Question

The energy of activation for the decomposition of \(2 \mathrm{~mol}\) of \(\mathrm{HI}\) to \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) in the gas phase is \(185 \mathrm{~kJ}\). The heat of formation of \(\mathrm{HI}(g)\) from \(\mathrm{H}_{2}(g)\) and \(\mathrm{I}_{2}(g)\) is \(-5.65 \mathrm{~kJ} / \mathrm{mol} .\) Find the energy of activation for the reaction of \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) and \(1 \mathrm{~mol}\) of \(\mathrm{I}_{2}\) to form 2 mol of HI in the gas phase.

Short answer

The energy of activation for the reaction of 1 mole of H2 and 1 mole of I2 to form 2 moles of HI is 86.85 kJ/mol.

Step-by-step solution

Understand the energy of activation

The energy of activation is the minimum amount of energy required to initiate a chemical reaction. For the decomposition of 2 moles of HI into H2 and I2, the energy of activation is given as 185 kJ.

Consider the stoichiometry

The given reaction involves 2 moles of HI forming H2 and I2. Therefore, the energy of activation for the decomposition per mole of HI is half of the total energy of activation.

Calculate activation energy per mole of HI

Divide the total energy of activation by the number of moles of HI to obtain the energy of activation per mole. \[\frac{185 \mathrm{~kJ}}{2 \mathrm{~mol}} = 92.5 \mathrm{~kJ/mol}\]

Understand the heat of formation

The heat of formation of HI from H2 and I2 is the energy change when 1 mole of HI is formed from its elements. It is given as -5.65 kJ/mol for HI indicating that the reaction releases energy and is exothermic.

Calculate the reaction energy change for 2 moles of HI

Since the heat of formation is per mole of HI, for 2 moles, the total energy released will be twice the amount. \[2 \times (-5.65 \mathrm{~kJ/mol}) = -11.3 \mathrm{~kJ}\]

Calculate the energy of activation for the reverse reaction

The formation of HI from H2 and I2 is the reverse of the decomposition reaction. To find the activation energy for the reverse reaction, we add the heat of formation to the activation energy per mole for decomposition. \[92.5 \mathrm{~kJ/mol} + (-5.65 \mathrm{~kJ/mol}) = 86.85 \mathrm{~kJ/mol}\] Since the question asks for the reaction involving 1 mole of H2 and 1 mole of I2 to form 2 moles of HI, this is the energy of activation required.

Key concepts

Heat of Formation

Heat of formation, commonly represented as \( \Delta H_f^\circ \), is a thermodynamic property referring to the energy change that occurs when one mole of a substance is formed from its elements in their standard states. This value is crucial to understanding the energy dynamics of chemical reactions. When the heat of formation is negative, as in the formation of hydrogen iodide (HI) from hydrogen (H₂) and iodine (I₂) with a value of \( -5.65 \, \text{kJ/mol} \), this indicates an exothermic process where energy is released to the surroundings.

For students studying chemical reactions, knowing the heat of formation can often be the gateway to determining the overall energy change in reactions. The heat of formation can be used to find enthalpy changes for reactions by combining the heats of formation of the reactants and the products—a fundamental concept in stoichiometry and thermochemistry.

Stoichiometry

Stoichiometry is the area of chemistry that relates to the quantities of substances involved in chemical reactions. It is essential for understanding the proportions in which reactants combine and the amounts of products formed. The stoichiometry of a reaction is based on the balanced chemical equation, which provides the mole ratio of reactants and products.

When dealing with the energy of activation or the heat of formation, stoichiometry helps us calculate the required or released energy per mole of reactant or product. For instance, in our exercise, determining the energy of activation for the formation of HI from H₂ and I₂ is made possible by first finding the energy for the decomposition of HI and then applying stoichiometric principles to find the reverse process.

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy, typically in the form of heat, to its environment. It is characterized by a negative heat of formation, indicating that the energy of the bonds formed in the products is greater than the energy of the bonds in the reactants.

Understanding exothermic reactions is important not just for theoretical chemistry but also for practical applications, such as in energy production or understanding combustion processes. In the context of the exercise regarding the formation of HI, the reaction is exothermic, denoted by a negative heat of formation value. This signifies that energy is being released when hydrogen and iodine combine to form hydrogen iodide.

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical processes and the factors that affect these rates. One of the key factors is the energy of activation, which is the minimum amount of energy needed to initiate a chemical reaction. The concept of energy of activation helps explain why some reactions occur spontaneously while others require a significant input of energy.

In the exercise provided, understanding the energy of activation is fundamental in identifying how the reaction rate can be influenced. By calculating the activation energy through the given steps, students learn how the kinetics of the reverse reaction (the formation of HI from H₂ and I₂) is related to the decomposition of HI, further cementing the role of energy in chemical kinetics.