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 the concentration of reactants decreases, leading to a lower collision frequency between reactant molecules and a slower reaction rate. The instantaneous rate depends on the reactant concentration at a specific point in time, decreasing as the reaction proceeds. Initial rates are used by convention because they offer easy measurement and comparison of various factors, simplify rate equations by focusing on the start of the reaction, and help distinguish between different reaction orders.

Step-by-step solution

1. Defining Average Rate, Instantaneous Rate, Initial Rate

The average rate of a reaction is the change in concentration of reactants or products divided by the time interval over which the change occurs. The instantaneous rate is the rate of the reaction at a specific moment in time. The initial rate is the instantaneous rate at the beginning of the reaction, when the reactant concentration is at its highest.

2. Understanding why the Average Rate decreases with time

The average rate decreases with time because as the reaction proceeds, the concentration of reactants decreases. The collision frequency between reactant molecules also decreases as fewer reactants are available. This leads to a lower probability of favorable collisions and a slower reaction rate.

3. Relationship between Instantaneous Rate and time

The instantaneous rate of a reaction depends on the reactant concentration at that specific point in time. As the reaction proceeds, the concentration of reactants decreases, causing the instantaneous rate to decrease as well. This decrease can be seen when plotting the rate vs. time, resulting in a downward curve.

4. Reasons for using Initial Rates

(1) Initial rates are used because at the start of a reaction, the concentration of reactants is at its highest, leading to a rapid reaction rate. This makes it easier to measure and compare the effects of various factors, such as temperature and catalysts, on reaction rates. (2) Using initial rates simplifies rate equations by focusing on the rate at the beginning of the reaction when other variables have minimal effect. (3) Initial rates can be used to distinguish between various reaction orders by analyzing reaction rate changes with respect to initial reactant concentration.