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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

Dinitrogen pentoxide gas decomposes to form nitrogen dioxide and oxygen. The reaction is first-order and has a rate constant of \(0.247 \mathrm{~h}^{-1}\) at \(25^{\circ} \mathrm{C}\). If a 2.50-L flask originally contains \(\mathrm{N}_{2} \mathrm{O}_{5}\) at a pressure of \(756 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\), then how many moles of \(\mathrm{O}_{2}\) are formed after 135 minutes? (Hint: First write a balanced equation for the decomposition.)

The decomposition of phosphine, \(\mathrm{PH}_{3}\), to \(\mathrm{P}_{4}(g)\) and \(\mathrm{H}_{2}(g)\) is firstorder. Its rate constant at a certain temperature is \(1.1 \mathrm{~min}^{-1}\). (a) What is its half-life in seconds? (b) What percentage of phosphine is decomposed after \(1.25 \mathrm{~min}\) ? (c) How long will it take to decompose one fifth of the phosphine?

Express the rate of the reaction $$2 \mathrm{~N}_{2} \mathrm{H}_{4}(l)+\mathrm{N}_{2} \mathrm{O}_{4}(l) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$$ in terms of (a) \(\Delta\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]\) (b) \(\Delta\left[\mathrm{N}_{2}\right]\)

Write the rate expression for each of the following elementary steps: (a) \(\mathrm{NO}_{3}+\mathrm{CO} \longrightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2}\) (b) \(\mathrm{I}_{2} \longrightarrow 2 \mathrm{I}\) (c) \(\mathrm{NO}+\mathrm{O}_{2} \longrightarrow \mathrm{NO}_{3}\)

The following reaction is second-order in A and first-order in B. $$\mathrm{A}+\mathrm{B} \longrightarrow \text { products }$$ (a) Write the rate expression. (b) Consider the following one-liter vessel in which each square represents a mole of \(\mathrm{A}\) and each circle represents a mole of \(\mathrm{B}\). What is the rate of the reaction in terms of \(k ?\) (c) Assuming the same rate and \(k\) as (b), fill the similar one-liter vessel shown in the figure with an appropriate number of circles (representing B).
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