Question

The energy of activation for the decomposition of 2 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 \(-5.68 \mathrm{kJ} / \mathrm{mol} .\) 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 mol of H2 and 1 mol of I2 to form 2 mol of HI in the gas phase is 173.64 kJ.

Step-by-step solution

Understanding the problem

We are given the energy of activation for the decomposition of 2 moles of HI and the heat of formation of HI from H2 and I2. We are asked to find the energy of activation for the reverse reaction, which is the formation of 2 moles of HI from 1 mole of H2 and 1 mole of I2.

Calculate the delta H for the reaction

For the formation of 2 moles of HI, the heat of formation would be 2 times the heat of formation for 1 mole of HI. Delta H (heat of reaction) for formation of 2 mol HI = 2 mol * -5.68 kJ/mol = -11.36 kJ.

Apply the energy profile relationship

The energy of activation for the reverse reaction equals the energy of activation for the forward reaction plus the heat of reaction (Delta H). We can use this relationship to find the energy of activation for the formation of 2 moles of HI from H2 and I2.

Calculate the energy of activation for the reverse reaction

Energy of activation for the reverse reaction = Energy of activation for the forward reaction (decomposition) + Delta H (heat of reaction). Thus, Energy of activation for the formation of 2 mol of HI = 185 kJ (given) + (-11.36 kJ) = 173.64 kJ.

Key concepts

Chemical Kinetics

Chemical kinetics is the field of chemistry that studies the rates of chemical reactions and how different conditions affect them. It delves into understanding the speed at which reactants are converted into products and the factors influencing this transformation. A fundamental term in kinetics is the 'rate of reaction', which quantifies the speed of a reaction, typically expressed as the change in concentration of reactants or products over time.

In the given exercise, the 'energy of activation' is crucial to chemical kinetics as it represents the minimum energy that reacting particles must have for a reaction to occur. The higher the energy of activation, the slower the reaction, as fewer particles will have enough energy to react at any given time. Conversely, a lower energy of activation implies that more particles can react, thus increasing the reaction rate. Knowing the energy of activation can help predict and control the speed of chemical processes, which is essential in various applications like manufacturing, pharmaceuticals, and environmental science.

Reaction Mechanisms

A reaction mechanism outlines the step-by-step sequence of elementary reactions by which overall chemical change occurs. It is a detailed description of how the reactants are converted into products at the molecular level, which includes the breakage and formation of bonds, the order in which these events occur, and the changes in energy throughout the process.

Each step has its own rate and energy profile. Key components of these mechanisms include the formation of intermediates, and sometimes, transition states, each with unique activation energies. The slowest step in the mechanism typically determines the overall reaction rate and is known as the 'rate-determining step'. The activation energy comes into play as it is required to reach the transition state from reactants. In the exercise, understanding the energy profile of the HI decomposition helps to predict the required conditions for the reaction to proceed, illuminating its mechanism.

Enthalpy Change

Enthalpy change, represented by \(\Delta H\), is a measure of the heat absorbed or released during a chemical reaction under constant pressure. It is a state function related to the internal energy of a system plus the product of its pressure and volume. A negative \(\Delta H\) signifies an exothermic reaction, releasing heat to the surroundings, while a positive \(\Delta H\) indicates an endothermic reaction, absorbing heat.

In the context of the exercise, the heat of formation of HI given is a negative value, implying that the formation of HI from \(H_2\) and \(I_2\) is an exothermic process. This releases energy, affecting the activation energy for the reverse reaction. The enthalpy change helps us understand the energy profile of reactions and predict the amount of heat released or absorbed, which is central to both the theoretical aspects of chemical thermodynamics and practical applications like energy generation or materials synthesis.