Three isomeric alkenes have the formula \(\mathrm{C}_{4} \mathrm{H}_{8}\) (see the following table). (a) Draw Lewis structures of these compounds. (b) Calculate \(\Delta G^{\circ}, \Delta H^{\circ}\), and \(\Delta S^{\circ}\) for the three reactions that interconvert each pair of compounds. (c) Which isomer is the most stable? (d) Rank the isomers in order of decreasing \(S_{m}{ }^{\circ}\). \(\begin{array}{lrc} \text { Compound } & \Delta \mathrm{H}_{\mathrm{f}}{ }^{\circ}\left(\mathrm{kJ} \cdot \mathrm{mol}^{-1}\right) & \Delta \mathrm{G}_{\mathrm{f}}^{\circ}\left(\mathrm{kJ} \cdot \mathrm{mol}^{-1}\right) \\ \hline \text { 2-methylpropene } & -16.90 & +58.07 \\ \text { cis-2-butene } & -6.99 & +65.86 \\ \text { trans-2-butene } & -11.17 & +62.97 \\ \hline \end{array}\)

Understanding the Lewis structures of molecules is the first step towards grasping their chemical properties and behavior. In the context of alkenes with the formula \(\mathrm{C}_{4}\mathrm{H}_{8}\), Lewis structures help us visualize the arrangement of atoms and the distribution of electrons among them. Drawing these structures involves representing the valence electrons as dots surrounding the atomic symbols and indicating chemical bonds as lines. For alkenes, one key feature to represent is the double bond, which signifies a shared pair of electrons between two carbon atoms. This visualization provides insight into the molecule's geometry and potential for isomerism, evidenced by the different possible arrangements for 2-methylpropene, cis-2-butene, and trans-2-butene. An understanding of the molecular structure is critical to predicting the physical and chemical properties of these compounds.

Thermodynamics in chemistry is a field that studies the energy and heat associated with chemical reactions and changes in states of matter. It examines the principles that govern the energy transfers and conversions, which are essential for understanding the spontaneity and feasibility of chemical reactions. At the heart of this discipline are the laws of thermodynamics that describe the conservation of energy and the increase in entropy. In the study of alkenes, thermodynamic parameters such as enthalpy (\(\Delta H^{\circ}\)) and entropy (\(\Delta S^{\circ}\)) provide invaluable information on the heat exchange during formation and the disorder within the molecules, respectively. These measures are crucial for assessing the stability and reactivity of different alkene isomers.

Gibbs free energy (\(\Delta G^\circ\)) is a thermodynamic quantity that predicts the direction of a chemical reaction under constant temperature and pressure. It represents the balance between enthalpy and entropy within a system, with its value indicating whether a reaction is spontaneous. The formula \(\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ\), where \(T\) stands for the temperature in Kelvin, signifies that a reaction with a negative \(\Delta G^\circ\) is energetically favorable at a given temperature. For the isomeric alkenes in our exercise, calculating \(\Delta G^\circ\) allows us to assess which transition between isomers is most likely to occur spontaneously, and generally, a lower \(\Delta G_{\text{f}}^\circ\) value correlates with increased stability of a compound.

Standard molar entropy (\(S_m{ }^\circ\)) is a measure of the randomness or disorder within a substance in its standard state. It reflects the various ways that the particles within a substance can be arranged while still preserving its macroscopic properties. Higher entropy values suggest greater disorder and higher energy dispersal in a substance's molecular structure. When comparing isomers of alkenes, differences in \(S_m{ }^\circ\) can arise due to variations in molecular symmetry, the presence of substituents, and the overall three-dimensional arrangement. Ranking isomers by decreasing entropy helps determine the relative freedom of molecular motion and can be indicative of physical properties like boiling points and melting points, which are related to the energy required to overcome these entropic contributions.

The stability of chemical compounds is often gauged by their tendency to resist change or decomposition under standard conditions. In thermodynamics, stability can be linked to Gibbs free energy. Compounds with lower \(\Delta G_{\text{f}}^\circ\) values are generally more stable, as they require an input of energy to be converted to other forms. In the exercise's context, comparing the \(\Delta G_{\text{f}}^\circ\) of the three alkene isomers allows us to infer their relative stabilities. The most stable molecule under standard conditions will have the lowest free energy of formation. This inherent stability has implications in practical applications, influencing aspects such as reactivity, rate of reaction, and product distribution during chemical processes.