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In the formula $\ce{(CH3)3-C-CH(CH3)-CH2-CH3}$, what do the parenthesized portions represent? What is the molecular structure, and how do I name the compound?

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The parentheses just have a grouping function: $\ce{(CH3)3-C -}$ represents a carbon atom to which 3 methyl groups are attached, $\ce{-CH(CH3)}-$ is a carbon atom in the chain to which one hydrogen atom and a methyl group are attached.

Draw the molecule, find the longest chain for the base name, determine the position of the substituents and you're done.

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    $\begingroup$ I think that the bad bad nasty (CH₃)₃−C− notation shouldn't be encouraged. I could live with (H₃C−)₃≡C−. (But the correct one in Loong's answer.) $\endgroup$ – mykhal Oct 16 '18 at 9:43
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The Graphical Representation Standards for Chemical Structure Diagrams (IUPAC Recommendations 2008), include recommendations for contracted labels (labels representing more than one non-hydrogen atom) and entire formulas (formulas may be considered as labels not connected to any bonds).

Such labels and formulas rely on the fact that many elements have consistent and well-understood bonding patterns. They can be interpreted with a simple application of valence rules; i.e. they are interpreted to fill as many valences as possible. For example, when reading the contracted label for a carboxylic acid group ($\ce{-COOH}$) from left to right, the carbon atom has three remaining valences. The next atom is oxygen, which has two available valences. Both valences are used to form a double bond with the carbon atom, which leaves the carbon atom with one remaining valence. The third atom is another oxygen, but only one of its valences can be used to create a single bond with the remaining valence on the carbon atom. That fills all of the valences for the carbon atom, but leaves one remaining valence on the oxygen atom. Finally, the fourth atom is a hydrogen atom. It fills the remaining valence on the oxygen atom.

Explicit single bonds are generally not necessary within contracted labels and should be avoided. Therefore, the formula $\ce{(CH3)3-C-CH(CH3)-CH2-CH3}$ that is given in the question should be written as $\ce{(CH3)3CCH(CH3)CH2CH3}$. Note that the first explicit single bond in $\ce{(CH3)3-C-CH(CH3)-CH2-CH3}$ is even wrong since a $\ce{(CH3)3-C-{}}$ group is not possible.

Parentheses are used to indicate branching. The corresponding IUPAC recommendations read as follows:

Simple branching patterns may be implied by the basic valence rules described above, and do not require special notation. More complex branching may be clarified by placing parentheses around all elements within a branch. One valence for the first element within the parentheses is used for connecting the previous atom outside the parentheses; subsequent atoms within the parenthesized section are then bound to the first or subsequent atoms, even if an atom outside the parentheses has remaining open valences.

For example, the $\ce{{}-CH(CH3)-{}}$ segment of the formula that is given in the question includes parentheses that are placed around the atoms of a methyl branch. One valence of the carbon atom within the parentheses is used to form a bond with the previous carbon atom outside the parentheses. This leaves one remaining valence on the carbon atom outside the parentheses when reading from left to right. The three hydrogen atoms within the parentheses fill the remaining valences on the carbon atom within the parentheses.

Therefore, the complete formula $\ce{(CH3)3CCH(CH3)CH2CH3}$ corresponds to the structure of 2,2,3-trimethylpentane.

2,2,3-trimethylpentane

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