Question

what is the order of decreasing bond length for a C-C bond composed of the following molecular orbitals?I. sp^3 - sp^3II. sp^2 - sp^2III. sp-spa) III>II>Ib)I>II>IIIc) I>III>IId) II>III>I

Answer 1

Answer:

The decreasing order of bond length in the carbon - carbon bonds will be:

$C-C>C=C>C\equiv C$

Explanation:

Bond length is defined as average distance between two nuclei of  bonded atoms in a molecule.Bond length is inversely  proportional to the number of bonds present between two atoms.

$\text{Bond length} \propto \frac{1}{\text{Number of bonds}}$...[1]

Bond energy is defied as amount of energy required to break apart the bond of 1 mole of molecule into their individual atom. Bond energy is directly proportional to the number of bonds present between two atoms.

$\text{Bond Energy} \propto \text{Number of bonds}$..[2]

From [1] and [2]:

$\text{Bond length} \propto \frac{1}{\text{Bond energy}}$

$C-C: sp_3$ hybridized

$C=C: sp_2$ hybridized

$C\equiv C: sp$ hybridized

Extent of overlapping of orbitals in these hybridization;

$C\equiv C> C=C > C-C$

Higher the overlapping of orbital more closer will be both atoms to each other and shorter will be the bond lenght.

So, the decreasing order of bond length in the carbon - carbon bonds will be:

$C-C>C=C>C\equiv C$