilization of the lone pair on nitrogen, which makes it less available for protonation.

5. **Final Order of Increasing Basicity**:
- Based on the analysis, the order of increasing basicity is:
- C6H5NH2 (Aniline) < NH3 (Ammonia) < C2H5NH2 (Ethylamine) < (C2H5)3N (Triethylamine)

### Conclusion:
The correct order of increasing basicity is:
C6H5NH2 < NH3 < C2H5NH2 < (C2H5)3N