Explanation:

To determine the number of different monocarboxylic isomers that can give the same 3-methyl pentane on decarboxylation with soda lime, we need to consider the possible structures and isomerism.

Step 1: Determine the structure of 3-methyl pentane.
3-methyl pentane has the following structure:
CH3-CH2-CH(CH3)-CH2-CH3

Step 2: Identify the possible monocarboxylic isomers that can give 3-methyl pentane on decarboxylation.
Decarboxylation of a monocarboxylic acid involves the removal of a carboxyl group (-COOH) from the molecule. This results in the formation of an alkane.

Step 3: Determine the possible structures of monocarboxylic acids that can give 3-methyl pentane on decarboxylation.
To determine the possible structures, we need to consider the different positions where the carboxyl group can be attached in the 3-methyl pentane molecule.

Key points:
- The carboxyl group can be attached to any of the carbon atoms in the chain of the 3-methyl pentane molecule.
- The carboxyl group cannot be attached to the methyl group, as it would result in a different compound.

Step 4: Count the number of different monocarboxylic isomers.
By considering the different positions where the carboxyl group can be attached, we can determine the number of different monocarboxylic isomers that can give 3-methyl pentane on decarboxylation.

Key points:
- There are two possible positions where the carboxyl group can be attached next to the methyl group (C2 and C4).
- There are three possible positions where the carboxyl group can be attached next to the ethyl group (C1, C3, and C5).
- There are two possible positions where the carboxyl group can be attached at the end of the chain (C6 and C7).

Therefore, there are a total of 2 x 3 x 2 = 12 possible monocarboxylic isomers that can give 3-methyl pentane on decarboxylation.

However, we need to consider that the isomers resulting from attachment at C2 and C7 are the same, as they result in the same compound. Similarly, the isomers resulting from attachment at C4 and C6 are the same. Therefore, we need to subtract these duplicate isomers.

Final answer:
12 - 4 = 8 different monocarboxylic isomers can give the same 3-methyl pentane on decarboxylation.