Question

The activation energy for the reaction $$ \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{CO}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{CO}_{2}(g) $$ is \(125 \mathrm{~kJ} / \mathrm{mol}\), and \(\Delta E\) for the reaction is \(-216 \mathrm{~kJ} / \mathrm{mol}\). What is the activation energy for the reverse reaction \(\left[\mathrm{NO}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{CO}(g)\right] ?\)

Short answer

The activation energy for the reverse reaction is \(-91 \mathrm{~kJ/mol}\).

Step-by-step solution

Recall the principle of microscopic reversibility

According to the principle of microscopic reversibility, the difference in activation energy for the forward and reverse reactions is equal to the change in energy, \(\Delta E\), for the reaction. Mathematically, it can be expressed as: \[E_\text{a, reverse} - E_\text{a, forward} = \Delta E\] Where: \(E_\text{a, forward}\) = Activation energy of the forward reaction \(E_\text{a, reverse}\) = Activation energy of the reverse reaction \(\Delta E\) = Change in energy of the reaction

Substitute known values into the equation

We are given the activation energy for the forward reaction, \(E_\text{a, forward} = 125 \mathrm{~kJ/mol}\), and the change in energy for the overall reaction, \(\Delta E = -216\mathrm{~kJ/mol}\). We want to find the activation energy of the reverse reaction, \(E_\text{a, reverse}\). Substitute these values into the equation: \[E_\text{a, reverse} - 125\mathrm{~kJ/mol} = -216\mathrm{~kJ/mol}\]

Solve for the activation energy of the reverse reaction

Now we can solve the equation for \(E_\text{a, reverse}\): \[E_\text{a, reverse} = 125\mathrm{~kJ/mol} - 216\mathrm{~kJ/mol}\] \[E_\text{a, reverse} = -91\mathrm{~kJ/mol}\] So, the activation energy for the reverse reaction is \(-91 \mathrm{~kJ/mol}\).

Key concepts

chemical kinetics

Chemical kinetics is the branch of chemistry that deals with the rates of chemical reactions. It helps us to understand how fast or slow a reaction occurs and the factors that influence these reaction rates.
In chemical kinetics, we explore various parameters, such as temperature, concentration, and catalysts, which can significantly affect the rate of reactions. Activation energy plays a crucial role here, as it is the minimum energy that reacting molecules must have for a chemical reaction to occur. It is like a hurdle that molecules need to overcome to turn reactants into products.
When studying reactions, it is crucial to consider why some reactions are fast, while others are slow. For instance:

• High activation energy usually makes a reaction slow because fewer molecules have the energy needed to overcome this barrier.
• Temperature increase generally speeds up reactions, as it provides more energy to the molecules, helping more of them to surpass the activation energy hurdle.

Grasping chemical kinetics is essential for everything from creating effective medicines to improving industrial processes and even understanding biological systems.

microscopic reversibility

The principle of microscopic reversibility is a fundamental concept in chemistry that states the forward and reverse reactions occur with the same molecular pathways. Each step in the forward reaction has its counterpart in the reverse.
Understanding microscopic reversibility is vital because it gives us valuable insights into reaction mechanisms and energetics. It helps chemists to predict how changing conditions can affect a reaction. According to this principle, if we know the activation energy for a forward reaction and the energy change (\(\Delta E\)), we can calculate the activation energy for the reverse reaction.
This principle also implies that:

• The same intermediate species are involved in both directions of a reversible reaction.
• The transition states of forward and reverse reactions relate, allowing for reciprocal energy calculations.

Understanding microscopic reversibility allows chemists to harness and effectively predict changes in reaction rates in both directions, which can significantly impact industrial and laboratory chemical processes.

thermochemistry

Thermochemistry studies the energy changes that occur during chemical reactions and changes of state. It focuses on the heat energy absorbed or released as reactants transform into products.
The central concept in thermochemistry is enthalpy change (\(\Delta H\)), which is the heat change at constant pressure. It tells us whether a reaction is endothermic or exothermic:

• Endothermic reactions absorb heat and have a positive \(\Delta H\).
• Exothermic reactions, like the given example, release heat and have a negative \(\Delta H\).

In the solved problem, \(\Delta E\) is given as -216 \(\text{kJ/mol}\), indicating an exothermic process.
Thermochemistry is crucial because it links energy considerations with chemical reactions, allowing scientists to predict whether a reaction will require heat input or release energy. This influences everything from industrial production efficiencies to environmental and safety considerations in chemical manufacturing.

energy changes in reactions

Energy changes in reactions are concerned with how energy is transferred or transformed in chemical processes.
Every reaction involves the breaking and forming of chemical bonds, which requires or releases energy. The net change in energy, \(\Delta E\), is the difference between bond energies of reactants and products.
By understanding energy changes, we can determine reaction spontaneity and calculate an activation energy for both forward and reverse reactions. In the provided reaction example:

• The activation energy for the forward reaction is given as 125 \(\text{kJ/mol}\), which is required to break the initial bonds.
• The \(\Delta E\) is -216 \(\text{kJ/mol}\), hinting at a release of energy, showcasing the products are more stable.

Energy changes help chemists in optimizing reactions, making them crucial in efforts to synthesize new materials, create more energy-efficient processes, and impact everyday energy considerations in both industry and laboratory contexts.