C−H bond length in organic compounds [duplicate]

Question

I am reading Fundamental concepts of organic chemistry by Dr. Anju Srivastava (12/04/2007).

It shows that carbon-hydrogen bond in ethane is 1.1 Å long, in ethene it's 1.08 Å, and in ethyne it's 1.06 Å. According to the book, it's clear that carbon-hydrogen bond decreases with increasing multiple bonds on the carbon atom onto which the bond is!

According to my understanding, the shorter the covalent bond, the stronger it is, and it's contrary to the fact that the hydrogen atoms in ethylene are more acidic than those of ethene and so is ethane. The more acidic the hydrogen atom, the weaker it is held in a bond.

Help please where am wrong, and also guide about the book concept.

Answer 1

Bond strength (bond dissociation energy, BDE) refers to homolytic cleavage of a bond ($\ce{C-H}$ in this case). Heterolytic cleavage is measured by $\mathrm{p}K_\mathrm{a}$. The two processes are the numerical inverse of one another. In the case of acetylene with $\mathrm{sp}$-hybridization (50% $\mathrm{s}$-character) of carbon, the electron density of the $\ce{C-H}$ bond lies closer to carbon when compared to ethylene (33% $\mathrm{s}$-character) and ethane (25% $\mathrm{s}$-character). Thus in acetylene, it is more difficult to break the $\ce{C-H}$ bond homolytically because the carbon is "unwilling" to give up an electron but is happy to keep both electrons and give up a proton. Thus, acetylene has a high BDE ($\pu{133 kcal/mol}$) and lower $\mathrm{p}K_\mathrm{a}$ ($=25$) than ethylene ($\pu{110 kcal/mol}$, $\mathrm{p}K_\mathrm{a} = 44$) and, ultimately, ethane ($\pu{101 kcal/mol}$; $\mathrm{p}K_\mathrm{a} \approx 50$).