A common shorthand notation to draw organic structures is to use lines to represent \(\mathrm{C}-\mathrm{C}\) bonds. For example, the short- hand notation for the two structural isomers of the formula \(\mathrm{C}_{4} \mathrm{H}_{10}\) are: At the end of each zigzag line is a carbon atom. The \(\mathrm{C}-\mathrm{H}\) bonds are omitted in such shorthand notation. Use line notation to illustrate the structural isomers of \(\mathrm{C}_{6} \mathrm{H}_{14}\)

For straight chain isomers, all carbon atoms are connected in a single straight line. In the case of C₆H₁₄, there's only one possible straight chain isomer – hexane: (CH₃-CH₂-CH₂-CH₂-CH₂-CH₃) Converting this to shorthand line notation: ``` H H H H H H | | | | | | H3C - C-C-C-C-C-CH3 ```

The branched isomers of C₆H₁₄ can be drawn as different carbon atom configurations with branches along the main carbon chain. The most common branched chain isomers are: 1. 2-Methylpentane: (CH₃-CH₂-CH(CH₃)-CH₂-CH₃) Shorthand line notation: ``` H H | | H3C -C-C-H | H3C-C-C-CH3 | H ``` 2.3-Methylpentane: (CH₃-CH(CH₃)-CH₂-CH₂-CH₃) Shorthand line notation: ``` H H H H | | | | H3C - C-C-C-C-CH3 | CH3 ``` 3. 2,2-Dimethylbutane: (CH₃-C(CH₃)₂-CH₂-CH₃) Shorthand line notation: ``` H H H | | | H3C - C-C-C-CH3 / CH3 ``` 4. 2,3-Dimethylbutane: (CH₃-CH(CH₃)-CH(CH₃)-CH₃) Shorthand line notation: ``` H // H | | | H3C - C-C-C-CH3 | CH3 ``` So, the structural isomers of C₆H₁₄ using shorthand line notation are Hexane, 2-Methylpentane, 3-Methylpentane, 2,2-Dimethylbutane, and 2,3-Dimethylbutane.