Chapter 58: Problem 14
For a certain chemical reaction \(\Delta G^{\circ}=200 \mathrm{~kJ} / \mathrm{mol}\). When the reactants are mixed, no chemical reaction is apparent. Is this reaction under thermodynamic or kinetic control?
Short Answer
Expert verified
The reaction is under both thermodynamic and kinetic control.
Step by step solution
01
Thermodynamic Analysis
The given reaction has \( \Delta G^{\circ} = 200 \mathrm{~kJ/mol} \). This positive value indicates that the reaction is not spontaneous under standard conditions, according to the equation: \( \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} \) where \( \Delta G^{\circ}, \Delta H^{\circ}, \) and \( \Delta S^{\circ} \) are the standard Gibbs free energy change, enthalpy change, and entropy change respectively, and \( T \) is the absolute temperature.
02
Kinetic Analysis
Even though the reaction is not spontaneous under standard conditions (thermodynamically unfavorable), it could still occur if it were kinetically favorable. However, the exercise states that no chemical reaction is apparent when the reactants are mixed. This suggests that, despite being thermodynamically unfavorable, the reaction is also kinetically unfavorable. Therefore, the reactants do not have enough energy to overcome the activation energy.
03
Conclusion of Control
Since both thermodynamics and kinetics are inhibiting the reaction, it can be concluded that the reaction is under both thermodynamic and kinetic control. This is because even if the reactants absorbed sufficient energy to overcome the activation energy (kinetic control), the reaction would still not be favorable due to the positive value of \( \Delta G^{\circ} \) (thermodynamic control).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Thermodynamic Control
When discussing chemical reactions, thermodynamic control refers to the scenario where the stability of the products is the primary factor determining the outcome of a reaction. This is governed by Gibbs free energy (\( \triangle G \)), a thermodynamic potential that can predict the direction of chemical processes.
Under thermodynamic control, reactions move towards the products that have lower energy and are more stable. For example, if a reaction has a positive Gibbs free energy change (\( \triangle G^{\text{o}} > 0 \times\), as in the given exercise, this suggests that the products are at a higher energy state compared to the reactants under standard conditions. It means the reaction is not spontaneous; it will not proceed without additional energy being provided.
In the context of the exercise, a positive value of 200 kJ/mol for the Gibbs free energy indicates the reaction is thermodynamically unfavorable. This is because the energy of the products is greater than the energy of the reactants, leading to an unfavorable equilibrium position under standard conditions.
Under thermodynamic control, reactions move towards the products that have lower energy and are more stable. For example, if a reaction has a positive Gibbs free energy change (\( \triangle G^{\text{o}} > 0 \times\), as in the given exercise, this suggests that the products are at a higher energy state compared to the reactants under standard conditions. It means the reaction is not spontaneous; it will not proceed without additional energy being provided.
In the context of the exercise, a positive value of 200 kJ/mol for the Gibbs free energy indicates the reaction is thermodynamically unfavorable. This is because the energy of the products is greater than the energy of the reactants, leading to an unfavorable equilibrium position under standard conditions.
Kinetic Control
Kinetic control is concerned with the rate at which a chemical reaction proceeds rather than the stability of the products. Even if a reaction is thermodynamically favorable, it might not occur if the kinetic barriers are too high. Kinetic barriers are typically linked to the concept of activation energy.
For a reaction to happen, the molecules must collide with sufficient energy to overcome this barrier. If the energy supplied to the reactants is insufficient to reach or surpass the activation energy threshold, the reaction will not take place even if it is favorable from a thermodynamic perspective. This scenario aligns with the given problem, as 'no chemical reaction is apparent' upon mixing the reactants, implying that the necessary activation energy is not attained. Kinetic control, hence, prevents the reaction that is already deemed unfavorable by thermodynamic control.
For a reaction to happen, the molecules must collide with sufficient energy to overcome this barrier. If the energy supplied to the reactants is insufficient to reach or surpass the activation energy threshold, the reaction will not take place even if it is favorable from a thermodynamic perspective. This scenario aligns with the given problem, as 'no chemical reaction is apparent' upon mixing the reactants, implying that the necessary activation energy is not attained. Kinetic control, hence, prevents the reaction that is already deemed unfavorable by thermodynamic control.
Activation Energy
Activation energy is a critical concept in understanding why some reactions don't proceed even when they're mixed under seemingly suitable conditions. It's the minimum amount of energy required for reactants to transform into products during a chemical reaction.
The concept is part of the larger kinetic theory, which explains how properties like temperature and molecular collisions affect reaction rates. The higher the activation energy, the slower the reaction rate, because fewer molecules will have enough energy to reach the transition state. In the exercise provided, the absence of a visible reaction suggests that the activation energy is not being met, thus providing an explanation from a kinetic viewpoint. This highlights the practical significance of activation energy in everyday chemical processes and industrial applications, where both reaction speed and outcome are important.
The concept is part of the larger kinetic theory, which explains how properties like temperature and molecular collisions affect reaction rates. The higher the activation energy, the slower the reaction rate, because fewer molecules will have enough energy to reach the transition state. In the exercise provided, the absence of a visible reaction suggests that the activation energy is not being met, thus providing an explanation from a kinetic viewpoint. This highlights the practical significance of activation energy in everyday chemical processes and industrial applications, where both reaction speed and outcome are important.