# Calculate the change in entropy for a system in going from a condition with 5 accessible microstates to 30 accessible microstates. (a) −2.5 × 10 −23 J/K (b) 9.4 × 10 −24 J/K (c) 25 × 10 −23 J/K (d) 8.3 × 10 −23 J/K

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

Chapter
Section

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18.3, Problem 2RC
Textbook Problem
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## Calculate the change in entropy for a system in going from a condition with 5 accessible microstates to 30 accessible microstates. (a) −2.5  × 10−23 J/K (b) 9.4 × 10−24 J/K (c) 25 × 10−23 J/K (d) 8.3 × 10−23 J/K

Interpretation Introduction

Interpretation: the value of change in entropy for the given system is to be identified from the given options.

Concept introduction:

In Spontaneous process, energy transfer from higher concentration to lower, or the energy is dispersed.

Entropy (S) is the quantity to measure the dispersal of energy in the spontaneous processes.

Microstates of system are the number of ways of distribution of its energy over its each atoms or particles.

According to Boltzmann, the entropy and the microstates of a system are directly proportional.

S=klnWΔS=k(lnWfinal/lnWinitial)

### Explanation of Solution

Reason for correct answer:

For the system,

Initial microstates are 5 and final microstates are 30.

According to Boltzmann, the entropy and the microstates of a system are directly proportional.

S=klnWΔS=k(lnWfinal/lnWinitial)

Therefore,

The change in entropy is,

ΔS=k(ln30/5)=1.381×1023J/K×1.79=2

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