Ch.14 - Chemical Kinetics

Problem 52

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Chapter 14, Problem 52

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?

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Identify the concentration of NO2 at the given time intervals from Table 14.1 and Figure 14.1.

Calculate the average rate of appearance of NO2 for each interval using the formula: \( \text{Average Rate} = \frac{[\text{NO}_2]_\text{final} - [\text{NO}_2]_\text{initial}}{t_\text{final} - t_\text{initial}} \).

For interval (a) 0 to 700 s, use the concentrations at 0 s and 700 s to find the average rate.

For interval (b) 100 to 600 s, use the concentrations at 100 s and 600 s to find the average rate.

Compare the average rates calculated for each interval to determine which is closest to the instantaneous rate at t = 350 s, considering that shorter intervals around 350 s provide a better estimate.

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Key Concepts

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

Instantaneous Rate vs. Average Rate

The instantaneous rate of a reaction refers to the rate at a specific moment in time, while the average rate is calculated over a defined time interval. To estimate the instantaneous rate at t = 350 s, one can analyze the average rates over various intervals that include this time point. Understanding the difference between these rates is crucial for accurately interpreting the data.

Rate of Reaction

The rate of reaction quantifies how quickly reactants are converted into products. It can be expressed in terms of the change in concentration of a reactant or product over time. In this case, the focus is on the appearance of NO2, which requires calculating the change in its concentration over the specified time intervals to determine the rate.

Data Interpretation from Graphs and Tables

Interpreting data from tables and graphs is essential for estimating rates of reaction. Table 14.1 likely provides concentration values at various times, while Figure 14.1 may illustrate the concentration changes graphically. Understanding how to extract and analyze this information allows for accurate calculations of average rates over the specified intervals.

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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:

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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.

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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)

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Textbook Question

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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Textbook Question

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