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Ch.14 - Chemical Kinetics
All textbooksMcMurry 8th EditionCh.14 - Chemical KineticsProblem 54a
Chapter 14, Problem 54a

From the plot of concentration–time data in Figure 14.1, estimate: (a) the instantaneous rate of decomposition of N2O5 at t = 200 s.

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Identify the concentration-time plot for the decomposition of \( \text{N}_2\text{O}_5 \).
Locate the point on the graph where \( t = 200 \text{ s} \).
Draw a tangent line to the curve at \( t = 200 \text{ s} \) to find the instantaneous rate.
Determine the slope of the tangent line, which represents the rate of change of concentration with respect to time.
Use the formula for the rate of decomposition: \( \text{Rate} = -\frac{d[\text{N}_2\text{O}_5]}{dt} \), where the slope of the tangent line gives \( \frac{d[\text{N}_2\text{O}_5]}{dt} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Instantaneous Rate of Reaction

The instantaneous rate of a reaction refers to the rate at which a reactant is consumed or a product is formed at a specific moment in time. It can be determined from the slope of the concentration vs. time graph at that particular time point. This concept is crucial for understanding how reaction rates change over time and allows for the calculation of rates at any given instant.
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Concentration-Time Graph

A concentration-time graph visually represents how the concentration of a reactant or product changes over time during a chemical reaction. The x-axis typically represents time, while the y-axis represents concentration. Analyzing the slope of the curve at a specific time provides insights into the reaction kinetics and helps estimate the instantaneous rate of reaction.
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Electrochemical Stoichiometric Chart (Time)

Decomposition Reaction

A decomposition reaction is a type of chemical reaction where a single compound breaks down into two or more simpler products. In this case, the decomposition of N2O5 involves the breakdown of dinitrogen pentoxide into nitrogen dioxide and oxygen. Understanding the nature of decomposition reactions is essential for analyzing their rates and mechanisms, particularly in the context of concentration changes over time.
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Related Practice
Textbook Question

Consider a reaction that occurs by the following mechanism:

A + BC → AC + B

AC + D → A + CD

The potential energy profile for this reaction is as follows:

(d) Is the reaction endothermic or exothermic? Add labels to the diagram that show the values of the energy of reaction ΔE and the activation energy Ea for the overall reaction.

Textbook Question
Draw a plausible transition state for the bimolecular reaction of nitric oxide with ozone. Use dashed lines to indicate the atoms that are weakly linked together in the transition state. NO(g) + O3(g) NO2(g) + O2(g)

Textbook Question
Use the information in Table 14.1 and Figure 14.1 to estimate the instantaneous rate of appearance of NO2 at t = 350 s by calculating the average rate of appearance of NO2 over the following time intervals centered on t = 350 s. (a) 0 to 700 s (b) 100 to 600 s (c) 200 to 500 s (d) 300 to 400 s Which is the best estimate, and why?
Textbook Question

From the plot of concentration–time data in Figure 14.1, estimate: (b) the initial rate of decomposition of N2O5.

Textbook Question

From a plot of the concentration–time data in Worked Example 14.9, estimate: (a) the instantaneous rate of decomposition of NO2 at t = 100 s.

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Textbook Question

From a plot of the concentration–time data in Worked Example 14.9, estimate: (b) the initial rate of decomposition of NO2.