For the given compound `CH_(3)-underset(overset(|)(OH))(CH)-CH=CH-CH_(3).`
(i) Total number of stereoisomers.
(ii) Number of opticallly active stereoisomers.
(iii) Total number of fractions on fractional distillation of all stereoisomers.

Answer

To solve the question regarding the compound `CH₃-CH(OH)-CH=CH-CH₃`, we will break it down into three parts as requested:

### Step 1: Total Number of Stereoisomers

1. **Identify the Structure**: The compound has a double bond between carbon atoms, which allows for geometrical isomerism (cis/trans isomerism).
2. **Identify the Double Bond**: The double bond is located between the second and third carbon atoms (C2=C3).
3. **Geometrical Isomers**: For the double bond to have geometrical isomers, the groups attached to the double-bonded carbons must be different. In this case:
- For C2 (attached to OH and CH₃) and C3 (attached to H and CH₂), we can have:
- **Cis Isomer**: OH and CH₃ on the same side.
- **Trans Isomer**: OH and CH₃ on opposite sides.
4. **Count the Isomers**: Since there is one double bond that can exhibit cis/trans isomerism, we can have 2 geometrical isomers.
5. **Consider Other Stereoisomers**: Additionally, we need to check for any chiral centers. In this compound, there is one chiral center at C2 (attached to OH, CH₃, H, and CH).
6. **Total Stereoisomers Calculation**: The total number of stereoisomers can be calculated using the formula:
\[ \text{Total Stereoisomers} = 2^n \text{ (where n is the number of chiral centers)} \times \text{(number of geometrical isomers)} \]
Here, \( n = 1 \) (one chiral center) and we have 2 geometrical isomers. Thus:
\[ \text{Total Stereoisomers} = 2^1 \times 2 = 4 \]

### Step 2: Number of Optically Active Stereoisomers

1. **Identify Chiral Centers**: As previously mentioned, we have one chiral center at C2.
2. **Optically Active Isomers Calculation**: The number of optically active stereoisomers can be calculated using the formula:
\[ \text{Optically Active Isomers} = 2^n \]
Where \( n \) is the number of chiral centers. Since \( n = 1 \):
\[ \text{Optically Active Isomers} = 2^1 = 2 \]

### Step 3: Total Number of Fractions on Fractional Distillation

1. **Identify Enantiomeric Pairs**: The optically active isomers are enantiomers (mirror images of each other). Since we have 2 optically active stereoisomers, we have 1 pair of enantiomers.
2. **Total Fractions Calculation**: The number of fractions obtained from fractional distillation is equal to the number of enantiomeric pairs. Thus:
\[ \text{Total Fractions} = 1 \text{ (pair of enantiomers)} \]

### Final Answers:
(i) Total number of stereoisomers: **4**
(ii) Number of optically active stereoisomers: **2**
(iii) Total number of fractions on fractional distillation of all stereoisomers: **2**

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