write the correct order of basic strength in gas phase is
(I) `CH_(3)-NH_(2)` (II) `(CH_(3))_(2)NH`
(III) `(CH_(3))_(3)N` (IV) `NH_(3)`

Answer

To determine the correct order of basic strength of the given compounds in the gas phase, we will analyze the basicity of the amines and ammonia based on their structure and the effects of alkyl groups.

### Step 1: Identify the Compounds
We have the following compounds:
1. **(I) CH₃-NH₂** (Methylamine - 1° amine)
2. **(II) (CH₃)₂NH** (Dimethylamine - 2° amine)
3. **(III) (CH₃)₃N** (Trimethylamine - 3° amine)
4. **(IV) NH₃** (Ammonia)

### Step 2: Understand Basicity in Gas Phase
In the gas phase, the basicity of amines primarily depends on the inductive effect of the alkyl groups rather than hydrogen bonding, which is significant in aqueous solutions. The basicity order will be influenced by the number of alkyl groups attached to the nitrogen atom.

### Step 3: Analyze the Inductive Effect
- **Inductive Effect**: Alkyl groups are electron-donating through the +I effect. The more alkyl groups attached to the nitrogen, the greater the electron density on the nitrogen atom, thus enhancing its ability to donate a lone pair of electrons and accept protons (H⁺).

- **1° amine (CH₃-NH₂)**: Has one alkyl group. Moderate basicity.
- **2° amine ((CH₃)₂NH)**: Has two alkyl groups. Higher basicity than 1° amine due to increased electron donation.
- **3° amine ((CH₃)₃N)**: Has three alkyl groups. Highest basicity due to maximum electron donation.
- **Ammonia (NH₃)**: No alkyl groups, thus the lowest basicity among the given compounds.

### Step 4: Order the Basic Strength
Based on the analysis:
- **(III) (CH₃)₃N** (Trimethylamine) will be the strongest base.
- **(II) (CH₃)₂NH** (Dimethylamine) will be the next strongest.
- **(I) CH₃-NH₂** (Methylamine) will follow.
- **(IV) NH₃** (Ammonia) will be the weakest base.

### Final Order of Basic Strength in Gas Phase
Thus, the correct order of basic strength in the gas phase is:
**(III) > (II) > (I) > (IV)**