Smartwork5 Printed Access Card for Use with Chemistry: The Science in Context 5th Edition (SmartWork Access Printed Access Card)
Smartwork5 Printed Access Card for Use with Chemistry: The Science in Context 5th Edition (SmartWork Access Printed Access Card)
5th Edition
ISBN: 9780393615296
Author: Rein V. Kirss (Author), Natalie Foster (Author), Geoffrey Davies (Author) Thomas R. Gilbert (Author)
Publisher: W. W. Norton
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Chapter 13, Problem 13.39QP
Interpretation Introduction

Interpretation: The data for the dimerization of ClO to Cl2O2 is given. The instantaneous rate of change at 1s for ClO and Cl2O2 is to be calculated.

Concept introduction: The change in the concentration of reactant or product at a particular instant of time is known as instantaneous rate of reaction.

To determine: The instantaneous rate of change at 1s for ClO and Cl2O2 .

Expert Solution & Answer
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Answer to Problem 13.39QP

Solution

The instantaneous rates of change at 1s for ClO and Cl2O2 is -0.64×1010molecules/cm3s_ and 0.33×1011molecules/cm3s_ .

Explanation of Solution

Explanation

Given

The given data is,

Time (s) [ClO](molecules/cm3)
0.0 2.60×1011
1.0 1.08×1011
2.0 6.83×1010
3.0 4.99×1010
4.0 3.93×1010
5.0 3.24×1010
6.0 2.76×1010

Table 1

The graph for the above equation is obtained as,

Smartwork5 Printed Access Card for Use with Chemistry: The Science in Context 5th Edition (SmartWork Access Printed Access Card), Chapter 13, Problem 13.39QP , additional homework tip  1

Figure 1

For finding out the instantaneous rate of change a tangent is drawn at 1s as shown above. Then the two points are chosen along the tangent.

The change in the concentration of reactant between the given time period is given as,

Rate of concentration change=(Final concentration of ClOInitial concentration of ClO)Final timeInitial time (1)

Substitute the value of initial and final concentration of ClO and initial and final time in the above equation,

Rate of concentration change=(6×1010(molecules/cm3)14×1010(molecules/cm3))1.75s0.5s=-0.64×1010molecules/cm3s_

The instantaneous reaction rate involving change in ClO is -0.64×1010molecules/cm3s_ .

The given reaction is,

2ClOCl2O2

Initially there was no Cl2O2 , therefore at 0s [Cl2O2]=0 .

The value of Δ[ClO]Δt is given as,

[Cl2O2]=(Final concentration of ClOInitial concentration of ClO)Final timeInitial time

Substitute this value of Δ[ClO]Δt in the above equation,

[Cl2O2]=12Δ[ClO] (2)

Substitute the value of final concentration and initial concentration of ClO for the time t=1s ,

[Cl2O2]=12Δ[ClO]=12(1.08×1011(molecules/cm3)2.60×1011(molecules/cm3))=0.76×1011(molecules/cm3)

Substitute the value of final concentration and initial concentration of ClO for the time t=2s ,

[Cl2O2]=12Δ[ClO]=12(6.83×1010(molecules/cm3)2.60×1011(molecules/cm3))=0.958×1011(molecules/cm3)

Substitute the value of final concentration and initial concentration of ClO for the time t=3s ,

[Cl2O2]=12Δ[ClO]=12(0.499×1011(molecules/cm3)2.60×1011(molecules/cm3))=1.05×1011(molecules/cm3)

Substitute the value of final concentration and initial concentration of ClO for the time t=4s ,

[Cl2O2]=12Δ[ClO]=12(0.393×1011(molecules/cm3)2.60×1011(molecules/cm3))=1.10×1011(molecules/cm3)

Substitute the value of final concentration and initial concentration of ClO for the time t=5s ,

Δ[Cl2O2]Δt=12Δ[ClO]=12(0.324×1011(molecules/cm3)2.60×1011(molecules/cm3))=1.14×1011(molecules/cm3)

Substitute the value of final concentration and initial concentration of ClO for the time t=6s ,

[Cl2O2]=12Δ[ClO]=12(0.276×1011(molecules/cm3)2.60×1011(molecules/cm3))=1.16×1011(molecules/cm3)

The obtained data is tabulated as,

Time (s) [ClO](molecules/cm3)
0.0 0
1.0 0.76×1011
2.0 0.958×1011
3.0 1.05×1011
4.0 1.10×1011
5.0 1.14×1011
6.0 1.16×1010

Table 2

The graph from the above table is obtained as,

Smartwork5 Printed Access Card for Use with Chemistry: The Science in Context 5th Edition (SmartWork Access Printed Access Card), Chapter 13, Problem 13.39QP , additional homework tip  2

Figure 2

The change in the concentration of reactant between the given time period is given as,

Rate of concentration change=(Final concentration of Cl2O2Initial concentration of Cl2O2)Final timeInitial time (3)

Substitute the value of initial and final concentration of Cl2O2 and initial and final time in the above equation,

Rate of concentration change=(0.95×1011(molecules/cm3)0.6×1011(molecules/cm3))1.55s0.5s=0.33×1011molecules/cm3s_

The instantaneous reaction rate involving change in Cl2O2 is 0.33×1011molecules/cm3s_ .

Conclusion

The instantaneous rates of change at 1s for ClO and Cl2O2 is -0.64×1010molecules/cm3s_ and 0.33×1011molecules/cm3s_ .

