Question

In the reaction \(A \longrightarrow\) products, at \(t=0\), the \([\mathrm{A}]=0.1565 \mathrm{M} .\) After \(1.00 \mathrm{min},[\mathrm{A}]=0.1498 \mathrm{M},\) and after \(2.00 \mathrm{min},[\mathrm{A}]=0.1433 \mathrm{M}\) (a) Calculate the average rate of the reaction during the first minute and during the second minute. (b) Why are these two rates not equal?

Short answer

The average rate of the reaction during the first minute is -0.0067 M/min and during the second minute is -0.0065 M/min. These rates are not equal because the concentration of reactant 'A' decreases over time, which in turn causes a decrease in the rate of the reaction as there are fewer 'A' molecules to participate in the reaction.

Step-by-step solution

Calculate the average rate for the first minute

The formula to calculate the average rate of reaction is \( \frac{{\Delta [A]}}{{\Delta t}} \). Here, \([A]\) denotes concentration and \(t\) stands for time. For the first minute, the initial concentration is 0.1565 M and final concentration is 0.1498 M. The change in concentration \(\Delta [A]\) is 0.1498 M - 0.1565 M = -0.0067 M and change in time \(\Delta t\) is 1 minute. So, the average rate would be \(\frac{{-0.0067}}{{1}}\) = -0.0067 M/min.

Calculate the average rate for the second minute

Apply the same formula to calculate the average rate for the second minute. This time, the initial concentration is 0.1498 M and final concentration 0.1433 M. The change in concentration \(\Delta [A]\) is 0.1433 M - 0.1498 M = -0.0065 M and change in time \(\Delta t\) is 1 minute. The average rate thus is \(\frac{{-0.0065}}{{1}}\) = -0.0065 M/min.

Explain why the two rates are not equal

The rates of reactions are generally not constant and can decrease over time. This happens mostly because as reactants are used up, there are fewer molecules to react with each other resulting in a slowdown of the reaction. In this case, it can be observed from the rate values computed that the average rate of reaction has decreased slightly in the second minute compared to the first minute. This is because there is less 'A' available to react at the start of the second minute as compared to the start of the reaction. Therefore, the rate is slightly lower during the second minute.

Key concepts

Average Rate of Reaction

When we talk about the average rate of reaction, we refer to the change in concentration of a reactant or product over a specific time period. It gives us an idea of how quickly a reaction is proceeding. For the reaction \(A \longrightarrow\) products, we determine the average rate by measuring the concentration of \([A]\) at different times and calculating the rate of change over those intervals.
This rate is expressed in terms like \([A]/ \Delta t\), where \([A]\) stands for the concentration change and \(\Delta t\) is the time elapsed. For example, in the first minute, the initial concentration of \(A\) was 0.1565 M, and it changed to 0.1498 M. Hence, that rate was \(-0.0067\) M/min.
Keep in mind, average implies we are considering an overall change, not an instantaneous one. Thus providing an overview of the reaction's pace over a period.

Rate of Reaction Calculation

The calculation of the reaction rate is a fundamental exercise in chemistry to quantify the speed of a reaction. We use the formula \( \frac{\Delta [A]}{\Delta t} \) to find the change in concentration over a change in time. This can vary based on the start and end points you select, such as the first minute or second minute of a reaction.
For precision, keep in mind:

• \(\Delta [A]\) reflects the difference between initial and final concentrations of the reactant \(A\).
• \(\Delta t\) is the interval over which you are calculating the rate, commonly measured in minutes or seconds.

In the example provided, using the formula resulted in rates of \(-0.0067\) M/min for the first minute and \(-0.0065\) M/min for the second. This simple computation helps us draw conclusions about the reaction progress.

Factors Affecting Reaction Rate

A variety of factors can impact the rate at which reactions occur. Understanding these elements gives us insights into how to control or predict reaction speeds. Some of these factors include:

• Concentration: Higher concentrations often increase reaction rates as there are more particles to collide and react.
• Temperature: Increasing temperature usually speeds up reactions as particles have more energy to collide more frequently and forcefully.
• Surface Area: Breaking solid reactants into smaller pieces results in a larger surface area that can lead to a faster reaction.
• Catalysts: Catalysts are substances that increase the rate without being consumed, reducing the activation energy needed for the reaction.

Reflection on why the rates changed in the example shows the impact of reactant concentration. Over time, as \(A\) was consumed, fewer molecules were available to participate in the reaction, causing a slight decline in the reaction rate.

Concentration Changes in Reactions

Concentration changes are a clear indicator of a reaction's progress. By monitoring how the concentration of a reactant decreases over time, we gain insight into how fast or slow a reaction is occurring.
Consider how the concentration of \(A\) declined from 0.1565 M to 0.1433 M over two minutes in the provided example. From these observations, we infer the reaction is proceeding steadily but at a slightly lower rate in the second minute compared to the first.
This decrease underscores

• Less \(A\) was available to react.
• The overall speed of reaction tends to reduce as reactants are depleted.

Monitoring such changes is crucial for chemists to evaluate the dynamics of chemical processes and fine-tune reaction conditions for improved efficiency.