The standard free energy of activation of a reaction A is 90 kJ mol^-1(21.5 kcal mol^-1) at 29

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The standard free energy of activation of a reaction A is 90...

The standard free energy of activation of a reaction $A$ is $90 \mathrm{~kJ} \mathrm{~mol}^{-1}\left(21.5 \mathrm{kcal} \mathrm{mol}^{-1}\right)$ at $298 \mathrm{~K}$. Reaction $B$ is one million times faster than reaction $A$ at the same temperature. The products of each reaction are $10 \mathrm{~kJ} \mathrm{~mol}^{-1}\left(2.4 \mathrm{kcal} \mathrm{mol}^{-1}\right)$ more stable than the reactants. (a) What is the standard free energy of activation of reaction $B$ ? (b) Draw reaction free-energy diagrams for the two reactions showing the two values of $\Delta G^{\circ}$ to scale. (c) What is the standard free energy of activation of the reverse reaction in each case?

The standard free energy of activation of a reaction $A$ is $90 \mathrm{~kJ} \mathrm{~mol}^{-1}\left(21.5 \mathrm{kcal} \mathrm{mol}^{-1}\right)$ at $298 \mathrm{~K}$. Reaction $B$ is one million times faster than reaction $A$ at the same temperature. The products of each reaction are $10 \mathrm{~kJ} \mathrm{~mol}^{-1}\left(2.4 \mathrm{kcal} \mathrm{mol}^{-1}\right)$ more stable than the reactants.
(a) What is the standard free energy of activation of reaction $B$ ?
(b) Draw reaction free-energy diagrams for the two reactions showing the two values of $\Delta G^{\circ}$ to scale.
(c) What is the standard free energy of activation of the reverse reaction in each case?

Key Concepts

Reverse Reaction Activation Energy

For a reversible reaction, the activation energy of the reverse process is related to the forward activation energy and the overall free energy change (?G°). Specifically, the activation energy for the reverse reaction can be determined by subtracting the reaction free energy change from the forward activation energy, reflecting the energy barrier that must be overcome for the products to revert back to reactants.

Free Energy Change of Reaction (?G°)

The standard free energy change (?G°) of a reaction indicates the overall thermodynamic favorability of a reaction. It is the difference in free energy between products and reactants under standard conditions, and it directly affects the activation energy of the reverse reaction. A more negative ?G° indicates that the products are more stable than the reactants.

Reaction Free-Energy Diagram

A reaction free-energy diagram visually represents the energy changes during a chemical reaction along the reaction coordinate. It plots the free energy of the reactants, transition state, and products, clearly displaying the activation energy for the forward reaction, the overall free energy change (?G°), and the relationship between the forward and reverse activation energies.

Standard Free Energy of Activation (?G‡)

This concept refers to the free energy difference between the reactants and the transition state. It is a crucial parameter in determining the rate at which a reaction proceeds, as it represents the energy barrier that must be overcome for the reaction to occur. A lower ?G‡ generally corresponds to a faster reaction because fewer molecules have the required energy to reach the transition state.

Relationship between Reaction Rate and Activation Energy

The rate of a chemical reaction is strongly influenced by the activation energy, typically described by the Arrhenius or Eyring equations. These relationships show that even small changes in the activation energy can lead to significant differences in reaction rates, as the reaction rate is exponentially dependent on the negative of the activation energy over the thermal energy (RT).

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