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Chapter 11: Problem 9

Experimental data are listed for the hypothetical reaction $$\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D}$$ $$\begin{array}{lcccccc}\hline \text { Time (s) } & 0 & 10 & 20 & 30 & 40 & 50 \\\\{[\mathrm{~A}]} & 0.32 & 0.24 & 0.20 & 0.16 & 0.14 & 0.12 \\ \hline\end{array}$$ (a) Plot these data as in Figure \(11.2\). (b) Draw a tangent to the curve to find the instantaneous rate at \(30 \mathrm{~s}\). (c) Find the average rate over the 10 to \(40 \mathrm{~s}\) interval. (d) Compare the instantaneous rate at \(30 \mathrm{~s}\) with the average rate over the thirty-second interval.

Short Answer

Expert verified
Question: Compare the instantaneous rate at 30 s and the average rate over the 30-second interval (from 10 s to 40 s) in a given reaction for the concentration of A.

Step by step solution

01

Plot the Data Points

Using the given data, plot concentration of A ([A]) versus time (s) on a graph paper or with a graphing software. Make sure to label the axes and add the data points properly.
02

Draw a Tangent at 30 s

On the plotted curve, draw a tangent line at time 30 s. To do this, you can use a ruler or a straight-edged object like an index card and make sure that the tangent line touches the curve only at the point corresponding to 30 s.
03

Determine the Instantaneous Rate at 30 s

The slope of the tangent line drawn at 30 s on the curve gives the instantaneous rate. To find the slope, choose any two points on the tangent line and use the formula: $$ slope = \frac{[A_2] - [A_1]}{t_2 - t_1} $$ where \([A_1]\) and \([A_2]\) are the concentrations at times \(t_1\) and \(t_2\). Record the value of the slope, which is the instantaneous rate at 30 s.
04

Calculate the Average Rate between 10 s to 40 s

To find the average rate over the interval 10 s to 40 s, use the following formula: $$ average \thinspace rate = \frac{[A_{40}] - [A_{10}]}{40 - 10} $$ where \([A_{10}]\) and \([A_{40}]\) are the concentrations at 10 s and 40 s, respectively. Using the data points given, calculate the average rate.
05

Compare the Instantaneous Rate and the Average Rate

Compare the values of the instantaneous rate at 30 s, which you found in step 3, and the average rate over the 30-second interval, which you found in step 4. Note any similarities or differences based on these values.

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Most popular questions from this chapter

Cold-blooded animals decrease their body temperature in cold weather to match that of their environment. The activation energy of a certain reaction in a cold-blooded animal is \(65 \mathrm{~kJ} / \mathrm{mol} .\) By what percentage is the rate of the reaction decreased if the body temperature of the animal drops from \(35^{\circ} \mathrm{C}\) to \(22^{\circ} \mathrm{C} ?\)

Ammonia is produced by the reaction between nitrogen and hydro- gen gases. (a) Write a balanced equation using smallest whole-number coefficients for the reaction. (b) Write an expression for the rate of reaction in terms of \(\Delta\left[\mathrm{NH}_{3}\right]\). (c) The concentration of ammonia increases from \(0.257 \mathrm{M}\) to \(0.815 \mathrm{M}\) in \(15.0 \mathrm{~min} .\) Calculate the average rate of reaction over this time interval.

At low temperatures, the rate law for the reaction $$\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{NO}(g)$$ is as follows: rate \(=\) constant \(\times\left[\mathrm{NO}_{2}\right]^{2}\). Which of the following mechanisms is consistent with the rate law? (a) \(\mathrm{CO}+\mathrm{NO}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{NO}\) (b) \(2 \mathrm{NO}_{2} \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4} \quad\) (fast) \(\mathrm{N}_{2} \mathrm{O}_{4}+2 \mathrm{CO} \longrightarrow 2 \mathrm{CO}_{2}+2 \mathrm{NO} \quad\) (slow) (c) \(2 \mathrm{NO}_{2} \longrightarrow \mathrm{NO}_{3}+\) NO \(\quad\) (slow) \(\mathrm{NO}_{3}+\mathrm{CO} \longrightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2} \quad\) (fast) (d) \(2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2} \quad\) (slow) \(\mathrm{O}_{2}+2 \mathrm{CO} \longrightarrow 2 \mathrm{CO}_{2} \quad\) (fast)

Nitrosyl bromide (NOBr) decomposes to nitrogen oxide and bromine. Use the following data to determine the order of the decomposition reaction of nitrosyl bromide. $$\begin{array}{cccccc}\hline \text { Time (s) } & 0 & 6 & 12 & 18 & 24 \\ \text { [NOBr] } & 0.0286 & 0.0253 & 0.0229 & 0.0208 & 0.0190 \\\\\hline\end{array}$$

Nitrosyl chloride (NOCl) decomposes to nitrogen oxide and chlorine gases. (a) Write a balanced equation using smallest whole-number coefficients for the decomposition. (b) Write an expression for the reaction rate in terms of \(\Delta[\mathrm{NOCl}] .\) (c) The concentration of NOCl drops from \(0.580 M\) to \(0.238 M\) in \(8.00 \mathrm{~min}\). Calculate the average rate of reaction over this time interval.
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