Question

Indicate whether each statement is true or false. If it is false, rewrite it so that it is true. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be faster. (b) A reaction that has a small rate constant must have a small frequency factor. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Short answer

(a) False: If you compare two reactions with similar collision factors, the one with the smaller activation energy will be faster. (b) False: A reaction that has a small rate constant could have a small frequency factor, a large activation energy, or a combination of both along with temperature. (c) True: Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Step-by-step solution

Statement (a) Analysis

In this statement, we compare two reactions with similar collision factors and state that the one with a larger activation energy will be faster. However, this is false, as the reaction with the larger activation energy generally has a lower reaction rate.

Statement (a) Rewrite

If you compare two reactions with similar collision factors, the one with the smaller activation energy will be faster.

Statement (b) Analysis

This statement suggests that a reaction with a small rate constant must have a small frequency factor. However, this statement is false because the rate constant also depends on the activation energy and temperature (via the Arrhenius equation), not just the frequency factor.

Statement (b) Rewrite

A reaction that has a small rate constant could have a small frequency factor, a large activation energy, or a combination of both along with temperature.

Statement (c) Analysis

This statement states that increasing the reaction temperature increases the fraction of successful collisions between reactants. This is true, as higher temperatures generally increase the reaction rate due to a higher number of molecules having enough energy to overcome the activation energy barrier. There is no need to rewrite Statement (c), as it is already true. To summarize, (a) False: If you compare two reactions with similar collision factors, the one with the smaller activation energy will be faster. (b) False: A reaction that has a small rate constant could have a small frequency factor, a large activation energy, or a combination of both along with temperature. (c) True: Increasing the reaction temperature increases the fraction of successful collisions between reactants.

Key concepts

Activation Energy

Understanding the concept of activation energy is fundamental in the study of chemical kinetics, the branch of chemistry that deals with reaction rates. Activation energy, denoted as E_a, is the minimum amount of energy required for reactants to transform into products during a chemical reaction.

Consider two hikers preparing to climb a hill. The hill represents the energy barrier that reactants must overcome to react. If one hill is smaller (lower activation energy) than the other (higher activation energy), the hiker climbing the smaller hill will reach the top more quickly. Similarly, a chemical reaction with a lower E_a will proceed faster than one with a higher E_a, assuming equal collision factors.

In our exercise, the misconception that a larger activation energy leads to a faster reaction was corrected by stating that it is actually the reaction with the smaller activation energy that will be faster, given similar collision factors.

Arrhenius Equation

The Arrhenius equation is a mathematical expression that describes how the rate constant (k) of a reaction changes with temperature and activation energy. The equation is given by: $$ k = A \times e^{-\frac{E_a}{RT}} $$where:

• k is the rate constant,
• A is the frequency factor, representing the number of times particles collide with the correct orientation,
• e is the base of natural logarithms,
• E_a is the activation energy,
• R is the gas constant, and
• T is the temperature (in Kelvin).

The form of the equation highlights the dependency of the reaction rate on both the frequency of collisions and the fraction of those collisions which have sufficient energy to overcome the activation barrier. A common misconception, illustrated in the exercise, is that a small rate constant implies a small frequency factor. However, as we can see from the equation, the activation energy and temperature also play crucial roles.

Collision Theory

Collision theory provides a molecular-level perspective on chemical reactions, proposing that for a reaction to occur, reactant molecules must collide with each other with sufficient energy and correct orientation. The theory is founded on two main principles:

1. Energy Criterion: Reacting molecules must have enough kinetic energy to overcome the activation energy barrier.
2. Orientation Criterion: Molecules must collide in a way that allows for the proper rearrangement of atoms to form products.

This theory connects to the idea that an increase in temperature, as mentioned in statement (c) of the exercise, leads to a higher fraction of successful collisions. At higher temperatures, more molecules have the kinetic energy needed to surpass the activation energy, thus increasing the reaction rate. It is due to these successful collisions that reactions can proceed, aligning well with our understanding of the relationship between reaction rates, temperature, and activation energy.