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What is the relation between the inductive effect on bond length and strength.
how would one rank the bond strength of
$\ce{CH3-H}$, $\ce{CH3CH2-H}$, and $\ce{(CH3)2CH-H}$
I know that alkyl groups donate electron density by induction, but how does electron density in a bond affect its length or strength?
Just as hyperconjugation stabilizes carbocations and radicals by sharing the electron density of adjacent $\ce{C-H}$ bonds with the unoccupied/partially occupied orbital, hyperconjugation destabilizes carbanions. So more substitution means less acidic and more ionizable. I had a hard time finding a single resource listing bond lengths, but they seem to correlate with bond-dissociation energy. The wikipedia page for methane states that its $\ce{C-H}$ bond length is 108.7 pm and an answer by Jan says ethane’s is 109.4 pm.
$$ \small \begin{array}{lcc} \hline \text{Hydrocarbon} & \mathrm{p}K_\mathrm{a} ^{[1]} & \text{BDE (kcal)}^{[2]}\\ \hline \ce{CH3-H} & 48 & 104\\ \ce{CH3CH2-H} & - & 98\\ \ce{(CH3)2CH-H} & 51 & 95\\ \ce{(CH3)3C-H} & 53 & 93\\ \hline \end{array} $$
$[1]$ Evan’s pKa Table
$[2]$ Wikipedia: Carbon-Hydrogen Bond
–I effect increase the bond strength and force constant, increase of bond strength is possible only by holding two atoms closer than earlier. hence -I effect reduces bond length and increases bond strength
since the inductive effect leads to ionic character in the bond,the increase in -I effect decreases the bond length.
