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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 103
Chapter 14, Problem 103

Cyclopentadiene (C5H6) reacts with itself to form dicyclopentadiene (C10H12). A 0.0400 M solution of C5H6 was monitored as a function of time as the reaction 2 C5H6 → C10H12 proceeded. The following data were collected: Time (s) | [C5H6] (M) 0.0 | 0.0400 50.0 | 0.0300 100.0 | 0.0240 150.0 | 0.0200 200.0 | 0.0174 Plot [C5H6] versus time, ln[C5H6] versus time, and 1/[C5H6] versus time. (b) What is the value of the rate constant?

Verified step by step guidance
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Step 1: Begin by plotting the concentration of cyclopentadiene, [C5H6], against time. This will help determine the order of the reaction by visual inspection. If the plot is linear, it indicates a zero-order reaction.
Step 2: Next, plot the natural logarithm of the concentration, ln[C5H6], versus time. A linear plot here would suggest a first-order reaction, where the rate of reaction is directly proportional to the concentration of C5H6.
Step 3: Then, plot the inverse of the concentration, 1/[C5H6], against time. A linear relationship in this plot would indicate a second-order reaction, where the rate is proportional to the square of the concentration of C5H6.
Step 4: Determine which of the three plots is linear. The linearity of the plot will indicate the order of the reaction: zero-order, first-order, or second-order.
Step 5: Once the order of the reaction is determined, use the slope of the linear plot to calculate the rate constant, k. For a first-order reaction, the slope of the ln[C5H6] vs. time plot is -k. For a second-order reaction, the slope of the 1/[C5H6] vs. time plot is k.

Key Concepts

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

Reaction Order

The reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. It helps determine how the rate of reaction depends on the concentration of reactants. For example, a first-order reaction has a rate that is directly proportional to the concentration of one reactant, while a second-order reaction depends on the square of the concentration. Understanding the order is crucial for analyzing concentration versus time plots.
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Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time and are derived from the differential rate laws. They provide equations that can be used to plot concentration data against time to determine the order of the reaction. For instance, for a first-order reaction, the plot of ln[C] versus time yields a straight line, while for a second-order reaction, the plot of 1/[C] versus time is linear. These plots are essential for calculating the rate constant.
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Rate Law Fundamentals

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that quantifies the speed of a reaction at a given temperature. Its value is influenced by factors such as temperature and the presence of catalysts. The units of k vary depending on the order of the reaction; for example, for a first-order reaction, k has units of s⁻¹, while for a second-order reaction, it has units of M⁻¹s⁻¹. Determining k is vital for understanding the kinetics of the reaction.
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Related Practice
Textbook Question

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 × 103 M-1 cm-1 at 520 nm.

(c) Calculate the half-life of the reaction.

Textbook Question

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 × 103 M-1 cm-1 at 520 nm.

(d) How long does it take for the absorbance to fall to 0.100?

Textbook Question

At 28 C, raw milk sours in 4.0 h but takes 48 h to sour in a refrigerator at 5 C. Estimate the activation energy in kJ>mol for the reaction that leads to the souring of milk.