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Chapter 14: Problem 4

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

Expert verified
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

01

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.
02

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.
03

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.

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Most popular questions from this chapter

According to collision theory, chemical reactions occur through molecular collisions. A unimolecular elementary process in a reaction mechanism involves dissociation of a single molecule. How can these two ideas be compatible? Explain.

In the first-order decomposition of substance A the following concentrations are found at the indicated times: \(t=0 \mathrm{s},[\mathrm{A}]=0.88 \mathrm{M} ; t=50 \mathrm{s},[\mathrm{A}]=0.62 \mathrm{M} ; t=100 \mathrm{s},[\mathrm{A}]=0.44 \mathrm{M} ; t=150 \mathrm{s},[\mathrm{A}]=0.31 \mathrm{M}.\) Calculate the instantaneous rate of decomposition at \(t=100 \mathrm{s}.\)

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