Question

Table \(12.2\) 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 because reactants are being used up, leading to a decrease in their concentration and thus a decrease in the reaction rate. The instantaneous rate of a reaction, which is the rate at a specific point in time, also tends to decrease as time progresses due to diminishing reactant concentrations. Initial rates are used by convention because they are easier to measure, simplify the mathematical analysis, and are essential for determining the reaction order and rate constant using the rate law.

Step-by-step solution

Understand the Average Rate of Reaction

The average rate of a chemical reaction is the change in concentration of a reactant or product per unit time. It is usually expressed in units of moles per liter per second (M/s). The average rate can decrease with time because reactants are being used up in the reaction, which leads to a decrease in the concentration of reactants, and consequently, a decrease in the rate.

Instantaneous Rate of Reaction and Time

The instantaneous rate of a reaction is the rate at a specific point in time. It is the slope of a tangent line to the curve representing the concentration of a reactant or product as a function of time. The instantaneous rate depends on the time, as it represents the reaction rate at any given moment during the reaction. However, it is important to note that for many reactions, the instantaneous rate will decrease as time progresses due to diminishing reactant concentrations.

Why are Initial Rates Used by Convention?

Initial rates are used by convention for several reasons: 1. Easier to Measure: It is often easier to measure the reaction rate at the beginning of the reaction before the system becomes too complex due to the formation of products and side reactions. 2. Simplification: By focusing on the initial rate, we can assume that only the reactants are present in the reaction mixture, which simplifies the mathematical treatment and analysis of the data. 3. Rate Laws: Initial rates are essential for determining the reaction order and rate constant by using the rate law. The rate law establishes the relation between reactant concentrations and the reaction rate, which is crucial for understanding the reaction mechanism and predicting the reaction behavior. Overall, understanding the concepts of average and instantaneous rates of reaction and the significance of initial rates allows us to better analyze and predict chemical reaction behavior.

Key concepts

average rate of reaction

The average rate of reaction is a fundamental concept in reaction kinetics, describing how fast a chemical reaction occurs over a period of time. It is defined as the change in concentration of a reactant or product divided by the duration of time over which the change occurs.
The formula for the average rate of reaction is:\[ \text{Average Rate} = \frac{\Delta [Reactant]}{\Delta t} \]where \(\Delta [Reactant]\) is the change in concentration and \(\Delta t\) is the change in time. Typically measured in units like moles per liter per second (M/s), the average rate gives a big-picture view of how the reactants transform into products. As time progresses, reactants are consumed, which means their concentrations decrease. Consequently, the average rate of the reaction decreases because there are fewer reactant molecules available to collide and react.

• Can be seen as a smoothed-out representation of reaction speed
• Helps compare the kinetics of different reactions over equivalent time spans

instantaneous rate of reaction

When chemists talk about the instantaneous rate of reaction, they are diving into the specifics of how quickly a reaction proceeds at an exact moment. It is the rate at a particular time point and is obtained by drawing a tangent line to the concentration vs. time curve at that point.
This slope provides a snapshot of the reaction rate. The formula is represented as:\[ \text{Instantaneous Rate} = \frac{d[Reactant]}{dt} \]The instantaneous rate heavily depends on the concentration of reactants at that specific time. Since reactions generally slow down as reactants are consumed, the instantaneous rate often decreases with time. However, there are exceptions where catalytic effects or other reaction conditions may maintain or increase the rate at later stages.

• Exact moment measure of reaction speed
• Determined using calculus as the derivative of concentration over time

initial rates

The concept of initial rates is a cornerstone in reaction kinetics, primarily because it provides a straightforward glimpse into the beginning of a chemical reaction where the conditions are most controlled and pure. Initial rates refer to how fast the reactants begin transforming into products immediately after the reaction starts.
These rates are preferred for several reasons:

• Simplicity: At the onset of the reaction, mixtures are far less complex, making the evaluation and measurement easier.
• Predictability: Early in the reaction, products and complex side reactions are minimal, simplifying calculations.
• Rate Laws: Initial rates are crucial for identifying reaction order and rate constants through the rate law equation, which links concentrations to reaction rates:
  \[ \text{Rate} = k [A]^m[B]^n \]

By focusing on initial rates, chemists can more accurately determine the kinetics of a reaction without interference from secondary reactions or catalyst deactivations.

reaction kinetics

Reaction kinetics is the science of understanding the speeds or rates at which chemical reactions occur. It provides insights into the mechanisms of reactions and factors influencing their rates, such as concentration, temperature, and catalysts.
This field of chemistry helps in:

• Mechanism Elucidation: Uncover how reactants convert to products step-by-step.
• Rate Laws: Establish a mathematical relationship between reactant concentrations and reaction rate.
• Optimization: Adjust conditions to maximize or minimize reaction rates.

Kinetic studies are essential in industries like pharmaceuticals, where reaction speed can be critical. Through experiments and models, chemists and engineers can predict how a system behaves over time and under different conditions.
By understanding reaction kinetics, we can design better chemical processes and develop more efficient ways to produce products.