(a)
Interpretation:
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
Concept introduction:
The rate law for second order reaction is represented as,
This represents the case in which identical reactants are present. In the second order kinetics,
Where,
•
•
•
Answer to Problem 20.23E
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
Explanation of Solution
It is given that the thermal decomposition of mercuric oxide follows second order kinetics and the rate constant is
The initial amount of
The number of moles of
Where,
•
•
•
•
•
Substitute the values of pressure, volume, gas constant and temperature in the above formula.
Thus, the number of moles of
The amount of
The molar mass of
Substitute the number of moles and molar mass of
The amount of
The amount of
Thus, the amount of
The rate law for the given second order reaction is given by,
Where,
•
•
•
Substitute the values of initial amount, amount at time
Under the assumption of standard temperature and pressure, units cancel out such that the equation becomes,
Thus, the time taken by the given thermal decomposition reaction of mercuric oxide to produce
On comparison of the time taken by first order kinetics and second order kinetics, it is observed that the amount of time taken in second order kinetics to produce the same amount of gas is higher than the first order kinetics.
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than the first order kinetics.
(b)
Interpretation:
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
Concept introduction:
The rate law for second order reaction is represented as,
This represents the case in which identical reactants are presents. In the second order kinetics rate of the reaction is proportional to the square of concentration of the reactant. The integrated rate law for second order reaction is represented as,
Where,
•
•
•
Answer to Problem 20.23E
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
Explanation of Solution
It is given that the thermal decomposition of mercuric oxide follows second order kinetics and the rate constant is
The initial amount of
The number of moles of
Where,
•
•
•
•
•
Substitute the values of pressure, volume, gas constant and temperature in the above formula.
Thus, the number of moles of
The amount of
The molar mass of
Substitute the number of moles and molar mass of
The amount of
The amount of
Thus, the amount of
The rate law for the given second order reaction is given by,
Where,
•
•
•
Substitute the values of initial amount, amount at time
Under the assumption of standard temperature and pressure, units cancel out such that the equation becomes,
Thus, the time taken by the given thermal decomposition reaction of mercuric oxide to produce
On comparison of the time taken by first order kinetics and second order kinetics, it is observed that the amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
The time taken by the given thermal decomposition reaction of mercuric oxide to produce
The amount of time taken in second order kinetics to produce the same amount of gas is higher than that of the first order kinetics.
Want to see more full solutions like this?
Chapter 20 Solutions
Physical Chemistry
- To a very good approximation, the cooling of a hot body to room temperature (298K) follows first-order kinetics. In this case, however, the unit that is changing is kelvins, not molarity. This idea is known as Newtons law of cooling. If the rate constant for a body is 0.0344s1, how long would it take for a piece of matter to go from 1000K to 298K?arrow_forwardOne can also define a third-life, t1/3, which is the amount of time necessary for one-third of an original amount of reactant to react. a For which order of kinetics is the third-life a constant? b Derive an expression for the t1/3 of a zeroth-order reaction. For how many third-lives will the reaction proceed before completion?arrow_forwardThe isomerization reaction CH3NCCH3CN obeys the first-order rate law rate=k[CH3NC] in the presence of an excess of argon. Measurementsat500 K reveal that in 520 s theconcentration of CH3NC decreases to 71% of its original value. Calculate the rateconstant k of the reaction at 500 K.arrow_forward
- An aqueous reaction that uses the solvent H2O as a reactant has a given rate law of rate=k[H2O][A] Where A is the other reactant species. Explain why, in most circumstances, this reaction can be defined in terms of pseudo first-order kinetics. What are the units on the rate constant?arrow_forwardWhat must the units on k be for the following rate law? rate=k[A]2[B]2arrow_forwardIf a reaction has the same rate constant, what time does it take for a reactant to decrease by 5 that is, still near the beginning of the reaction process if the kinetics are zeroth-order, first-order, and second-order with respect to that reactant?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage LearningChemistry: Matter and ChangeChemistryISBN:9780078746376Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl WistromPublisher:Glencoe/McGraw-Hill School Pub Co
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning