A certain compound A is converted into a compound B in a...

A certain compound $A$ is converted into a compound $B$ in a reaction without intermediates. The reaction has an equilibrium constant $K_{\text {eq }}=[B] /[A]=150$ and, with the free energy of $A$ as a reference point, a standard free energy of activation of $96 \mathrm{~kJ} \mathrm{~mol}^{-1}\left(23 \mathrm{kcal} \mathrm{mol}^{-1}\right)$. (a) Draw a reaction free-energy diagram for this process, showing the relative free energies of $A, B,$ and the transition state for the reaction. (b) What is the standard free energy of activation for the reverse reaction $B \rightarrow A$ ? How do you know?

A certain compound $A$ is converted into a compound $B$ in a reaction without intermediates. The reaction has an equilibrium constant $K_{\text {eq }}=[B] /[A]=150$ and, with the free energy of $A$ as a reference point, a standard free energy of activation of $96 \mathrm{~kJ} \mathrm{~mol}^{-1}\left(23 \mathrm{kcal} \mathrm{mol}^{-1}\right)$.
(a) Draw a reaction free-energy diagram for this process, showing the relative free energies of $A, B,$ and the transition state for the reaction.
(b) What is the standard free energy of activation for the reverse reaction $B \rightarrow A$ ? How do you know?

Key Concepts

Equilibrium Constant and Gibbs Free Energy Relationship

The equilibrium constant (Keq) is related to the standard Gibbs free energy change (?G°) of a reaction by the equation ?G° = –RT ln Keq. This relationship connects the thermodynamic favorability of a reaction with the relative concentrations of products and reactants at equilibrium. A large Keq indicates that the product’s free energy is significantly lower than that of the reactants, making the reaction spontaneous under standard conditions.

Activation Free Energy

Activation free energy is the free energy difference between the reactants and the transition state for the forward reaction, and between the products and the transition state for the reverse reaction. It represents the minimum energy barrier that must be overcome for the reaction to proceed. The difference between the activation energies for the forward and reverse reactions is equal to the overall free energy change of the reaction, making it crucial in understanding both the kinetics and the thermodynamics of a chemical process.

Reaction Free Energy Diagram

A reaction free energy diagram is a graphical representation that shows how the free energy of a system changes along the reaction coordinate. It includes the free energy levels of the reactants, the products, and the highest energy point known as the transition state. This diagram helps in visualizing the activation energy needed for the transformation, as well as the overall free energy change of the reaction.

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