ATKINS' PHYSICAL CHEMISTRY-ACCESS
ATKINS' PHYSICAL CHEMISTRY-ACCESS
11th Edition
ISBN: 9780198834700
Author: ATKINS
Publisher: OXF
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Chapter 17, Problem 17B.17P

(a)

Interpretation Introduction

Interpretation:

The integrated form of a third-order rate law is derived and the reactant present initially in their stoichiometric proportions in terms of rate law has to be expresses.

(a)

Expert Solution
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Explanation of Solution

Given,

  2A+BP

Rate equation is shown below,

  Rate=-12d[A]dt=d[B]dtrate=k[A]2[B]-d[A]dt=2k[A]2[B]d[A]dt=-2k[A]2[B]

Here,

Initial concentration of reactant: A =A0

Initial concentration of reactant: B =B0

Concentration of A at time t [A] =A0- 2x

Concentration of A at time t [B] =B0- x

  d[A]dt=-2k[A]2[B]

The reaction is rearranged,

  d[A]dt=-2k[A]2[B]-2dxdt=-2k([A]0- 2x)2([B]0-x)dxdt=k([A]0- 2x)2(12[A]0-x)dxdt=12k([A]0- 2x)3

(b)

Interpretation Introduction

Interpretation:

The rate law in terms of the reactant presents initially in twice that amount has to be expressed.

(b)

Expert Solution
Check Mark

Explanation of Solution

The reaction is integrated,

  12k0tdt =0xdx([A]0- 2x)3kt =14[(1([A]0- 2x))2(1[A]0)2]kt =2x([A]0- x)[A]02([A]0- 2x)2

Where, [A]0 =[B]0, therefore,

  dxdt =k([A]0- 2x)2([B]0- x)dxdt =k([A]0- 2x)2([A]0- x)kt =0xdx([A]0- 2x)2([A]0- x)1([A]0- 2x)2([A]0- x)=α([A]0- 2x)2+β([A]0- 2x)+λ([A]0- x)

By using partial fraction,

  1([A]0- 2x)2([A]0- x)=α([A]0- 2x)2+β([A]0- 2x)+γ([A]0- x)α([A]0- x)([A]0- 2x)([A]0- x)([A]0- 2x)2=1([A]0α+[A]02β+[A]02γ)-(α+3β[A]0+4γ[A]0)x+(2β+4γ)x2=1[A]0α+[A]02β+[A]02γ=1α+3[A]0β+[A]02γ=03β+4γ=0

Therefore,

  α=2[A]0,β=2[A]02 andγ=1[A]02

Now,

  kt=0x2[A]0([A]0- 2x)2-2[A]02([A]0- 2x)+1[A]02([A]0- x)kt =(1[A]0([A]0- 2x)+1[A]02ln([A]0- 2x)-1[A]02ln([A]0- x))0xkt =(2x[A]02([A]0- 2x))+(1[A]02)ln(([A]0- 2x)([A]0- x))

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Chapter 17 Solutions

ATKINS' PHYSICAL CHEMISTRY-ACCESS

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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