The `IUPAC` name of the compound with formula `C_(n)H_(2n+2)`, having the lowest possible molecular mass and capable of showing enantiomerism, is:

Options

A. `3`- Methyl hexane
B. `2,3`-Dimethyl pentane
C. Methane
D. Both (a) and (b)

Explanation

To determine the IUPAC name of the compound with the formula \( C_nH_{2n+2} \), having the lowest possible molecular mass and capable of showing enantiomerism, we can follow these steps:

### Step 1: Understand the Formula
The formula \( C_nH_{2n+2} \) represents alkanes, which are saturated hydrocarbons. The general formula indicates that for every \( n \) carbon atoms, there are \( 2n + 2 \) hydrogen atoms.

### Step 2: Identify the Lowest Molecular Mass
To find the compound with the lowest molecular mass that fits this formula, we start with the smallest values of \( n \):
- For \( n = 1 \): \( C_1H_4 \) (Methane) - Not chiral
- For \( n = 2 \): \( C_2H_6 \) (Ethane) - Not chiral
- For \( n = 3 \): \( C_3H_8 \) (Propane) - Not chiral
- For \( n = 4 \): \( C_4H_{10} \) (Butane) - Not chiral
- For \( n = 5 \): \( C_5H_{12} \) (Pentane) - Not chiral
- For \( n = 6 \): \( C_6H_{14} \) (Hexane) - Not chiral
- For \( n = 7 \): \( C_7H_{16} \) (Heptane) - Not chiral

### Step 3: Find Chiral Compounds
Next, we need to find a compound with a chiral carbon:
- **3-Methylhexane**: This has a chiral center and its molecular formula is \( C_7H_{16} \) with a molecular weight of 100 g/mol.
- **2,3-Dimethylpentane**: This also has a chiral center and its molecular formula is \( C_7H_{16} \) with a molecular weight of 99 g/mol.

### Step 4: Compare Molecular Weights
Among the compounds identified:
- 3-Methylhexane has a molecular weight of 100 g/mol.
- 2,3-Dimethylpentane has a molecular weight of 99 g/mol.

Since 2,3-Dimethylpentane has the lowest molecular weight and is capable of showing enantiomerism, it is the correct answer.

### Conclusion
The IUPAC name of the compound with the formula \( C_nH_{2n+2} \) that has the lowest possible molecular mass and can show enantiomerism is **2,3-Dimethylpentane**.

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