Question

(a) In which of the following reactions would you expect the orientation factor to be least important in leading to reaction? \(\mathrm{NO}+\mathrm{O} \longrightarrow \mathrm{NO}_{2}\) or \(\mathrm{H}+\mathrm{Cl} \longrightarrow \mathrm{HCl}\) ? (b) How does the kinetic-molecular theory help us understand the temperature dependence of chemical reactions?

Short answer

The orientation factor is least important in the reaction \(\mathrm{H}+\mathrm{Cl} \longrightarrow \mathrm{HCl}\), as it involves two single atoms forming a diatomic molecule and their approach will always lead to proper bond formation. The kinetic-molecular theory helps us understand the temperature dependence of chemical reactions as it states that with increasing temperature, the average kinetic energy of particles increases, resulting in more frequent and energetic collisions, thus increasing the reaction rate.

Step-by-step solution

(a) Determine the Molecule Structure and Bonding

To determine the importance of the orientation factor, we will analyze the structure and bonding of the molecules involved in both reactions. The orientation factor is typically important for reactions involving larger and more complex molecules, because the probability of them forming the desired products depends on their relative orientations during collisions. Reaction 1: \(\mathrm{NO}+\mathrm{O} \longrightarrow \mathrm{NO}_{2}\) In this reaction, the nitrogen monoxide (\(\mathrm{NO}\)) molecule and the oxygen atom (\(\mathrm{O}\)) form nitrogen dioxide (\(\mathrm{NO}_{2}\)). Considering the simplicity of the molecules, the orientation factor does not play a large role in this reaction, as the oxygen atom can easily collide with the nitric oxide molecule. Reaction 2: \(\mathrm{H}+\mathrm{Cl} \longrightarrow \mathrm{HCl}\) In this reaction, the hydrogen atom (\(\mathrm{H}\)) and the chlorine atom (\(\mathrm{Cl}\)) form hydrogen chloride (\(\mathrm{HCl}\)). Since this reaction involves two single atoms forming a diatomic molecule, the orientation factor will also not be significant because the two atoms can collide readily.

(a) Compare the Importance of Orientation Factors

Given that both reactions involve relatively small and simple molecules, the orientation factor will not be particularly important in either case. However, comparing the two reactions, the orientation factor will be even less important for the reaction \(\mathrm{H}+\mathrm{Cl} \longrightarrow \mathrm{HCl}\), as it involves two single atoms forming a diatomic molecule and their approach will always lead to the proper bond formation.

(b) Explain Kinetic-Molecular Theory

The kinetic-molecular theory of gases provides an understanding of how gas particles behave and move and how changes in temperature or pressure affect their movements. According to the kinetic-molecular theory, gas particles move randomly and independently, and the average kinetic energy of the particles is directly proportional to the temperature in Kelvin.

(b) Importance of Temperature in Kinetic-Molecular Theory

The kinetic-molecular theory helps us understand the temperature dependence of chemical reactions because it explains that with increasing temperature, the average kinetic energy of the particles increases, causing them to move more rapidly. When the particles move faster, they collide more frequently and with greater energy, which results in a higher probability of overcoming the activation energy barrier for the reaction. Consequently, the rate of the reaction increases with increasing temperature.

Key concepts

Orientation Factor

The orientation factor, also known as the steric factor, refers to the spatial arrangement or relative alignment of reactant molecules during a collision. It is a key component in determining whether a chemical reaction will occur once reactant molecules collide. Simple reactions, such as those involving small molecules or atoms, tend to have a low dependence on orientation. This is because small particles can easily orient themselves in the right way for a reaction to occur upon collision.
However, for larger and more complex molecules, the orientation becomes crucial. If the molecules do not align correctly, even a perfectly energetic collision might not result in a reaction. The alignment needs to be just right for bonds to form or break as needed for the reaction products to be created.
In summary, the orientation factor is less significant in reactions involving smaller, simpler molecules or atoms like those in \( ext{H} + ext{Cl} ightarrow ext{HCl} \), where any collision tends to result in product formation. But it is more important in reactions with larger molecules that require precise alignment.

Kinetic-Molecular Theory

The kinetic-molecular theory explains the behavior of gases at the molecular level. It is grounded on several postulates that describe how molecules move and interact. According to this theory, particles are in constant random motion, colliding with each other and the walls of their container. These collisions are perfectly elastic, meaning there's no energy lost during collisions.
The theory also states that the volume of the individual particles is negligible compared to the volume of the container. Because of this, gases are compressible, and their properties change with changes in pressure and temperature. This molecular motion is a reflection of the kinetic energy of the particles, which is directly related to the temperature of the system.
This theory allows chemists to understand macro behaviors of gases, such as pressure and temperature changes, by considering the motion and energy of particles on a microscopic scale.

Temperature Dependence

Chemical reactions are highly sensitive to temperature changes, and this dependence is well explained by the kinetic-molecular theory. As temperature increases, so does the kinetic energy of particles. An increase in temperature means that particles are moving faster due to their higher kinetic energy. This results in more frequent and more energetic collisions among particles.
Because reactions require a certain energy threshold to proceed (known as activation energy), a higher temperature increases the chances of collisions having sufficient energy to overcome this threshold. Consequently, the reaction rate tends to increase with temperature because more molecules have the necessary energy to react when they collide.

• Higher temperature ➜ Faster particles
• More frequent, energetic collisions
• More particles reaching enough energy to react

This relationship is an essential concept in understanding how reactions can be controlled or accelerated by manipulating temperature.

Activation Energy

Activation energy is the minimum energy needed for a reaction to occur. It acts as a barrier that reactants must overcome to be converted into products. Even though molecules may collide frequently, only those with enough energy to surpass this barrier will successfully react.
The activation energy is dependent on the nature of the chemical bonds in the reactants and the mechanism by which they transform into products. High activation energy implies that only molecules with significant kinetic energy will react, making the reaction slower. Conversely, a low activation energy means that the reaction can proceed more easily at lower temperatures.
Catalysts are often used in reactions to lower the activation energy, thus increasing the rate of reaction without the need for increasing the temperature. By necessitating less energy, more particles can reach the energy needed to surpass the activation energy barrier, leading to more frequent successful collisions.

Collision Theory

Collision theory provides a framework for understanding how and why reactions occur between particles. According to this theory, for a reaction to take place, particles must collide with sufficient energy and with the correct orientation. These are known as effective collisions.
Not every collision leads to a reaction. The energy of the collision must be equal to or greater than the activation energy of the reaction. Moreover, particles must be oriented appropriately. This is directly linked to the orientation factor, where the spatial arrangement of approaching molecules determines if a collision will be effective.

• Particles must collide with enough energy
• Orientation must allow correct bond formation
• Only some collisions are effective in leading to the reaction

The collision theory ties together concepts of kinetic energy, orientation factor, and activation energy, offering a comprehensive picture of the dynamics of molecular interactions during chemical reactions.