Consider three reactions with different values of E_a and ΔE:
Reaction 1. E_a = 20 kJ>mol; ΔE = -60 kJ/mol
Reaction 2. E_a = 10 kJ>mol; ΔE = -20 kJ/mol
Reaction 3. E_a = 40 kJ>mol; ΔE = +15 kJ/mol
(b) Assuming that all three reactions are carried out at the same temperature and that all three have the same frequency factor A, which reaction is the fastest and which is the slowest?

Verified step by step guidance

1. Identify the given values for each reaction: Activation energy (E_a) and change in energy (ΔE).
2. Recall that the rate of a reaction is influenced by the activation energy (E_a) according to the Arrhenius equation: k = A * e^(-E_a/RT), where k is the rate constant, A is the frequency factor, R is the gas constant, and T is the temperature.
3. Understand that a lower activation energy (E_a) results in a higher rate constant (k), making the reaction faster, assuming the frequency factor (A) and temperature (T) are constant.
4. Compare the activation energies of the three reactions: Reaction 1 (E_a = 20 kJ/mol), Reaction 2 (E_a = 10 kJ/mol), and Reaction 3 (E_a = 40 kJ/mol).
5. Determine that Reaction 2, with the lowest activation energy (E_a = 10 kJ/mol), is the fastest, and Reaction 3, with the highest activation energy (E_a = 40 kJ/mol), is the slowest.

Key Concepts

Activation Energy (E_a)

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. A lower activation energy typically indicates that a reaction can proceed more quickly, as fewer energy collisions are needed to reach the transition state.

Change in Energy (ΔE)

The change in energy (ΔE) of a reaction indicates the difference in energy between the reactants and products. A negative ΔE signifies an exothermic reaction, where energy is released, while a positive ΔE indicates an endothermic reaction, where energy is absorbed. This energy change can influence the spontaneity and rate of the reaction.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. It is expressed as k = A * e^(-E_a/RT), where k is the rate constant, A is the frequency factor, R is the gas constant, and T is the temperature in Kelvin. This equation shows that a lower activation energy and higher temperature lead to a faster reaction rate.