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Chapter 14: Problem 72

What is meant by the term rate-determining step?

Short Answer

Expert verified
The rate-determining step (RDS) is the slowest step in a chemical reaction or process that determines the overall rate at which the reaction occurs. In a multi-step reaction, the slowest step acts as a bottleneck controlling the overall rate, as other steps cannot proceed until the slowest step has occurred. This concept is crucial in understanding chemical kinetics and designing strategies to control reaction rates in various applications.

Step by step solution

01

Definition of Rate-determining step

The rate-determining step, often abbreviated as RDS, is the slowest step in a chemical reaction or process that determines the overall rate at which the reaction occurs.
02

Importance of Rate-determining step

In a multi-step reaction, the rate at which the reaction proceeds depends on the rates of each individual step. The slowest step has the lowest rate, and in turn, controls the overall rate of the reaction. This is because other steps cannot proceed until the slowest step has occurred, which acts as a bottleneck.
03

Example of Rate-determining step

Let's consider a simple two-step reaction: 1. A + B → C (fast step) 2. C + D → E (slow step) Since the second step is slower, it determines the overall rate of the reaction. Even if the first step occurs rapidly, it does not speed up the formation of the final product E, because the second step is still slow. Thus, the rate of the reaction is determined by the slow step, which is the rate-determining step. The concept of rate-determining step is essential in understanding chemical kinetics and designing appropriate strategies to control reaction rates in various applications, such as industrial production, catalysis, and energy conversion.

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Most popular questions from this chapter

(a) The reaction \(\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\frac{1}{2} \mathrm{O}_{2}(g)\) is first order. Near room temperature, the rate constant equals \(7.0 \times 10^{-4} \mathrm{~s}^{-1} .\) Calculate the half-life at this temperature. (b) At \(415^{\circ} \mathrm{C},\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}\) decomposes in the gas phase, \(\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{CO}(g) .\) If the reaction is first order with a half-life of 56.3 min at this temperature, calculate the rate constant in \(\mathrm{s}^{-1}\).

The isomerization of methyl isonitrile \(\left(\mathrm{CH}_{3} \mathrm{NC}\right)\) to acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) was studied in the gas phase at \(215^{\circ} \mathrm{C},\) and the following data were obtained: $$ \begin{array}{rl} \hline \text { Time (s) } & {\left[\mathrm{CH}_{3} \mathrm{NC}\right](\boldsymbol{M})} \\ \hline 0 & 0.0165 \\ 2,000 & 0.0110 \\ 5,000 & 0.00591 \\ 8,000 & 0.00314 \\ 12,000 & 0.00137 \\ 15,000 & 0.00074 \\ \hline \end{array} $$ (a) Calculate the average rate of reaction, in \(M / s\), for the time interval between each measurement. (b) Calculate the average rate of reaction over the entire time of the data from \(t=0\) to \(t=15,000 \mathrm{~s}\). (c) Graph [CH \(\left._{3} \mathrm{NC}\right]\) versus time and determine the instantaneous rates in \(M /\) s at \(t=5000 \mathrm{~s}\) and \(t=8000 \mathrm{~s}\).

Explain why rate laws generally cannot be written from balanced equations. Under what circumstance is the rate law related directly to the balanced equation for a reaction?

The gas-phase decomposition of \(\mathrm{NO}_{2}, 2 \mathrm{NO}_{2}(g) \longrightarrow\) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g),\) is studied at \(383{ }^{\circ} \mathrm{C}\), giving the following data: $$ \begin{array}{rl} \hline \text { Time }(\mathbf{s}) & {\left[\mathrm{NO}_{2}\right](M)} \\ \hline 0.0 & 0.100 \\ 5.0 & 0.017 \\ 10.0 & 0.0090 \\ 15.0 & 0.0062 \\ 20.0 & 0.0047 \\ \hline \end{array} $$ (a) Is the reaction first order or second order with respect to the concentration of \(\mathrm{NO}_{2} ?\) (b) What is the rate constant? (c) If you used the method of initial rates to obtain the order for \(\mathrm{NO}_{2},\) predict what reaction rates you would measure in the beginning of the reaction for initial concentrations of \(0.200 \mathrm{M}, 0.100 \mathrm{M},\) and \(0.050 \mathrm{M} \mathrm{NO}_{2}\)

As described in Exercise \(14.43,\) the decomposition of sulfuryl chloride \(\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right)\) is a first-order process. The rate constant for the decomposition at \(660 \mathrm{~K}\) is \(4.5 \times 10^{-2} \mathrm{~s}^{-1}\). (a) If we begin with an initial \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) pressure of 450 torr, what is the pressure of this substance after \(60 \mathrm{~s} ?\) (b) At what time will the pressure of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decline to one-tenth its initial value?
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