Question

The molecules cis-dichloroethylene and transdichloroethylene shown on p. 324 can be interconverted by heating or irradiation. (a) Starting with cis-dichloroethylene, show that rotating the \(\mathrm{C}=\mathrm{C}\) bond by \(180^{\circ}\) will break only the pi bond but will leave the sigma bond intact. Explain the formation of trans- dichloroethylene from this process. (Treat the rotation as two, stepwise \(90^{\circ}\) rotations.) (b) Account for the difference in the bond enthalpies for the pi bond (about \(270 \mathrm{~kJ} / \mathrm{mol}\) ) and the sigma bond (about \(350 \mathrm{~kJ} / \mathrm{mol}\) ). (c) Calculate the longest wavelength of light needed to bring about this conversion.

Short answer

Starting from cis-dichloroethylene, rotating the C=C bond by 180 degrees will break the weaker pi bond, resulting in the formation of trans-dichloroethylene. The sigma bond has a higher enthalpy because it is stronger than the pi bond. The wavelength of light needed to bring about this conversion can be found using the relation between the energy of light and its wavelength, given by the formula \(\lambda = hc/E\), where h is Plank's constant, c is the speed of light, and E is the energy associated with the bond.

Step-by-step solution

Understand and illustrate isomer conversion

Observe the structure of cis-dichloroethylene. Rotating the C=C bond by 90 degrees twice will only break the pi bond without disturbing the sigma bond as the sideways overlapping p orbitals forming the pi bond are weaker and can easily get disconnected due to rotation. After this π bond breakage, when we rotate it by another 90 degrees, we get trans-dichloroethylene.

Analyze the bond enthalpies

A σ bond (sigma bond) is stronger than a π bond (pi bond). This is because sigma bonds form from the end-to-end overlapping and hence the electron density lies between the nuclei of the bonding atoms, which ultimately decreases the potential energy and makes the bond stronger. Thus, σ bond (350 kJ/mol) has larger enthalpy than π bond (270 kJ/mol).

Calculate the wavelength of light

The energy required to break the pi bond and initiate the transformation can be found from the enthalpy of the pi bond, given by \(270 kJ/mol\). Convert this to J/mol using the conversion \(1 kJ = 1000 J\). The energy of a photon is given by the Plank's equation: \(E = h\nu\), where h is Plank's constant and \(\nu\) is the frequency. The frequency can be related to the wavelength as: \(\nu = c/\lambda\), where c is the speed of light and \(\lambda\) is the wavelength. Thus, substituting \(\nu = c/\lambda\) in \(E = h\nu\) gives: \(E = hc/\lambda\). Rearranging for wavelength, we get: \(\lambda = hc/E\). Substituting the known values of h, c, and E(from the enthalpy calculation) will give the required wavelength.

Key concepts

C=C bond rotation

In chemistry, the concept of bond rotation is crucial for understanding how molecules can change shapes. Focusing on the specific case of a carbon-carbon double bond, or a \(C=C\) bond, helps us understand this process better. In a \(C=C\) bond, there are two types of bonds: sigma (\(\sigma\)) and pi (\(\pi\)) bonds. The sigma bond acts as the backbone by being the first bond between the two carbon atoms.
This bond remains intact because of strong end-to-end overlapping of orbitals. On the other hand, the pi bond is more fragile due to sideways overlap of p orbitals, sitting above and below the axis of the bond.

• The pi bond is responsible for preventing rotational freedom.
• Rotating a \(C=C\) bond means twisting one carbon atom relative to the other.
• When rotation is enforced, the pi bond breaks as the p orbitals can no longer align and overlap.

This is why when you rotate cis-dichloroethylene by \(180^{\circ}\), the pi bond breaks while the sigma bond persists. This eventually converts the molecule into trans-dichloroethylene.

Pi vs Sigma bond enthalpy

The concepts of pi and sigma bonds are essential in understanding molecular stability. These differences come into stark contrast when you consider their bond enthalpies or bond energies. Sigma bonds are significantly stronger than pi bonds due to their formation from direct orbital overlap. This overlap makes them more stable and hence harder to break.

Pi bonds, formed from side-to-side overlap, have weaker interactions. Thus they have less energy associated with breaking them. The approximate bond enthalpies reflect this strength difference:

• Sigma bond: \(350 \mathrm{kJ/mol}\)
• Pi bond: \(270 \mathrm{kJ/mol}\)

Why does this matter? Well, when heating or irradiating molecules, it is the pi bonds that are more likely to break first. This ensures that rotations can occur in double bonds, as seen in the rotation of \(C=C\) bonds during isomerization events.

Photon wavelength calculation

Calculating the wavelength of light capable of breaking a pi bond can be done using basic principles of photochemistry and physics. We utilize Planck's equation to find the energy of a photon: \(E = hu\). Here, \(h\) represents Planck's constant, and \(u\) is the frequency. Wavelength \(\lambda\) can be substituted into this equation with \(u = c/\lambda\), where \(c\) is the speed of light.

The energy needed for the pi bond in a molecule like cis-dichloroethylene is around \(270 \, \text{kJ/mol}\). This conversion process involves:

• Converting energy units: \(1 \, \text{kJ} = 1000 \, \text{J}\)
• Applying the equation: \(E = hc/\lambda\)
• Rearranging to find wavelength: \(\lambda = hc/E\)

After substituting known values for \(h\), \(c\), and the energy of a pi bond, the result is the longest wavelength of light needed to prompt isomerization. This entire process shows how energy from light can cause chemical reactions by providing the necessary energy to break weaker pi bonds.