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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 44a
Chapter 14, Problem 44a

The first-order rate constant for the decomposition of N2O5, 2 N2O5(g) → 4 NO2(g) + O2(g), at 70°C is 6.82×10-3 s-1. Suppose we start with 0.0250 mol of N2O5(g) in a volume of 2.0 L. (a) How many moles of N2O5 will remain after 5.0 min?

Verified step by step guidance
1
Identify the type of reaction and the order: The problem states that the decomposition of \( \text{N}_2\text{O}_5 \) is a first-order reaction.
Use the first-order rate equation: \( [A]_t = [A]_0 e^{-kt} \), where \([A]_t\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, \(k\) is the rate constant, and \(t\) is the time.
Calculate the initial concentration \([A]_0\): \([A]_0 = \frac{\text{moles of } \text{N}_2\text{O}_5}{\text{volume}} = \frac{0.0250 \text{ mol}}{2.0 \text{ L}}\).
Convert the time from minutes to seconds: \(5.0 \text{ min} = 5.0 \times 60 \text{ s/min} = 300 \text{ s}\).
Substitute the known values into the first-order rate equation to find \([A]_t\): \([A]_t = [A]_0 e^{-6.82 \times 10^{-3} \text{ s}^{-1} \times 300 \text{ s}}\).

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Key Concepts

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

First-Order Kinetics

First-order kinetics refers to a reaction rate that is directly proportional to the concentration of one reactant. In this case, the decomposition of N2O5 follows first-order kinetics, meaning the rate of reaction can be expressed as rate = k[N2O5], where k is the rate constant. This relationship allows us to use the integrated rate law to calculate the concentration of N2O5 over time.
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First-Order Reactions

Integrated Rate Law

The integrated rate law for a first-order reaction is given by the equation ln([A]0/[A]) = kt, where [A]0 is the initial concentration, [A] is the concentration at time t, k is the rate constant, and t is time. This equation allows us to determine the concentration of a reactant at any given time, which is essential for solving the problem of how many moles of N2O5 remain after a specified duration.
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Rate Law Fundamentals

Molarity and Moles

Molarity (M) is defined as the number of moles of solute per liter of solution. To find the remaining moles of N2O5 after a certain time, we first need to calculate the initial molarity using the initial moles and volume. Understanding the relationship between moles, volume, and molarity is crucial for converting between these units and applying the integrated rate law effectively.
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Related Practice
Textbook Question

The first-order rate constant for the decomposition of N2O5, 2 N2O5(g) → 4 NO2(g) + O2(g), at 70°C is 6.82×10-3 s-1. Suppose we start with 0.0250 mol of N2O5(g) in a volume of 2.0 L. (c) What is the half-life of N2O5 at 70°C?

Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (a) If we begin with an initial SO2Cl2 pressure of 450 torr, what is the partial pressure of this substance after 60 s?

Textbook Question

From the following data for the first-order gas-phase isomerization of CH3NC to CH3CN at 215°C, calculate the first-order rate constant and half-life for the reaction:

Time (s) Pressure CH3NC (torr)

0 502

2000 335

5000 180

8000 95.5

12,000 41.7

15,000 22.4