Question

Apply collision theory to explain two reasons why increasing the temperature of a reaction by 10 \(\mathrm{K}\) often doubles the reaction rate.

Short answer

In summary, increasing the temperature of a reaction by 10 K often doubles the reaction rate due to two main factors: 1) The increased temperature raises the kinetic energy of the particles, causing them to collide more frequently, and 2) A greater proportion of particles possess the required activation energy for the reaction, leading to more successful collisions. These combined effects boost the reaction rate according to collision theory.

Step-by-step solution

1. Understand the effect of temperature on particle frequency

Increasing the temperature of a reaction causes the particles to gain kinetic energy. This increased energy causes the particles to move faster and collide more frequently with each other. The increased frequency of these collisions creates more opportunities for reactions to occur.

2. Understand the effect of temperature on activation energy

The activation energy, denoted as \(E_a\), is the minimum amount of energy required for a reaction to take place when reactant particles collide. As temperature increases, the distribution of kinetic energy among particles broadens and shifts to higher energies. This means a greater proportion of particles will have energy equal to or greater than the activation energy. Consequently, there will be more successful collisions resulting in the reaction occurring.

3. The effect of a 10 K temperature increase

As per the Arrhenius equation, which describes the relationship between temperature and reaction rate, just a small increase in temperature can significantly affect the reaction rate. When increasing the temperature by 10 K (about 18 °F), it is commonly observed that the reaction rate doubles, as a result of the combined effects of increased collision frequency and a greater proportion of particles having the required activation energy.

4. Recap of the explanation of collision theory application

In conclusion, applying collision theory to explain why increasing the temperature of a reaction by 10 K often doubles the reaction rate, we can attribute it to two main reasons: 1. The increased temperature causes particles to gain kinetic energy and move faster, resulting in more frequent collisions between reactant particles. 2. The distribution of kinetic energy broadens and shifts to higher energies with increased temperature, causing a greater proportion of particles to possess the required activation energy for the reaction, leading to more successful collisions.

Key concepts

Understanding Reaction Rate

In chemistry, the term reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It's an indicator of how quickly a reaction progresses over time. For many students, the concept of reaction rate can be likened to a runner's pace in a race—the faster the runner (or reaction), the quicker they reach the finish line (or completion of the reaction).

Factors such as temperature, concentration of reactants, surface area, and the presence of catalysts can influence the reaction rate. A particularly interesting manifestation of this is when temperature increases, leading to an often-observed doubling of the reaction rate when the temperature is raised by 10 K. This is because elevated temperatures provide reactant particles with more kinetic energy, which translates to more frequent and energetic collisions, thereby facilitating the formation of products at a quicker pace.

The Role of Activation Energy in Chemical Reactions

The concept of activation energy (E_a) is pivotal in understanding why some reactions occur spontaneously while others require additional energy input. Activation energy is essentially the 'entry fee' for a chemical reaction to occur. It's the minimum energy barrier that must be overcome for reactants to transform into products during a collision.

Imagine activation energy as a hill that reactants must climb over to react and form products. If the reactants don't have enough kinetic energy to get over this hill, they simply bounce off each other without reacting. When the temperature of the system increases, it's like giving the reactants a boost—more of them are able to reach or exceed the activation energy, thus increasing the number of successful collisions and speeding up the reaction.

Kinetic Energy's Impact on Reaction Rates

Digging deeper into the concept of kinetic energy, we find that it's the energy an object possesses due to its motion. In the context of atoms and molecules, kinetic energy is related to how fast they are moving. When temperatures rise, the kinetic energy of these particles also increases. They move more rapidly and collide more frequently with greater force. This heightened activity is a booster for the chemical reaction rate since more collisions can lead to a higher chance of overcoming the activation energy.

High school physics often compares kinetic energy with the energy of a ball rolling down a hill; the steeper the hill, the faster the ball will roll. Similarly, with a greater kinetic energy (a steeper 'temperature hill'), reactant particles collide more energetically, making the successful formation of product particles more likely.

The Arrhenius Equation: Linking Temperature and Reaction Rates

The Arrhenius equation is a mathematical expression that shows the quantitative relationship between the rate constant of a chemical reaction and the temperature. This equation helps to quantify the effect of temperature on reaction rates, providing a formulaic explanation for phenomena chemists observe in the lab. It is represented as:\[\begin{equation}k = A e^{-\frac{E_a}{RT}}\end{equation}\]where

• (k) is the rate constant,
• (A) is the frequency factor reflecting the number of times reactants approach each other with the correct orientation,
• (E_a) is the activation energy,
• (R) is the gas constant, and
• (T) is the temperature in Kelvin.

As you can see, the rate constant (k) and, by extension, the reaction rate increases exponentially with an increase in temperature (T). Thus, according to this equation, even a slight increase in temperature, like 10 K, can have a significant impact on the rate at which a reaction proceeds.