Valence orbitals: H (1s), C (2s, 2p) QUESTION: In the structure below, which of these bonds is the longest? A. the C-C bond, B. the C=C bond, C. the C-H bond Valence orbitals: H (1s), C (2s, 2p) Starting from left, steric number of C: 4, 3, and 3 Hybridization: sp3, sp2, sp2 Bonding is due to the following overlaps: C-C: sp3-sp2, C=C: sp2-sp2 Covalent radii: H (s: 31 pm), C (sp3: 76 pm, sp2: 73 pm) C-C: 76+73=149 pm, C=C: 73+73=146 pm In the structure below, which of these bonds is the longest? A. the Carbon to carbon single bond B. the carbon-to-carbon double bond C. the carbon-to-hydrogen bond PAUSE CLICK In valence bond theory, a bond between two atoms is said to be due the overlap of their valence orbitals. The only orbital used for bonding by hydrogen is the 1s orbital. The valence orbitals of carbon are in the second shell. Therefore, we expect any Carbon-to-hydrogen bond to be shorter than a carbon-to-carbon bond. CROSS OUT C As far as the carbon-to-carbon bonds are concerned, a single bond is expected to be longer than a double bond, which is expected to be longer than a triple bond. Therefore, the correct answer is A. Let’s see how valence bond theory explains this. CLICK The steric numbers of carbon shown in the structure, from left to right, are 4, 3 and 3 THe first carbon is a tetrahedral center. Its hybridization is sp3. The second and third carbon are trigonal planar centers. Their hybridization is sp2. CLICK Therefore the bonding between the carbon atoms are due to the following orbital overlaps CLICK For the single bond, the overlap is sp3 to sp2. For the double bond, the overlap is sp2 to sp2 We expect the sp3 to sp2 overlap to be longer because electrons in an sp3 orbital stretches out farther from the nucleus than those in an sp2 orbital... p orbitals stretch out farther from the nucleus than s orbitals.... and sp3 orbitals have more p character than sp2 orbitals. In fact we can estimate what all these bond lengths are using covalent radii that we can look up. From webelements.com, the values you’ll find are 31 picometers for hydrogen, 76 picometers for an sp3 orbital of carbon, and 73 picometers for an sp2 orbital of carbon. The bond lengt is just equal to the sum of the covalent radii. Therefore, the carbon-to-carbon single bond here is expected to be 149 picometers. 76+73 equals 149. HIGHLIGHT 149 pm THis is 3 picometers longer than the the carbon-to-carbon single bond. HIGHLIGHT 146 pm The carbon-to-carbon bonds are at least 30 picometers longer than the carbon-to-hydrogen bonds since the hydrogen atom’s covalent radius is only 31 pm. CLICK PAUSE END RECORDING

Video ID: 3-14-4 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08