Compounds having same molecular formula but different connectivity of atoms or groups are called structure isomers. Structrue isomers are futher classify according to their dissimilarities.
In the following skelton `Z` can be, if the molecular formula is `C_(5)H_(10)O_(2)`:
`CH_(3)-CH_(2)-undersetunderset(Z)(|)(CH)-CH_(3)`
(i)A carboxylic acid , (ii)An ester
(iii)Hydroxyaldehyde , (iv)Alkanediol

Options

A. i & ii
B. iii & iv
C. i & iv
D. ii ^ iii

Answer

To determine the possible structures for the compound with the molecular formula \( C_5H_{10}O_2 \) based on the provided skeleton, we will analyze each option step by step.

### Step 1: Analyze the Given Skeleton
The skeleton provided is:
\[ CH_3-CH_2-Z(|)(CH)-CH_3 \]

From this skeleton, we can identify that there are 5 carbon atoms (C) and the rest of the structure must accommodate the remaining hydrogen (H) and oxygen (O) atoms according to the molecular formula \( C_5H_{10}O_2 \).

### Step 2: Count Atoms in the Skeleton
- **Carbons (C)**: 4 carbons are already present in the skeleton (from the \( CH_3 \), \( CH_2 \), and \( CH \) groups).
- **Hydrogens (H)**: The skeleton provides 9 hydrogens (3 from \( CH_3 \), 2 from \( CH_2 \), and 3 from \( CH \)).
- **Oxygens (O)**: There are no oxygen atoms in the skeleton yet.

Thus, we have:
- 4 Carbons used, leaving 1 Carbon remaining.
- 9 Hydrogens used, leaving 1 Hydrogen remaining.
- 2 Oxygens are still needed.

### Step 3: Evaluate Each Option
1. **Carboxylic Acid**:
- Structure: \( R-COOH \) (where \( R \) is an alkyl group).
- This can be formed by adding \( -COOH \) to the skeleton, using 1 Carbon, 1 Oxygen for the carbonyl (C=O), and 1 Oxygen for the hydroxyl (O-H).
- This is a valid structure.

2. **Ester**:
- Structure: \( RCOOR' \).
- We can form an ester by adding \( -COOR' \) to the skeleton.
- This also uses 1 Carbon and 2 Oxygens, making it a valid structure.

3. **Hydroxyaldehyde**:
- Structure: \( R-CHO \) with an additional hydroxyl group.
- This would require 2 Oxygens and would not fit the remaining hydrogen count, as it would need more than 1 hydrogen to satisfy the structure. Thus, this is not a valid structure.

4. **Alkanediol**:
- Structure: \( R-CH(OH)-CH(OH)-R' \).
- This would require at least 2 hydroxyl groups, which would also not fit the remaining hydrogen count. Thus, this is not a valid structure.

### Conclusion
The valid structures for \( Z \) based on the molecular formula \( C_5H_{10}O_2 \) are:
- (i) A carboxylic acid
- (ii) An ester

### Final Answer
The correct options for \( Z \) are:
(i) A carboxylic acid
(ii) An ester