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Chapter 11: Problem 34

Consider the decomposition of Q. Use the following data to determine the order of the decomposition. $$ \begin{array}{lccccc} \hline \text { Time (min) } & 0 & 4 & 8 & 12 & 16 \\ {[\mathrm{Q}]} & 0.334 & 0.25 & 0.20 & 0.167 & 0.143 \\ \hline \end{array} $$

Short Answer

Expert verified
Question: Determine the order of the reaction for the decomposition of compound Q based on the given concentration data and elapsed time during the decomposition process.

Step by step solution

01

Determine the change in concentration and time

Calculate the change in concentration and time for each time interval in the given data. This will help us in comparing the relationship between the decreasing concentration of Q and the elapsed time.
02

Calculate the reaction rates

For each time interval, calculate the reaction rates by dividing the change in concentration by the change in time.
03

Test for a 0th order reaction

In a zero-order reaction, the rate is constant with respect to the concentration. Test if the calculated rates are constant or not. If constant, this could be a 0th order reaction.
04

Test for a 1st order reaction

In a first order reaction, the rate is proportional to the concentration. Use the integrated rate law for the 1st order reaction: $$-\ln\frac{[\mathrm{Q}]}{[\mathrm{Q}]_0} = kt$$ Plot ln([Q]) vs time and check if the plot is linear. If linear, then the reaction is likely 1st order.
05

Test for a 2nd order reaction

In a second order reaction, the rate is proportional to the square of the concentration. Use the integrated rate law for the 2nd order reaction: $$\frac{1}{[\mathrm{Q}]}-\frac{1}{[\mathrm{Q}]_0} = kt$$ Plot 1/([Q]) vs time and check if the plot is linear. If linear, then the reaction is likely 2nd order.
06

Determine the order of the reaction

Based on the linearity of each of the plots, determine which order (0th, 1st, or 2nd order) best fits the decomposition of Q. This will be the order of the reaction.

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Most popular questions from this chapter

28\. Diethylhydrazine reacts with iodine according to the following equation: $$ \left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}(l)+\mathrm{I}_{2}(a q) \longrightarrow\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{~N}_{2}(l)+2 \mathrm{HI}(a q) $$ The rate of the reaction is followed by monitoring the disappearance of the purple color due to iodine. The following data are obtained at a certain temperature. $$ \begin{array}{cccc} \hline \text { Expt. } & {\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}\right]} & {\left[\mathrm{I}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h}) \\ \hline 1 & 0.150 & 0.250 & 1.08 \times 10^{-4} \\ 2 & 0.150 & 0.3620 & 1.56 \times 10^{-4} \\ 3 & 0.200 & 0.400 & 2.30 \times 10^{-4} \\ 4 & 0.300 & 0.400 & 3.44 \times 10^{-4} \\ \hline \end{array} $$ (a) What is the order of the reaction with respect to diethylhydrazine, iodine, and overall? (b) Write the rate expression for the reaction. (c) Calculate \(k\) for the reaction. (d) What must \(\left[\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2}(\mathrm{NH})_{2}\right]\) be so that the rate of the reaction is \(5.00 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{h}\) when \(\left[\mathrm{I}_{2}\right]=0.500 \mathrm{M}\) ?

Consider the following hypothetical reaction: $$ \mathrm{X}(g) \longrightarrow \mathrm{Y}(g) $$ A \(200.0-\mathrm{mL}\) flask is filled with 0.120 moles of \(\mathrm{X}\). The disappearance of \(\mathrm{X}\) is monitored at timed intervals. Assume that temperature and volume are kept constant. The data obtained are shown in the table below. $$ \begin{array}{lccccc} \hline \text { Time (min) } & 0 & 20 & 40 & 60 & 80 \\ \text { moles of X } & 0.120 & 0.103 & 0.085 & 0.071 & 0.066 \\ \hline \end{array} $$ (a) Make a similar table for the appearance of \(\mathrm{Y}\). (b) Calculate the average disappearance of \(\mathrm{X}\) in \(\mathrm{M} / \mathrm{s}\) in the first two 20 -minute intervals. (c) What is the average rate of appearance of Y between the 20 - and 60 -minute intervals?

Azomethane decomposes into nitrogen and ethane at high temperatures according to the following equation:$$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{6}(g) $$ The following data are obtained in an experiment: $$\begin{array}{cc}\hline \text { Time (h) } & {\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2}\right]} \\\\\hline 1.00 & 0.905 \\\2.00 & 0.741 \\ 3.00 & 0.607 \\\4.00 & 0.497 \\\\\hline\end{array}$$ (a) By plotting the data, show that the reaction is first-order. (b) From the graph, determine \(k\). (c) Using \(k\), find the time (in hours) that it takes to decrease the concentration to \(0.100 M\). (d) Calculate the rate of the reaction when $\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2}\right]=0.415 \mathrm{M}$.

When a base is added to an aqueous solution of chlorine dioxide gas, the following reaction occurs: \(2 \mathrm{ClO}_{2}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{ClO}_{3}^{-}(a q)+\mathrm{ClO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}\) The reaction is first-order in \(\mathrm{OH}^{-}\) and second-order for \(\mathrm{ClO}_{2}\). Initially, when \(\left[\mathrm{ClO}_{2}\right]=0.010 \mathrm{M}\) and \(\left[\mathrm{OH}^{-}\right]=0.030 \mathrm{M}\), the rate of the reaction is \(6.00 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s} .\) What is the rate of the reaction when \(50.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{ClO}_{2}\) and \(95.0 \mathrm{~mL}\) of \(0.155 \mathrm{M} \mathrm{NaOH}\) are added?

The decomposition of \(\mathrm{N}_{2} \mathrm{O}_{5}\) to \(\mathrm{NO}_{2}\) and \(\mathrm{NO}_{3}\) is a firstorder gas-phase reaction. At \(25^{\circ} \mathrm{C},\) the reaction has a half-life of \(2.81 \mathrm{~s}\). At \(45^{\circ} \mathrm{C}\), the reaction has a half-life of \(0.313 \mathrm{~s}\). What is the activation energy of the reaction?
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