Let variable completely represent the absolute total number of exclusively -hydrogen atoms strategic — Haloalkanes and Haloarenes Chemistry Question
Question
Let variable $X$ completely represent the absolute total number of exclusively $\beta$ -hydrogen atoms strategically available for direct abstraction in the molecule 2-bromo-2,3-dimethylbutane. Let variable $Y$ definitively represent the total number of distinct alkene structural isomers that can potentially be formed during its aggressive E2 elimination. What is the precise numerical value of the mathematical product $(X \times Y)$?
💡 Solution & Explanation
The exact structure of 2-bromo-2,3-dimethylbutane is $CH_3-C(Br)(CH_3)-CH(CH_3)_2$. Let's identify the $\beta$ -hydrogens. The $\alpha$ -carbon is strictly C2, which is bonded to the bromine atom. The structurally adjacent $\beta$ -carbons are: 1) The C1 methyl group ($-CH_3$): Contains exactly 3 $\beta$ -hydrogens. 2) The other identical methyl group attached to C2 ($-CH_3$): Contains exactly 3 $\beta$ -hydrogens. 3) The C3 carbon ($-CH(CH_3)_2$): Contains exactly 1 $\beta$ -hydrogen. Total $\beta$ -hydrogens ($X$) = $3 + 3 + 1 = 7$. Now, let's strictly determine the distinct alkene structural isomers formed ($Y$): 1) Abstraction from either of the completely equivalent C1/C2 methyl groups yields the exact same terminal alkene: 2,3-dimethyl-1-butene. 2) Abstraction from the deeply internal C3 carbon yields the highly substituted: 2,3-dimethyl-2-butene (tetramethylethene). Total distinct structural isomers ($Y$) = 2. The mathematical product $X \times Y = 7 \times 2 = 14$.