Understanding Organic Reactions ch6

Writing Equations for Organic Reactions

• Equations for organic reactions typically use a single reaction arrow ($\rightarrow$) between starting material and product.
• The reagent, which is the chemical substance that reacts with an organic compound, can be written on the left side of the equation along with other reactants or above the arrow.
• Solvents are often omitted from the equation, even though most organic reactions occur in a liquid solvent.
• The solvent and temperature may be indicated above or below the reaction arrow.
• The symbols "hν" and "$\Delta$" represent reactions requiring light and heat, respectively.
• Sequential reactions carried out without showing an intermediate compound are numbered above or below the reaction arrow, indicating the order of steps and addition of reagents.

Kinds of Organic Reactions

• Substitution: An atom or group of atoms is replaced by another.
  • Involves sigma ($\sigma$) bonds: one $\sigma$ bond breaks and another forms at the same carbon atom.
  • Common when Z is hydrogen or a heteroatom more electronegative than carbon.
• Elimination: Elements are removed from the starting material, forming a pi ($\pi$) bond.
  • Two $\sigma$ bonds are broken, and a $\pi$ bond forms between adjacent atoms.
  • Common when X = H and Y is a heteroatom more electronegative than carbon.
• Addition: Elements are added to the starting material.
  • A $\pi$ bond is broken, and two $\sigma$ bonds are formed.
• Addition and elimination reactions are opposite processes; elimination forms a $\pi$ bond, while addition breaks a $\pi$ bond.

Bond Making and Bond Breaking

• A reaction mechanism describes how bonds break and form during the conversion of starting material to product.
• Reactions can occur in one step or a series of steps.
• Bonds can break in two ways:
  • Homolysis: Electrons in the bond are divided equally.
  • Heterolysis: Electrons in the bond are divided unequally.
• Homolysis and heterolysis require energy.
• Homolysis generates uncharged reactive intermediates (radicals) with unpaired electrons.
• Heterolysis generates charged intermediates (carbocations or carbanions).
• Half-headed curved arrows (fishhooks) indicate the movement of a single electron; full-headed curved arrows show the movement of an electron pair.
• Radicals: Reactive intermediates with a single unpaired electron; highly unstable because they lack an octet.
• Carbocations: Carbon atoms surrounded by only six electrons; unstable intermediates.
• Carbanions: Carbon atoms with a negative charge on carbon; unstable intermediates.
• Radicals and carbocations are electrophiles (electron-deficient).
• Carbanions are nucleophiles (carbon with a lone pair).
• Bond formation:
  • Two radicals each donate one electron to form a two-electron bond.
  • Two ions with unlike charges combine, with the negatively charged ion donating both electrons.
• Bond formation always releases energy.
• Different types of arrows are used to describe organic reactions.

Bond Dissociation Energy

• Enthalpy change or heat of reaction ($\Delta H^0$) is the energy absorbed or released in a reaction.
• Bond dissociation energy is $\Delta H^0$ for homolysis of a covalent bond.
• Bond breaking requires energy, so bond dissociation energies are positive, and homolysis is endothermic.
• Bond formation releases energy and is exothermic.
• Comparing bond dissociation energies indicates bond strength; stronger bonds have higher bond dissociation energies.
• Bond dissociation energies decrease down a column of the periodic table.
• Shorter bonds are generally stronger bonds.
• Bond dissociation energies can calculate the enthalpy change ($\Delta H^0$) in a reaction where multiple bonds are broken and formed.
• Oxidation of isooctane and glucose to $CO2$ and $H2O$ have negative $\Delta H^0$ values, indicating exothermic reactions.
• Products in these reactions have stronger bonds than the reactants, thus releasing energy.
• Limitations of bond dissociation energies:
  • They only represent overall energy changes and do not reveal the reaction mechanism or rate.
  • Determined in the gas phase, while most organic reactions occur in a liquid solvent where solvation energy contributes.
  • They are imperfect indicators, but provide a useful approximation of energy changes when bonds are broken and formed.

