Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
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Chapter 17, Problem 17B.15P

(a)

Interpretation Introduction

Interpretation:

An nth order in a reaction A is given by an equation t1/2 has to be shown

Concept introduction:

Rate law for the nth order is given below,

  d[A]dt=kr[A]n

(a)

Expert Solution
Check Mark

Explanation of Solution

Rate law for the nth order is given below,

  d[A]dt=kr[A]n

Here,

Initial concentration of reactant is [A].

Rate constant of the reaction is kr.

The reaction is rearranged,

  d[A]dt=kr[A]n

The reaction is integrated,

  -[A0][A]d[A][A]n =kr0tdt-11-n(1[A]n-1)[A0][A] =krt-11-n(1[A]n-1-1[A]0n-1)[A0][A] =krt [A]1-n[A]01-n=krt(n-1)

An nth order in a reaction A is given by an equation t1/2 is given.

(b)

Interpretation Introduction

Interpretation:

Time for the concentration of a substance to fall to one·third the initial value in an nth·order reaction has to be derived.

Concept introduction:

Balancing reaction:

Refer to part (a)

(b)

Expert Solution
Check Mark

Explanation of Solution

Half-life of the reaction is t1/2.

Half-life of the nth order reaction is given below,

Lets,

  [A]=0.5[A]0

Therefore,

    [A]1-n[A]01-n=krt(n-1)[0.5A]01-n[A]01-n=krt1/2(n-1)[A]01-n(0.51-n-1)=krt1/2(n-1)[A]01-n((2-1)1-n-1)=krt1/2(n-1)

  t1/2=[A]01-n((2-1)1-n-1)kr(n-1)t1/2=2n-1-1[A]01-nkr(n-1)t1/2=2n-1-1(n-1)kr[A]0n-1

Time is calculated when the concentration of a substance to fall to one third the initial value in an nth·order reaction.

  [A]1-n[A]01-n=krt(n-1)[(13)A]01-n[A]01-n=krt(n-1)3n1[A]01-n[A]01-n=krt(n-1)[A]01-n(3n1-1)=krt1/2(n-1)t=[A]01-n(3n1-1)kr(n-1)t1/2=3n-1-1(n-1)kr[A]0n-1

Time for the concentration of a substance to fall to one·third the initial value in an nth·order reaction is shown.

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Chapter 17 Solutions

Atkins' Physical Chemistry

Ch. 17 - Prob. 17A.2DQCh. 17 - Prob. 17A.3DQCh. 17 - Prob. 17A.4DQCh. 17 - Prob. 17A.1AECh. 17 - Prob. 17A.1BECh. 17 - Prob. 17A.2AECh. 17 - Prob. 17A.2BECh. 17 - Prob. 17A.3AECh. 17 - Prob. 17A.3BECh. 17 - Prob. 17A.4AECh. 17 - Prob. 17A.4BECh. 17 - Prob. 17A.5AECh. 17 - Prob. 17A.5BECh. 17 - Prob. 17A.6AECh. 17 - Prob. 17A.6BECh. 17 - Prob. 17A.7AECh. 17 - Prob. 17A.7BECh. 17 - Prob. 17A.9AECh. 17 - Prob. 17A.9BECh. 17 - Prob. 17A.1PCh. 17 - Prob. 17A.2PCh. 17 - Prob. 17A.3PCh. 17 - Prob. 17B.1DQCh. 17 - Prob. 17B.2DQCh. 17 - Prob. 17B.3DQCh. 17 - Prob. 17B.1BECh. 17 - Prob. 17B.2AECh. 17 - Prob. 17B.2BECh. 17 - Prob. 17B.3AECh. 17 - Prob. 17B.3BECh. 17 - Prob. 17B.4AECh. 17 - Prob. 17B.4BECh. 17 - Prob. 17B.5AECh. 17 - Prob. 17B.5BECh. 17 - Prob. 17B.6BECh. 17 - Prob. 17B.3PCh. 17 - Prob. 17B.4PCh. 17 - Prob. 17B.5PCh. 17 - Prob. 17B.6PCh. 17 - Prob. 17B.7PCh. 17 - Prob. 17B.8PCh. 17 - Prob. 17B.9PCh. 17 - Prob. 17B.10PCh. 17 - Prob. 17B.11PCh. 17 - Prob. 17B.12PCh. 17 - Prob. 17B.14PCh. 17 - Prob. 17B.15PCh. 17 - Prob. 17B.16PCh. 17 - Prob. 17B.17PCh. 17 - Prob. 17B.18PCh. 17 - Prob. 17C.1DQCh. 17 - Prob. 17C.2DQCh. 17 - Prob. 17C.1BECh. 17 - Prob. 17C.2AECh. 17 - Prob. 17C.2BECh. 17 - Prob. 17C.6PCh. 17 - Prob. 17D.1DQCh. 17 - Prob. 17D.1AECh. 17 - Prob. 17D.1BECh. 17 - Prob. 17D.2AECh. 17 - Prob. 17D.2BECh. 17 - Prob. 17D.3AECh. 17 - Prob. 17D.3BECh. 17 - Prob. 17D.4AECh. 17 - Prob. 17D.4BECh. 17 - Prob. 17D.5BECh. 17 - Prob. 17D.1PCh. 17 - Prob. 17D.3PCh. 17 - Prob. 17D.4PCh. 17 - Prob. 17D.5PCh. 17 - Prob. 17D.6PCh. 17 - Prob. 17E.1DQCh. 17 - Prob. 17E.2DQCh. 17 - Prob. 17E.3DQCh. 17 - Prob. 17E.4DQCh. 17 - Prob. 17E.5DQCh. 17 - Prob. 17E.6DQCh. 17 - Prob. 17E.1AECh. 17 - Prob. 17E.1BECh. 17 - Prob. 17E.2AECh. 17 - Prob. 17E.2BECh. 17 - Prob. 17E.3AECh. 17 - Prob. 17E.3BECh. 17 - Prob. 17E.4PCh. 17 - Prob. 17F.1DQCh. 17 - Prob. 17F.3DQCh. 17 - Prob. 17F.4DQCh. 17 - Prob. 17F.1AECh. 17 - Prob. 17F.1BECh. 17 - Prob. 17F.2AECh. 17 - Prob. 17F.2BECh. 17 - Prob. 17F.3AECh. 17 - Prob. 17F.3BECh. 17 - Prob. 17F.4AECh. 17 - Prob. 17F.4BECh. 17 - Prob. 17F.2PCh. 17 - Prob. 17F.3PCh. 17 - Prob. 17F.4PCh. 17 - Prob. 17F.6PCh. 17 - Prob. 17F.7PCh. 17 - Prob. 17G.1AECh. 17 - Prob. 17G.1BECh. 17 - Prob. 17G.2AECh. 17 - Prob. 17G.2BECh. 17 - Prob. 17G.3AECh. 17 - Prob. 17G.3BECh. 17 - Prob. 17G.1PCh. 17 - Prob. 17G.2PCh. 17 - Prob. 17G.7PCh. 17 - Prob. 17.3IACh. 17 - Prob. 17.6IACh. 17 - Prob. 17.7IA
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