Question

Table \(11-2\) illustrates how the average rate of a reaction decreases with time. Why does the average rate decrease with time? How does the instantaneous rate of a reaction depend on time? Why are initial rates used by convention?

Short answer

The average rate of a reaction decreases with time due to the depletion of reactants and the establishment of equilibrium, leading to fewer collisions between reactant molecules and slower overall rate. The instantaneous rate depends on time, as it is directly related to the concentration of reactants, which decreases over time. Initial rates are used by convention because they enable easier comparison of different reactions, minimize the impact of side reactions, and simplify the kinetics analysis.

Step-by-step solution

Understanding the given data

Table \(11-2\) shows that the average rate of a reaction decreases with time. This means that as time progresses, the reaction becomes slower and slower. It is crucial to understand why this is happening and how it relates to the instantaneous rate of a reaction.

Reasons for the decrease in the average rate with time

The decrease in the average rate of a reaction over time can be attributed to the following factors: 1. Depletion of reactants: As the reaction proceeds, the concentration of reactants decreases. This results in fewer collisions between the reactant molecules, leading to a slower overall rate. 2. Equilibrium establishment: For most reactions, an equilibrium is eventually established. At equilibrium, the forward and reverse reaction rates are equal, and the net change in the concentrations of reactants and products is zero. When a reaction approaches the equilibrium state, its rate decreases.

Instantaneous rate of a reaction and time

The instantaneous rate of a reaction refers to the rate at any particular instant during the reaction. It can be determined by taking the derivative of the concentration of a reactant with respect to time. The instantaneous rate is directly related to the concentration of the reactants. As the concentration of the reactants decreases over time, the instantaneous rate of the reaction also decreases.

Why initial rates are used by convention

Initial rates are used for several reasons: 1. Easier comparisons: Using the initial rate allows for the comparison of different reactions under the same conditions. It is more difficult to compare reaction rates at different points in time, as the concentration of reactants decreases at varying rates for different reactions. 2. Minimization of side reactions: In many cases, the initial rate is the fastest rate of the reaction, which occurs before the buildup of products or the onset of side reactions that may affect the overall reaction rate. 3. Simplification of kinetics analysis: Evaluating reaction rates at the beginning of the reaction simplifies the mathematical analysis of reaction kinetics, as it eliminates the need to consider the effects of equilibrium or other factors that may impact the rate later in the reaction. In conclusion, the average rate of a reaction decreases with time due to the depletion of reactants and the establishment of equilibrium. The instantaneous rate of the reaction also depends on time, as it is directly related to the concentration of reactants. Using initial rates as a convention simplifies the analysis, comparison of reactions, and reduces the impact of side reactions and equilibrium.

Key concepts

Average Rate of a Reaction

The average rate of a reaction is a measure of how quickly the concentrations of reactants or products change over a period of time. It's the change in concentration divided by the time interval over which this change occurs. In simple terms, think of it like the average speed of a car traveling from one city to another. The rate will generally decrease over time as the reactants are used up leading to fewer collisions and effective reactions between molecules. This slowdown is not linear and can vary significantly as the reaction proceeds, often decreasing until the reaction reaches equilibrium where the rate stabilizes.

When tackling problems involving the average rate, students should clearly understand that this rate is not constant but tends to decrease as the reaction moves towards completion. It's important not just to use the initial and final states to calculate this average rate but to consider intervals within the reaction's progression for a more accurate representation.

Instantaneous Reaction Rate

The instantaneous reaction rate is, as the name suggests, all about the 'now' of a reaction. Capturing the rate at a specific moment in time, it’s the equivalent to the current speed of a car at an exact second during the journey, not just the average speed over the trip. Mathematically, it's determined as the derivative of the concentration of the reactants at a certain time, providing a snapshot of the reaction's velocity.

To help students grasp this, analogies like the speed of a car on a highway or a snapshot photo can be effective. By observing how the rate changes at different time intervals, one can understand the dynamics of the chemical process. The decreasing concentration of reactants over time makes the instantaneous rate probably the truest reflection of a reaction’s progress, highlighting the reason why rates are often sampled early on.

Chemical Kinetics

Chemical kinetics is the study of the speeds at which chemical reactions occur and the factors that affect these speeds. Like a dance choreographer analyzing the movements of dancers, chemical kinetics looks at how reactants move and interact to form products. Factors influencing reaction rates include the concentration of reactants, temperature, presence of a catalyst, and the physical state of the reactants.

When teaching this concept, it’s beneficial to focus on its practical applications like in pharmaceuticals where kinetics govern how quickly a medicine can act, or in environmentally-focused processes where the breakdown speed of pollutants is crucial. Remember to explain the collision theory—that reactant molecules must collide with enough energy and in the right orientation to react—since this is the basis for understanding why certain factors affect the reaction rate.

Reaction Equilibrium

Reaction equilibrium is the state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. This is a balancing act, where reactions occur simultaneously in both directions at the same speed. It's like two teams of equally strong tug-of-war competitors where the rope doesn't move to either side.

In explaining equilibrium to students, emphasize it’s not a static 'stopped' state but a dynamic one where reactions continue happening. Equilibrium constants can be used to predict the direction of the reaction and the extent of the reactants converted to products. An understanding of Le Chatelier's principle, which predicts how changes in conditions (concentration, temperature, pressure) can shift the position of equilibrium, is also fundamental for students studying reaction equilibrium.