15 5 Transition state theory free energy diagrams
Substitution and Elimination Reactions
Focus on free energy diagrams which arise from transition state theory.
Free Energy Changes
Exergonic Reactions:
Negative free energy change (ΔG < 0).
Releases energy to surroundings.
Transition to a more stable species.
Example: SN2 reaction with ΔG = -100 kJ/mol, indicating a highly exergonic process.
Endergonic Reactions:
Positive free energy change (ΔG > 0).
Requires energy input.
Transition to a less stable species.
Relationship Between ΔG, ΔH, and ΔS:
ΔG can be expressed in terms of ΔH (enthalpy change) and ΔS (entropy change).
Negative ΔH indicates an exothermic reaction, while positive ΔH indicates an endothermic reaction.
Calculating Equilibrium Constant (K_eq)
Standard relationship between ΔG and K_eq:
ln(K_eq) = -ΔG / RT, where R is the gas constant (0.00831 kJ/mol·K) and T is temperature (in Kelvin).
Example Calculation:
Given ΔG = -100 kJ/mol and T = 333 K:
ln(K_eq) = -(-100 kJ/mol) / (0.00831 kJ/mol·K × 333 K)
Resulting K_eq = 5 x 10^15, indicating a significant favoring of products.
Free Energy Diagram Analysis
Axes:
Y-axis: Energy
X-axis: Reaction coordinate (progress from reactants to products).
Transition State:
High-energy state where both nucleophile and leaving group are present in an SN2 reaction.
Transition states exist for a very short time (10^-12 seconds) and cannot be observed directly.
Free Energy of Activation (ΔG‡):
Amount of energy needed to reach the transition state from reactants.
Differentiated from the overall free energy change (ΔG°) which compares reactants and products directly.
Comparison of Exergonic and Endergonic Reactions
Exergonic Reaction Diagram:
Reactants at lower energy than products, negative ΔG.
Endergonic Reaction Diagram:
Reactants at higher energy than products, positive ΔG.
Effects of Temperature on Reaction Rates
Reaction rates increase with temperature due to more molecules having sufficient energy for successful collisions.
Distribution of molecular collisions illustrated by a graph with:
X-axis: Energy
Y-axis: Number of collisions.
As temperature increases:
More collisions occur at higher energies, increasing likelihood of reaching the transition state.
Rule of Thumb: A 10-degree Celsius increase in temperature approximately doubles the reaction rate.
Substitution and Elimination Reactions
Overview
Substitution and elimination reactions are fundamental types of reactions in organic chemistry. They are crucial for understanding the mechanisms by which reactants convert into products. The study of these reactions often involves the analysis of free energy diagrams based on transition state theory, which elucidates the energy changes associated with these processes.
Free Energy Changes
Exergonic Reactions
Definition: Exergonic reactions are characterized by a negative free energy change (ΔG < 0).
Energy Release: These reactions result in the release of energy to the surrounding environment, facilitating the transition of reactants to a more stable product state.
Example: An SN2 reaction exhibiting a ΔG of -100 kJ/mol demonstrates a highly exergonic process, indicating that the products are significantly more stable than the reactants and that the reaction proceeds spontaneously under standard conditions.
Endergonic Reactions
Definition: In contrast, endergonic reactions involve a positive free energy change (ΔG > 0).
Energy Requirement: Such reactions necessitate an input of energy, leading to the transition of reactants to a less stable product state.
Relationship Between ΔG, ΔH, and ΔS
The free energy change (ΔG) can be represented in terms of enthalpy change (ΔH) and entropy change (ΔS) using the equation:
[ \Delta G = \Delta H - T \Delta S ]
Enthalpy (ΔH): A negative ΔH indicates an exothermic reaction (energy released), whereas a positive ΔH suggests an endothermic reaction (energy absorbed).
Entropy (ΔS): Entropy is a measure of disorder; an increase in ΔS contributes to a more favorable (negative) ΔG, promoting spontaneous reactions.
Calculating Equilibrium Constant (K_eq)
The standard relationship between the free energy change and the equilibrium constant (K_eq) can be expressed as:
[ \ln(K_{eq}) = -\frac{\Delta G}{RT} ]
where R is the gas constant (0.00831 kJ/mol·K) and T is the absolute temperature in Kelvin.
Example Calculation: Given ΔG = -100 kJ/mol and T = 333 K, the calculation proceeds as follows:
[ \ln(K_{eq}) = -\left(-100 \frac{kJ}{mol}\right) / (0.00831 \frac{kJ}{mol\cdot K} \times 333 K) ]
The resulting equilibrium constant K_eq = 5 x 10^15 indicates a strong favorability towards the formation of products, suggesting that, at equilibrium, the products overwhelmingly dominate the reaction mixture.
Free Energy Diagram Analysis
Axes: The free energy diagram typically features energy on the Y-axis and the reaction coordinate (the progress from reactants to products) on the X-axis.
Transition State: The highest point on the diagram represents the transition state, a high-energy state where both the nucleophile and leaving group are present in an SN2 reaction.
Free Energy of Activation (ΔG‡): This refers to the energy barrier that must be overcome to reach the transition state from the reactants. It is differentiated from the overall free energy change (ΔG°), which is a comparison between the energies of reactants and products directly.
Comparison of Exergonic and Endergonic Reactions
Exergonic Reaction Diagram: In the diagram, reactants are positioned at a lower energy level than products (due to negative ΔG), indicating a spontaneous and favorable reaction.
Endergonic Reaction Diagram: Conversely, reactants have higher energy than products (due to positive ΔG), reflecting a non-spontaneous process requiring an energy input to occur.
Effects of Temperature on Reaction Rates
Temperature Impact: Reaction rates typically increase with temperature, as higher temperatures provide reactant molecules with greater kinetic energy, enhancing effective collisions.
Collision Theory: The distribution of molecular collisions can be illustrated graphically with:
X-axis: Energy
Y-axis: Number of collisions.
Temperature Effects: As temperature increases, a greater proportion of molecules possess sufficient energy to overcome the activation energy barrier, significantly increasing the likelihood of reaching the transition state.
Rule of Thumb: A 10-degree Celsius increase in temperature approximately doubles the reaction rate, highlighting the profound effect temperature has on reaction kinetics.