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Chapter 13 Solutions

Smartwork5 Printed Access Card for Use with Chemistry: The Science in Context 5th Edition (SmartWork Access Printed Access Card)

Ch. 13.5 - Prob. 11PECh. 13.5 - Prob. 12PECh. 13.6 - Prob. 13PECh. 13 - Prob. 13.1VPCh. 13 - Prob. 13.2VPCh. 13 - Prob. 13.3VPCh. 13 - Prob. 13.4VPCh. 13 - Prob. 13.5VPCh. 13 - Prob. 13.6VPCh. 13 - Prob. 13.7VPCh. 13 - Prob. 13.8VPCh. 13 - Prob. 13.9VPCh. 13 - Prob. 13.10VPCh. 13 - Prob. 13.11VPCh. 13 - Prob. 13.12VPCh. 13 - Prob. 13.13QPCh. 13 - Prob. 13.14QPCh. 13 - Prob. 13.15QPCh. 13 - Prob. 13.16QPCh. 13 - Prob. 13.17QPCh. 13 - Prob. 13.18QPCh. 13 - Prob. 13.19QPCh. 13 - Prob. 13.20QPCh. 13 - Prob. 13.21QPCh. 13 - Prob. 13.22QPCh. 13 - Prob. 13.23QPCh. 13 - Prob. 13.24QPCh. 13 - Prob. 13.25QPCh. 13 - Prob. 13.26QPCh. 13 - Prob. 13.27QPCh. 13 - Prob. 13.28QPCh. 13 - Prob. 13.29QPCh. 13 - Prob. 13.30QPCh. 13 - Prob. 13.31QPCh. 13 - Prob. 13.32QPCh. 13 - Prob. 13.33QPCh. 13 - Prob. 13.34QPCh. 13 - Prob. 13.35QPCh. 13 - Prob. 13.36QPCh. 13 - Prob. 13.37QPCh. 13 - Prob. 13.38QPCh. 13 - Prob. 13.39QPCh. 13 - Prob. 13.40QPCh. 13 - Prob. 13.41QPCh. 13 - Prob. 13.42QPCh. 13 - Prob. 13.43QPCh. 13 - Prob. 13.44QPCh. 13 - Prob. 13.45QPCh. 13 - Prob. 13.46QPCh. 13 - Prob. 13.47QPCh. 13 - Prob. 13.48QPCh. 13 - Prob. 13.49QPCh. 13 - Prob. 13.50QPCh. 13 - Prob. 13.51QPCh. 13 - Prob. 13.52QPCh. 13 - Prob. 13.53QPCh. 13 - Prob. 13.54QPCh. 13 - Prob. 13.55QPCh. 13 - Prob. 13.56QPCh. 13 - Prob. 13.57QPCh. 13 - Prob. 13.58QPCh. 13 - Prob. 13.59QPCh. 13 - Prob. 13.60QPCh. 13 - Prob. 13.61QPCh. 13 - Prob. 13.62QPCh. 13 - Prob. 13.63QPCh. 13 - Prob. 13.64QPCh. 13 - Prob. 13.65QPCh. 13 - Prob. 13.66QPCh. 13 - Prob. 13.67QPCh. 13 - Prob. 13.68QPCh. 13 - Prob. 13.69QPCh. 13 - Prob. 13.70QPCh. 13 - Prob. 13.71QPCh. 13 - Prob. 13.72QPCh. 13 - Prob. 13.73QPCh. 13 - Prob. 13.74QPCh. 13 - Prob. 13.75QPCh. 13 - Prob. 13.76QPCh. 13 - Prob. 13.77QPCh. 13 - Prob. 13.78QPCh. 13 - Prob. 13.79QPCh. 13 - Prob. 13.80QPCh. 13 - Prob. 13.81QPCh. 13 - Prob. 13.82QPCh. 13 - Prob. 13.83QPCh. 13 - Prob. 13.84QPCh. 13 - Prob. 13.85QPCh. 13 - Prob. 13.86QPCh. 13 - Prob. 13.87QPCh. 13 - Prob. 13.88QPCh. 13 - Prob. 13.89QPCh. 13 - Prob. 13.90QPCh. 13 - Prob. 13.91QPCh. 13 - Prob. 13.92QPCh. 13 - Prob. 13.93QPCh. 13 - Prob. 13.94QPCh. 13 - Prob. 13.95QPCh. 13 - Prob. 13.96QPCh. 13 - Prob. 13.97QPCh. 13 - Prob. 13.98QPCh. 13 - Prob. 13.99QPCh. 13 - Prob. 13.100QPCh. 13 - Prob. 13.101QPCh. 13 - Prob. 13.102QPCh. 13 - Prob. 13.103QPCh. 13 - Prob. 13.104QPCh. 13 - Prob. 13.105QPCh. 13 - Prob. 13.106QPCh. 13 - Prob. 13.107QPCh. 13 - Prob. 13.108QPCh. 13 - Prob. 13.109QPCh. 13 - Prob. 13.110QPCh. 13 - Prob. 13.111QPCh. 13 - Prob. 13.112QPCh. 13 - Prob. 13.113QPCh. 13 - Prob. 13.114QPCh. 13 - Prob. 13.115QPCh. 13 - Prob. 13.116QPCh. 13 - Prob. 13.117APCh. 13 - Prob. 13.118APCh. 13 - Prob. 13.119APCh. 13 - Prob. 13.120APCh. 13 - Prob. 13.121APCh. 13 - Prob. 13.122APCh. 13 - Prob. 13.123APCh. 13 - Prob. 13.124APCh. 13 - Prob. 13.125APCh. 13 - Prob. 13.126APCh. 13 - Prob. 13.127APCh. 13 - Prob. 13.128APCh. 13 - Prob. 13.129APCh. 13 - Prob. 13.130AP
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