Question

Butadiene, \(\mathrm{C}_{4} \mathrm{H}_{6}\) is a planar molecule that has the following carbocarbon bond lengths: (a) Predict the bond angles around each of the carbon atoms and sketch the molecule. (b) From left to right, what is the hybridization of each carbon atom in butadiene? (c) The middle \(C-\) bond length in butadiene \((1.48\) A) is a little shorter than the average \(\mathrm{C}-\mathrm{C}\) single bond length \((1.54 \hat{\mathrm{A}}) .\) Does this imply that the middle \(\mathrm{C}-\mathrm{Cbond}\) in butadiene is weaker or stronger than the average \(\mathrm{C}-\mathrm{C}\)? (\mathbf{d} ) Based on your answer for part ( c ),discuss what additional aspects of bonding in butadiene might support the shorter middle \(\mathrm{C}-\) C bond.

Short answer

In butadiene, bond angles around sp2 hybridized carbons (1, 2, 3, and 4) are approximately 120°, while bond angles around sp3 hybridized carbons (2 and 3) are approximately 109.5°. The middle C-C bond length (1.48 Å) is shorter than the average C-C single bond length (1.54 Å), indicating a stronger bond due to electron delocalization and resonance, providing extra stability to the molecule.

Step-by-step solution

Sketch the molecule and predict bond angles

To sketch the molecule, we need to know the structural formula of butadiene. The structural formula for butadiene is \(\mathrm{H_{2}C=CH-CH=CH_{2}}\). Now we can predict the bond angles. In butadiene, carbon 1 and carbon 4 are sp2 hybridized, as both of them form a double bond with their adjacent carbon atoms. This means that the bond angles around carbon 1 and carbon 4 should be approximately 120°. Carbon 2 and carbon 3, on the other hand, are sp3 hybridized due to the presence of one double bond and one single bond. This indicates that the bond angles around carbon 2 and carbon 3 should be approximately 109.5°.

Determine the hybridization of each carbon atom

To determine the hybridization of each carbon atom, we need to identify the type of bonds formed by each carbon atom in butadiene: - Carbon 1: forms one double bond and one single bond, hence it is sp2 hybridized. - Carbon 2: forms one double bond and one single bond, hence it is sp2 hybridized. - Carbon 3: forms one double bond and one single bond, hence it is sp2 hybridized. - Carbon 4: forms one double bond and one single bond, hence it is sp2 hybridized. In conclusion, all carbon atoms in butadiene are sp2 hybridized.

Compare the middle C-C bond length with average C-C single bond length

The middle C-C bond length in butadiene is given as 1.48 Å, while the average C-C single bond length is 1.54 Å. Since the middle C-C bond length in butadiene is shorter than the average C-C single bond length, it indicates that the bond is stronger than the average C-C single bond.

Discuss additional aspects of bonding in butadiene

The shorter middle C-C bond in butadiene can be attributed to the delocalization of electrons across the double and single bonds between the carbon atoms. This delocalization of electrons results in the formation of a partial pi bond across the middle C-C bond, leading to stronger and shorter bonding. This phenomenon is known as resonance or conjugation in butadiene, which provides extra stability to the molecule and explains the shorter middle C-C bond.