BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Solutions

Chapter
Section
BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

The decomposition of dinitrogen pentaoxide

N2O5(g) → 2 NO2(g) + ½ O2(g)

has the following rate equation: Rate = k[N2O5]. It has been found experimentally that the decomposition is 20.5% complete in 13.0 hours at 298 K. Calculate the rate constant and the half-life at 298 K.

Interpretation Introduction

Interpretation:

For the given reaction and the rate constant and the half-life at 298K has to be calculated.

Concept introduction:

Arrhenius equation:

  • Arrhenius equation is a formula that represents the temperature dependence of reaction rates
  • The Arrhenius equation has to be represented as follows

  k=AeEa/RTlnk=lnAeEa/RTlnk=(EaR)(1T)+lnA

  • Ea represents the activation energy and it’s unit is kJ/mol
  • R represents the universal gas constant and it has the value of 8.314 J/K.mol
  • T represents the absolute temperature
  • A represents the frequency factor or collision frequency
  • e represents the base of natural logarithm
  •  Arrhenius equation equation was proposed by Svante Arrhenius in 1889.

In order to establish the plausibility of a mechanism, one must compare the rate law of the rate determining step to the experimentally determined rate law.

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: The order of each reactant in a reaction is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction.  The order of the reaction is directly proportional to the concentration of the reactants.

Half-life: It is defined as the time required reducing the concentration of the reactant to one of its initial value.

Explanation

Examining the given rate law of the reaction clearly says that the given reaction is a first order reaction hence the expressions for first order reaction should be used.

In order to find the rate constant at given temperature the following first order rate reaction should be used.

    k=1tln[A]0[A]

With known concentration of the reactant at given time the rate constant is determined as follows,

  k=1tln[A]0[A]=113ln[A]00

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 14 Solutions

Show all chapter solutions add

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

Which of the following values is found on food labels? Recommended Dietary Allowances Dietary Reference Intakes...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What is population genetics?

Human Heredity: Principles and Issues (MindTap Course List)

A group of identical capacitors is connected first in series and then in parallel. The combined capacitance in ...

Physics for Scientists and Engineers, Technology Update (No access codes included)

Why do you think the mid-ocean ridges are higher than the surrounding seabed?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin