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Chapter 12: Problem 15

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

Expert verified
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

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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.
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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.
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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.
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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.

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Most popular questions from this chapter

Describe at least two experiments you could perform to determine a rate law.

The rate law for the decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) is $$ \text { Rate }=-\frac{\Delta\left[\mathrm{PH}_{3}\right]}{\Delta t}=k\left[\mathrm{PH}_{3}\right] $$ It takes \(120 .\) s for \(1.00 M \mathrm{PH}_{3}\) to decrease to \(0.250 \mathrm{M}\). How much time is required for \(2.00 \mathrm{M} \mathrm{PH}_{3}\) to decrease to a concentration of \(0.350 \mathrm{M} ?\)

One of the concerns about the use of Freons is that they will migrate to the upper atmosphere, where chlorine atoms can be generated by the following reaction: $$ \mathrm{CCl}_{2} \mathrm{~F}_{2} \stackrel{\mathrm{hv}}{\longrightarrow} \mathrm{CF}_{2} \mathrm{Cl}+\mathrm{Cl} $$ Chlorine atoms can act as a catalyst for the destruction of ozone. The activation energy for the reaction $$ \mathrm{Cl}+\mathrm{O}_{3} \longrightarrow \mathrm{ClO}+\mathrm{O}_{2} $$ is \(2.1 \mathrm{~kJ} / \mathrm{mol}\). Which is the more effective catalyst for the destruction of ozone, \(\mathrm{Cl}\) or \(\mathrm{NO}\) ? (See Exercise \(69 .\) )

One mechanism for the destruction of ozone in the upper atmosphere is $$ \begin{array}{ll} \mathrm{O}_{3}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) & \text { Slov } \\ \mathrm{NO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \text { Fast } \\ \hline \end{array} $$ Overall reaction \(\mathrm{O}_{3}(\mathrm{~g})+\mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{O}_{2}(\mathrm{~g})\) a. Which species is a catalyst? b. Which species is an intermediate? c. \(E_{\mathrm{a}}\) for the uncatalyzed reaction $$ \mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2 \mathrm{O}_{2} $$ is \(14.0 \mathrm{~kJ} . E_{\mathrm{a}}\) for the same reaction when catalyzed is \(11.9 \mathrm{~kJ}\). What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at \(25^{\circ} \mathrm{C}\) ? Assume that the frequency factor \(A\) is the same for each reaction.

Consider the following statements: "In general, the rate of a chemical reaction increases a bit at first because it takes a while for the reaction to get 'warmed up.' After that, however, the rate of the reaction decreases because its rate is dependent on the concentrations of the reactants, and these are decreasing." Indicate everything that is correct in these statements, and indicate everything that is incorrect. Correct the incorrect statements and explain.
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