Thermodynamics

• For a practical reaction, the equilibrium must favor products, and the reaction rate must be fast enough.
• Thermodynamics describes the energy comparison between reactants and products and their relative amounts at equilibrium.
• Kinetics describes reaction rates.
• The equilibrium constant ($K_{eq}$) relates the amount of starting material and product at equilibrium.
• $K_{eq} > 1$ indicates that equilibrium favors products.
• $K_{eq} < 1$ indicates that equilibrium favors starting materials.
• A useful reaction must have $K_{eq} > 1$.
• The position of equilibrium is determined by the relative energies of reactants and products.
• $\Delta G^0$ is the overall energy difference between reactants and products.
• $\Delta G^0$ is related to $K{eq}$ by the equation: \Delta G^0 = -RT \log K{eq}
  • Where:
    • R is the gas constant (8.314 \frac{J}{mol \cdot K} or 1.987 \frac{cal}{mol \cdot K}).
    • T is the temperature in Kelvin.
• When $K{eq} > 1$, \log K{eq} is positive, so $\Delta G^0$ is negative, and energy is released; equilibrium favors products.
• When $K{eq} < 1$, \log K{eq} is negative, so $\Delta G^0$ is positive, and energy is absorbed; equilibrium favors reactants.
• Lower energy compounds have increased stability.
• Small changes in energy correspond to significant differences in the relative amounts of starting material and product at equilibrium.
• Monosubstituted cyclohexanes exist as chair conformations that interconvert, favoring the equatorial position.

Enthalpy and Entropy

• $\Delta G^0$ depends on $\Delta H^0$ (enthalpy change) and $\Delta S^0$ (entropy change).
• Entropy change ($\Delta S^0$) measures the change in the randomness of a system; more disorder means higher entropy.
• Gases have higher entropy than liquids; cyclic molecules have lower entropy than acyclic molecules due to restricted bond rotation.
• $\Delta S^0$ is (+) when products are more disordered than reactants and (-) when products are less disordered.
• Reactions with increased entropy are favored.
• $\Delta G^0$ is related to $\Delta H^0$ and $\Delta S^0$ by the equation: \Delta G^0 = \Delta H^0 - T\Delta S^0
• The total energy change is due to changes in bonding energy and disorder.
• Bonding energy changes can be calculated from bond dissociation energies.
• Entropy changes are important when:
  • The number of molecules differs between starting material and product.
  • Acyclic molecules cyclize or cyclic molecules become acyclic.
• In most other reactions (not at high temperatures), the entropy term (T\Delta S^0) is small compared to the enthalpy term ($\Delta H^0$) and can often be neglected.

Energy Diagrams

• An energy diagram shows energy changes as reactants convert to products.
• It plots energy on the y-axis versus the reaction coordinate on the x-axis.
• The energy difference between reactants and products is $\Delta H^0$; exothermic reactions release energy, while endothermic reactions consume energy.
• The transition state is the unstable energy maximum during the reaction and cannot be isolated.
• The energy of activation ($E_a$) is the energy difference between the transition state and the starting material.
• The larger the $E_a$, the slower the reaction rate.
• The transition state structure is between the starting material and product, with partially formed or broken bonds (dashed lines) and partial charges.
• Transition states are written in brackets with a double dagger superscript ($\ddagger$).
• Energy diagrams are provided for various examples, showing positive and negative $\Delta H^0$ values with large and low $E_a$ values, indicating slow/endothermic, slow/exothermic, fast/endothermic, and fast/exothermic reactions.
• For a two-step reaction, an energy diagram must be drawn for each step and then combined.
• Each step has its own energy barrier with a transition state at the energy maximum.

Kinetics

• Kinetics is the study of reaction rates.
• $E_a$ is the energy barrier that must be exceeded for reactants to become products.
• Higher concentrations and temperatures increase reaction rates.
• $\Delta G^0$, $\Delta H^0$, and $K_{eq}$ do not determine the reaction rate; they indicate the equilibrium direction and relative energy of reactants/products.
• A rate law or rate equation shows the relationship between the reaction rate and reactant concentrations and is determined experimentally.
• Fast reactions have large rate constants; slow reactions have small rate constants.
• The rate constant ($k$) and $Ea$ are inversely related; a high $Ea$ corresponds to a small $k$.
• A rate equation contains concentration terms for all reactants in a one-step mechanism and only for reactants in the rate-determining step of a multi-step reaction.
• The order of a rate equation is the sum of the exponents of the concentration terms.
• A two-step reaction has a slow rate-determining step and a fast step; the reaction cannot proceed faster than its rate-determining step.

Catalysts

• Some reactions require a catalyst to proceed at a reasonable rate.
• A catalyst speeds up the rate of a reaction, is recovered unchanged, and does not appear in the product.

Enzymes

• Enzymes are biochemical catalysts of amino acids in a specific shape.
• An enzyme contains an active site that binds an organic reactant (substrate), forming an enzyme-substrate complex.
• The substrate undergoes a specific reaction at an enhanced rate, and the products are released.