Problem 25 - Chemistry: An Atoms-Focused Approach

Question

Explain the difference between the average rate and the instantaneous rate of a chemical reaction.

Step-by-Step Solution

Answer

Answer: The main differences between the average rate and the instantaneous rate of a chemical reaction are: 1. The average rate focuses on the change in concentration over a specified time interval, while the instantaneous rate focuses on the rate at a specific point in time. 2. The average rate is calculated by dividing the difference in concentration by the time interval, whereas the instantaneous rate is calculated as the derivative of the concentration with respect to time. 3. The average rate depends on the time interval chosen and does not provide information about the exact rate at any specific moment during the reaction, while the instantaneous rate provides the rate at a specific moment during the reaction. 4. The average rate is generally used for studying slow, long-lasting reactions, while the instantaneous rate is more appropriate for studying fast reactions where the rate changes rapidly with time.

Step 1: Define the average rate of a chemical reaction

The average rate of a chemical reaction is the change in the concentration of a reactant or product over a specified time interval. It is calculated by dividing the difference in concentration by the time interval. Mathematically, the average rate can be expressed as: Average rate = \(\frac{\Delta \textrm{concentration}}{\Delta \textrm{time}}\) where \(\Delta \textrm{concentration}\) is the change in concentration and \(\Delta \textrm{time}\) is the time interval.

Step 2: Define the instantaneous rate of a chemical reaction

The instantaneous rate of a chemical reaction is the rate at a specific point in time. In other words, it is the rate of the reaction at an exact moment during its course. The instantaneous rate can be determined by taking the derivative of the concentration with respect to time. Mathematically, the instantaneous rate can be expressed as: Instantaneous rate = \(\frac{d(\textrm{concentration})}{dt}\) where \(d(\textrm{concentration})\) is the change in concentration and \(dt\) is an infinitesimal change in time.

Step 3: Differences between average rate and instantaneous rate

The main differences between average rate and instantaneous rate can be summarized as follows: 1. Definition: The average rate is the change in concentration over a specified time interval, while the instantaneous rate is the rate at a specific point in time. 2. Calculation: The average rate is calculated by dividing the difference in concentration by the time interval, while the instantaneous rate is calculated as the derivative of the concentration with respect to time. 3. Time dependency: The average rate is dependent on the time interval chosen, and it does not give any information about the exact rate at any particular instant during the reaction. The instantaneous rate provides the rate at a specific moment during the reaction. 4. Application: The average rate is generally used to study slow, long-lasting reactions, where the rate does not change significantly over time. The instantaneous rate is more appropriate for studying fast reactions, where the rate changes rapidly with time. In summary, the average rate and the instantaneous rate of a chemical reaction are two different ways of determining the rate of change of concentration of a reactant or product, with the average rate focusing on a time interval and the instantaneous rate focusing on a specific point in time.