The order of decreasing stability of the following carbanions is
(i) `(CH_(3))_(3)C^(-)`
(ii) `(CH_(3))_(2)CH^(-)`
(iii) `CH_(3)CH_(2)^(-)`
(iv) `C_(6)H_(5)CH_(2)^(-)`

Options

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

Explanation

To determine the order of decreasing stability of the given carbanions, we need to analyze the inductive effects and resonance stabilization associated with each carbanion. Let's break down the analysis step by step.

### Step 1: Identify the Carbanions
The carbanions given are:
1. `(CH₃)₃C⁻` (tert-butyl carbanion)
2. `(CH₃)₂CH⁻` (isopropyl carbanion)
3. `CH₃CH₂⁻` (ethyl carbanion)
4. `C₆H₅CH₂⁻` (benzyl carbanion)

### Step 2: Analyze Inductive Effects
Inductive effects refer to the electron-donating (+I) or electron-withdrawing (-I) effects of substituents attached to the carbanion. The more alkyl groups attached to the carbanion, the more stable it becomes due to the +I effect, which helps to stabilize the negative charge.

- **(i) `(CH₃)₃C⁻`**: Has three methyl groups. Strong +I effect, stabilizing the negative charge.
- **(ii) `(CH₃)₂CH⁻`**: Has two methyl groups. Moderate +I effect, stabilizing the negative charge.
- **(iii) `CH₃CH₂⁻`**: Has one methyl group. Weaker +I effect compared to the previous two.
- **(iv) `C₆H₅CH₂⁻`**: The benzyl carbanion can participate in resonance, which provides significant stabilization to the negative charge.

### Step 3: Analyze Resonance Effects
Resonance is a key factor in determining the stability of carbanions. The benzyl carbanion can delocalize its negative charge through resonance with the benzene ring, which greatly enhances its stability.

- **(iv) `C₆H₅CH₂⁻`**: Most stable due to resonance stabilization.
- **(i) `(CH₃)₃C⁻`**: Next in stability due to three +I groups.
- **(ii) `(CH₃)₂CH⁻`**: Less stable than the tert-butyl carbanion but more stable than the ethyl carbanion.
- **(iii) `CH₃CH₂⁻`**: Least stable due to the absence of resonance and having only one +I group.

### Step 4: Order of Stability
Based on the analysis:
1. `C₆H₅CH₂⁻` (benzyl carbanion) - most stable due to resonance.
2. `(CH₃)₃C⁻` (tert-butyl carbanion) - stabilized by three +I groups.
3. `(CH₃)₂CH⁻` (isopropyl carbanion) - stabilized by two +I groups.
4. `CH₃CH₂⁻` (ethyl carbanion) - least stable due to the absence of resonance and only one +I group.

### Final Order of Decreasing Stability
The order of decreasing stability of the carbanions is:
**(iv) > (i) > (ii) > (iii)**