For cyclopropane, the C-C-C bond angles are 60o which is a distortion of 49o from the preferred angle of 109o. There are three C-C-C angles in cyclopropane, so the strain due to bond bending is given by:
Eq = 3 x 0.042 x (49)2
= 302.5 KJmol-1
If the strain due to bond stretching is to equal the strain due to bond bending, then:
1470 x (Dr)2 = 302.5
so that Dr = 0.45 nm.
There are three C-C bonds in cyclopropane, so each of them would have
to be distorted by 0.45 / 3 = 0.15nm in order for the strain due to bond
stretching to be
equal to the strain due to bond bending.
For cyclobutane, the C-C-C bond angles are 87o which is a distortion of 22o from the preferred angle of 109o. There are four C-C-C angles in cyclobutane, so the strain due to bond bending is given by:
Eq = 4 x 0.042 x (22)2
= 81.3 KJmol-1
If the strain due to bond stretching is to equal the strain due to bond bending, then:
1470 x (Dr)2 = 81.3
so that Dr = 0.23 nm.
There are four C-C bonds in cyclobutane, so each of them would have to be distorted by 0.23 / 4 = 0.06nm in order for the strain due to bond stretching to be equal to the strain due to bond bending.
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