The problem asks to name the given organic compounds (alkanes) based on their structures and write out all the possible non-cyclic isomers for $C_5H_{12}$, $C_6H_{12}$ and $C_7H_{12}$, then name each isomer.

1. Problem Description

The problem asks to name the given organic compounds (alkanes) based on their structures and write out all the possible non-cyclic isomers for $C_5H_{12}$, $C_6H_{12}$ and $C_7H_{12}$, then name each isomer.

2. Solution Steps

Part 1: Naming the compounds

a) $CH_3-CH(CH_3)-CH(CH_3)-CH_2-CH_3$

The longest chain has 5 carbons. Number the chain such that the substituents have the lowest possible numbers. The compound has methyl groups at positions 2 and

3. Therefore, the name is 2,3-dimethylpentane.

b) $CH_3-C(CH_3)_2-CH_3$

The longest chain has 3 carbons. There are two methyl groups attached to carbon

2. Therefore, the name is 2,2-dimethylpropane.

c) $CH_3-C(CH_3)(C_4H_9)-CH-CH_3(CH_2-CH_3)$

This compound is written in a confusing way. Let us re-draw the compound: $CH_3-C(CH_3)(CH_2CH_2CH_2CH_3)-CH(CH_2CH_3)-CH_3$. The longest chain has 6 carbons. So it is a hexane. The numbering should start from the left. There is a methyl group at carbon 2 and a butyl group on the same carbon, and an ethyl group on carbon

3. The name is 3-ethyl-2-methyl-2-butylhexane. However, the butyl group has formula $C_4H_9$, which suggests an error since there is an alkyl group, $C_2H_5$, on carbon

3. In the original image, there is $C_4H_9$ on the compound. But if we change this to $CH_2CH_2CH_2CH_3$, the correct name is 3-ethyl-2-methylhexane. I will assume that the structure should be $CH_3-C(CH_3)(CH_2CH_2CH_2CH_3)-CH(CH_2CH_3)-CH_3$ so the name is 3-ethyl-2-methylhexane.

d) $CH_3-CH_2-C(CH_2-CH_3)_2-CH_2-CH_3$

The longest chain has 5 carbons. There are two ethyl groups attached to carbon

3. Thus, it is 3,3-diethylpentane.

e) $CH_3-CH(CH_3)-CH(CH_2CH_3)-CH(CH_3)-CH_2-CH_2-CH_3$

The longest chain has 7 carbons. There is a methyl group at carbon 2, an ethyl group at carbon 3 and a methyl group at carbon

4. Thus, it is 3-ethyl-2,4-dimethylheptane.

f) $CH_3-C(CH_3)(CH_2CH_3)-C(CH_3)(CH_2CH_3)-CH_2-CH_3$

The longest chain has 6 carbons. There is a methyl and ethyl group attached to carbon

2. There is a methyl and ethyl group attached to carbon

3. Thus, it is 2,3-diethyl-2,3-dimethylhexane.

Part 2: Writing isomers and naming them.

$C_5H_{12}$:

1. Pentane: $CH_3-CH_2-CH_2-CH_2-CH_3$

2. 2-Methylbutane (Isopentane): $CH_3-CH(CH_3)-CH_2-CH_3$

3. 2,2-Dimethylpropane (Neopentane): $CH_3-C(CH_3)_2-CH_3$

$C_6H_{14}$:

1. Hexane: $CH_3-CH_2-CH_2-CH_2-CH_2-CH_3$

2. 2-Methylpentane: $CH_3-CH(CH_3)-CH_2-CH_2-CH_3$

3. 3-Methylpentane: $CH_3-CH_2-CH(CH_3)-CH_2-CH_3$

4. 2,2-Dimethylbutane: $CH_3-C(CH_3)_2-CH_2-CH_3$

5. 2,3-Dimethylbutane: $CH_3-CH(CH_3)-CH(CH_3)-CH_3$

$C_7H_{16}$:

1. Heptane: $CH_3-CH_2-CH_2-CH_2-CH_2-CH_2-CH_3$

2. 2-Methylhexane: $CH_3-CH(CH_3)-CH_2-CH_2-CH_2-CH_3$

3. 3-Methylhexane: $CH_3-CH_2-CH(CH_3)-CH_2-CH_2-CH_3$

4. 2,2-Dimethylpentane: $CH_3-C(CH_3)_2-CH_2-CH_2-CH_3$

5. 2,3-Dimethylpentane: $CH_3-CH(CH_3)-CH(CH_3)-CH_2-CH_3$

6. 2,4-Dimethylpentane: $CH_3-CH(CH_3)-CH_2-CH(CH_3)-CH_3$

7. 3,3-Dimethylpentane: $CH_3-CH_2-C(CH_3)_2-CH_2-CH_3$

8. 3-Ethylpentane: $CH_3-CH_2-CH(CH_2CH_3)-CH_2-CH_3$

9. 2,2,3-Trimethylbutane: $CH_3-C(CH_3)_2-CH(CH_3)-CH_3$

3. Final Answer

a) 2,3-dimethylpentane

b) 2,2-dimethylpropane

c) 3-ethyl-2-methylhexane

d) 3,3-diethylpentane

e) 3-ethyl-2,4-dimethylheptane

f) 3,4-diethyl-3,4-dimethylhexane. But the longest chain must be 7 carbons. The name is 2,3-diethyl-2,3-dimethylhexane.

$C_5H_{12}$: Pentane, 2-Methylbutane, 2,2-Dimethylpropane

$C_6H_{14}$: Hexane, 2-Methylpentane, 3-Methylpentane, 2,2-Dimethylbutane, 2,3-Dimethylbutane

$C_7H_{16}$: Heptane, 2-Methylhexane, 3-Methylhexane, 2,2-Dimethylpentane, 2,3-Dimethylpentane, 2,4-Dimethylpentane, 3,3-Dimethylpentane, 3-Ethylpentane, 2,2,3-Trimethylbutane