Question

Table 12.2 illustrates how the average rate of a reaction decreases with time. Why does the average rate of a reaction generally decrease with time? How does the instantaneous rate of a reaction depend on time? Why are initial rates of a reaction primarily used by convention?

Short answer

The average rate of a reaction generally decreases with time because, as the reaction progresses, the concentrations of reactants decrease, leading to fewer reactant particles available to collide and react. The instantaneous rate of a reaction is the rate at which reactants are consumed or products are generated at an exact moment in time (\(\frac{d[R]}{dt}\) or \(\frac{d[P]}{dt}\) respectively), and may decrease, increase, or remain constant with time, depending on the reaction and the orders of reactants. Initial rates of a reaction are primarily used by convention because they offer a consistent starting point for comparing reactions, are easier to determine experimentally, and help researchers to understand the reaction mechanisms by determining the rate law (order and rate constant).

Step-by-step solution

Understanding Average Reaction Rates

The average rate of a chemical reaction refers to the speed at which reactants are transformed into products over a certain time interval. As the reaction progresses, the concentrations of the reactants decrease, which generally leads to a slower reaction rate. Since there are fewer reactant particles available to collide and react, the overall average rate of the reaction decreases with time.

Instantaneous Reaction Rates and Time

The instantaneous rate of a reaction is the rate at which reactants are consumed or products are generated at an exact moment in time. Mathematically, it is the derivative of the concentration of reactants or products with respect to time (\(\frac{d[R]}{dt}\) or \(\frac{d[P]}{dt}\) respectively). Depending on the reaction and the orders of the reactants, the instantaneous rate may either decrease, increase, or remain constant with time. However, oftentimes, it will follow a similar trend to the average rate, decreasing as the reaction progresses and reactant concentrations drop.

Use of Initial Rates in Reactions

Initial rates are reaction rates measured at the beginning of a reaction when the concentration of reactants is at its highest. There are a few reasons why initial rates are primarily used by convention: 1. The initial rate offers a consistent starting point for comparing reactions, as it eliminates the impact of changing concentrations as the reaction progresses. 2. Initial rates are easier to determine experimentally and can provide a clear indication of how changing reactants' concentrations affect the overall rate of a chemical reaction. 3. The initial rates are useful to determine the rate law (order and rate constant) in kinetics studies, helping researchers to understand the reaction mechanisms. In summary, understanding the behavior of reaction rates, such as average and instantaneous rates, is crucial in the study of chemical kinetics. Initial rates are primarily used to simplify and standardize the study of reactions and better understand their mechanisms.

Key concepts

Average Reaction Rate

When studying chemical reactions, the average reaction rate is a crucial concept. It represents the speed at which reactants turn into products over a specified time frame. Imagine it as the measure of the reaction's progress over a bigger picture.
As a reaction unfolds, the reactants are consumed. This means there are fewer molecules available to collide and cause reactions, so naturally, the rate tends to drop over time.
In many scenarios, concentrations of reactants decrease steadily, causing the average rate to slowly decline. That's why when scientists discuss the average rate, they often note that it's higher at the beginning when reactants are plentiful and decreases as they are used up.

Instantaneous Reaction Rate

The instantaneous reaction rate zooms in on a specific moment during a reaction, providing a snapshot of how fast reactants are consumed or products are formed at that precise point. It's akin to checking the speedometer on a car at one instant during a journey.
Mathematically, it's the derivative of the concentration of a reactant or product over time, expressed as \( \frac{d[R]}{dt} \) for reactants or \( \frac{d[P]}{dt} \) for products. This makes it a more dynamic measure compared to average rates.
Just like the average rate, the instantaneous rate can also show trends. Sometimes it stays constant, but more often it decreases as the reaction proceeds, aligning with the dropping reactant concentrations. This detailed view helps chemists understand minute changes as a reaction progresses.

Initial Reaction Rates

Initial reaction rates focus on the very start of a reaction, when conditions are fresh, and reactants are at their peak concentrations.
Scientists often prefer this initial snapshot for a few reasons:

• It provides a stable reference point, using a consistent beginning to compare different reactions.
• Measuring the initial rate simplifies experimental procedures and gives clear insights into how changing reactant amounts influence the reaction rate.
• Understanding initial rates is key in deciphering the reaction's rate law, revealing the mechanism behind the reaction's progress.

These elements make studying initial rates a standardized method in chemical kinetics research, providing clarity and uniformity across studies.

Chemical Kinetics

Chemical kinetics is a field in chemistry that delves into understanding reaction rates and the factors influencing them. It covers broader patterns, such as temperature and concentration effects on reaction speed.
By examining kinetics, scientists can predict how quickly a reaction occurs and alter conditions to achieve desired results.
Key concepts include:

• Reaction mechanisms, which are step-by-step sequences detailing how reactions proceed.
• Rate laws that express the relationship between the rates and concentrations of reactants.
• Activation energy, the minimum energy required for a reaction to take place.

Overall, chemical kinetics helps in deciphering complex reactions and applying this knowledge in fields ranging from pharmacology to environmental science.