Problem 101 - Chemistry A Molecular Approach

Question

This reaction has an activation energy of zero in the gas phase: $$ \mathrm{CH}_{3}+\mathrm{CH}_{3} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6} $$ a. Would you expect the rate of this reaction to change very much with temperature? b. Why might the activation energy be zero? c. What other types of reactions would you expect to have little or no activation energy?

Step-by-Step Solution

Answer

Given that the reaction has zero activation energy, one would not expect its rate to change significantly with temperature. The activation energy might be zero due to the involvement of highly reactive radical species or rapid reaction kinetics. Similar behavior is expected in other radical reactions or rapid exothermic reactions with minimal energy barriers.

Step 1: Understanding Activation Energy

Activation energy is the minimum amount of energy that reactant molecules must possess in order to undergo a specific chemical reaction. A reaction with zero activation energy implies that the reaction can proceed even without an energy barrier.

Step 2: Temperature Dependence of Reaction Rate

The rate of a reaction with zero activation energy is theoretically independent of temperature since molecules do not require additional energy to overcome an energy barrier. Therefore, based on the Arrhenius equation, where the rate coefficient is not exponentially dependent on temperature due to the zero activation energy, the reaction rate should not change much with temperature.

Step 3: Possible Reason for Zero Activation Energy

An activation energy of zero could suggest a few scenarios, such as the reaction involving highly reactive radical species which can react spontaneously upon collision without an energy barrier, or it might be an approximation when the reaction occurs very rapidly and any activation energy is too small to measure.

Step 4: Types of Reactions With Little or No Activation Energy

Reactions involving free radicals, single electron transfer mechanisms, or some kind of chain reactions are often characterized by having little or no activation energy. Additionally, certain exothermic reactions where energy is released immediately upon reactant collision can also have minimal activation energy.

Key Concepts

Activation Energy

Activation energy is a critical concept in understanding how chemical reactions occur. It is the energy threshold that reactants must overcome for a reaction to proceed. Imagine it as the height of a hill that reactants must climb before they can roll down and transform into products. A reaction with zero activation energy behaves quite uniquely. This fascinating situation implies that reactants can transform into products without any additional energy input; they can react as soon as they come into contact. This characteristic can be found in reactions involving highly reactive species that spontaneously react, for instance, in some combustion processes.

Arrhenius Equation

The Arrhenius equation mathematically describes how the rate of a chemical reaction is influenced by temperature and activation energy. The equation is written as:
\( k = A \times e^{(-E_a / (R \times T))} \),
where \( k \) is the rate constant, \( A \) is the frequency factor, \( E_a \) represents the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. The exponential term reflects the sensitivity of the reaction rate to temperature changes. However, for reactions with zero activation energy, like the one between two methyl radicals forming ethane, the equation simplifies as the exponential term becomes one. Thus, the temperature's effect on the reaction rate is significant only through the frequency factor \( A \), which does not change dramatically with temperature variations.

Temperature Dependence of Reaction Rate

Normally, the rate of chemical reactions increases with temperature. This is commonly observed in everyday phenomena: food cooks faster at higher temperatures, and substances dissolve quicker when heated. The temperature dependence of the reaction rate is due to molecules moving faster and colliding more frequently with greater energy at higher temperatures. But, in the unusual case of a reaction with zero activation energy, as theoretically predicted and applied to our gas phase reaction of methyl radicals, the rate does not significantly increase with temperature because there's no energy barrier to overcome. This is an exception to the rule that higher temperature speeds up reactions.

Free Radical Reactions

Free radicals are highly reactive atoms or molecules that have unpaired electrons, making them extremely eager to react. Free radical reactions often proceed with low or zero activation energy since these species do not require a significant energy input to react with each other. They can simply collide and react, forming new bonds instantly. It's like a spontaneous burst of reactivity. This quality is essential in understanding chain reactions, as found in polymerization or combustion processes, which proceed through a series of steps involving radicals and often exhibit behaviors consistent with low activation energy barriers.