The gas-phase reaction Cl(g) + HBr(g) → HCl(g) + Br(g) has an overall energy change of -66 kJ. The activation energy for the reaction is 7 kJ. (b) What is the activation energy for the reverse reaction?

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Identify the given values: the overall energy change (\(\Delta H\)) for the forward reaction is -66 kJ, and the activation energy (\(E_a\)) for the forward reaction is 7 kJ.

Understand that the activation energy for the reverse reaction can be calculated using the relationship: \(E_a^{reverse} = E_a^{forward} + \Delta H\).

Substitute the given values into the equation: \(E_a^{reverse} = 7 \text{ kJ} - 66 \text{ kJ}\).

Calculate the sum to find the activation energy for the reverse reaction.

Interpret the result: if the activation energy for the reverse reaction is positive, it indicates that energy is required to initiate the reverse reaction; if negative, it suggests an unusual scenario in chemical kinetics.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Activation Energy

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. In this context, the activation energy for the forward reaction is given as 7 kJ, indicating the energy needed to initiate the reaction between Cl(g) and HBr(g).

Enthalpy Change

The enthalpy change (ΔH) of a reaction is the difference in energy between the products and reactants. A negative ΔH, such as -66 kJ in this reaction, indicates that the reaction is exothermic, meaning it releases energy. This value is crucial for determining the activation energy of the reverse reaction, as it affects the energy landscape of the reaction pathway.

Reverse Reaction Activation Energy

The activation energy for the reverse reaction can be calculated by adding the enthalpy change to the activation energy of the forward reaction. In this case, the activation energy for the reverse reaction is the sum of the activation energy of the forward reaction (7 kJ) and the absolute value of the enthalpy change (-66 kJ), resulting in a higher energy barrier for the reverse process.

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Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.

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(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.6) is 160 kJ>mol. Calculate the fraction of methyl isonitrile molecules that has an energy equal to or greater than the activation energy at 500 K. (b) Calculate this fraction for a temperature of 520 K. What is the ratio of the fraction at 520 K to that at 500 K?

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Textbook Question

The gas-phase reaction Cl(g) + HBr(g) → HCl(g) + Br(g) has an overall energy change of -66 kJ. The activation energy for the reaction is 7 kJ. (a) Sketch the energy profile for the reaction, and label Ea and ΔE.

Textbook Question

Indicate whether each statement is true or false. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

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