Chapter 19 Workshop Activity - Entropy PDF

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Chapter 19 Workshop Activity - Entropy...

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2021/3/15

Chapter 19 Workshop Activity - Entropy

Chapter 19 Workshop Activity - Entropy Due: 12:00am on Thursday, May 13, 2021 To understand how points are awarded, read the Grading Policy for this assignment.

Exercise 19.30 - Enhanced - with Feedback MISSED THIS? Read Section 19.3 (Pages 850 - 856) . Suppose two systems, each composed of three particles represented by circles, have 30

of total energy.

System A: 10 System B: 12 10 8

Part A In how many energetically equivalent ways can you distribute the particles in System A? Express your answer as an integer. ANSWER: 1

Correct There is only one arrangement for System A, because all the particles occupy the same level.

Part B In how many energetically equivalent ways can you distribute the particles in System B? Express your answer as an integer. ANSWER: 6

Correct There are three different energy levels in System B. Each particle can occupy only one energy level to maintain the total energy of 30 . One can count the number of equivalent ways by rearranging particles among the levels, or use permutation ( ), where is the number of distinct possibilities. Thus, for three particles there are energetically equivalent ways to distribute the particles in System B.

Part C Which system has greater entropy? ANSWER: System A has the greater entropy. System B has the greater entropy.

Correct The entropy of a macrostate of a system increases with the number of energetically equivalent ways to arrange the components of the system. Since System B has a greater number of energetically equivalent ways to distribute the particles, it has the greater entropy.

Exercise 19.31 - Enhanced - with Feedback and Hints https://session.masteringchemistry.com/myct/assignmentPrintView?assignmentID=9839194

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Chapter 19 Workshop Activity - Entropy

MISSED THIS? Read Section 19.4 (Pages 856 - 860) ; Watch IWE 19.2 .

Part A Calculate the change in entropy that occurs in the system when 2.00 .

of isopropyl alcohol

melts at its melting point (

89.5

).

Express your answer in joules per kelvin to three significant figures.

Hint 1. Convert the temperature to kelvins Calculations of thermodynamic functions typically require the temperature to be reported using the Kelvin scale. Convert the melting point to kelvins. Express your answer in kelvins to four significant figures. ANSWER: = 183.7

ANSWER: = 58.5

Correct Begin with the conversion of the melting point from degrees Celsius to kelvins. The conversion is summarized in the hint for this part. Then, substitute all the given values into the expression for the entropy for a reversible process. Be sure to convert the energy unit from to to obtain the final answer in . In summary,

Exercise 19.38 - Enhanced - with Feedback MISSED THIS? Read Section 19.4 (Pages 856 - 860) , 19.5 (Page) ; Watch IWE 19.3 . Without doing any calculations, identify the signs of

and

for each of the following chemical reactions.

Part A 566.0 ANSWER: , , , ,

Correct There are 3 of gas on the left side of the equation and 2 of moles of gas implies a negative ( ). Since the process is exothermic (

of gas on the right side of the equation. A decrease in the number

), the entropy of the surroundings increases (

).

Part B +113.1 ANSWER:

https://session.masteringchemistry.com/myct/assignmentPrintView?assignmentID=9839194

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Chapter 19 Workshop Activity - Entropy , , , ,

Correct There are 2 of gas on the left side of the equation and 3 of moles of gas implies a positive ( ). Since the process is endothermic (

of gas on the right side of the equation. An increase in the number

), the entropy of the surroundings decreases (

).

Part C 483.6 ANSWER: , , , ,

Correct There are 3 of gas on the left side of the equation and 2 of moles of gas implies a negative ( ). Since the process is exothermic (

of gas on the right side of the equation. A decrease in the number

), the entropy of the surroundings increases (

).

Part D +393.5 ANSWER: , , , ,

Correct There is 1 of gas on the left side of the equation and there is 1 of gas on the right side of the equation. Since the molecule is more complex than the molecule, has a greater entropy than and therefore the entropy decreases during the process ( ). Since the process is endothermic (

), the entropy of the surroundings decreases (

).

Part E In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction in each part will be spontaneous. Drag the appropriate items to their respective bins. ANSWER:

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Chapter 19 Workshop Activity - Entropy Reset

Help

from Part A from Part B

from Part D

from Part C

Correct For any spontaneous process, the entropy of the universe increases ( the entropy changes for the system and the surroundings:

The value of

). The entropy change for the universe is the sum of

is temperature dependent: (constant

which means that, as temperature increases, the magnitude of

)

decreases. According to that relationship then, for , and the reaction is spontaneous at low temperatures , and the reaction is spontaneous at high temperatures , and the reaction is spontaneous at low temperatures , and the reaction is nonspontaneous at all temperatures

Conceptual Connection 19.2 - Enhanced - with Feedback

Part A Consider these three changes in the possible distributions of six gaseous particles within three interconnected boxes. Which change has a positive ? ANSWER:

Correct The more spread out the particles are between the three boxes, the greater the entropy. Therefore, this entropy change is positive.

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Chapter 19 Workshop Activity - Entropy

Exercise 19.35 - Enhanced - with Feedback MISSED THIS? Read Section 19.4 (Pages 856 - 860) .

Part A Without doing any calculations, determine the sign of

for each of the following chemical reactions.

Drag the appropriate items to their respective bins. ANSWER:

Reset

Help

Correct The sign on the change in entropy, , is positive as long as the entropy of a process increases, which only occurs in the reactions given when a gas is generated from a solid.

Exercise 19.41 - Enhanced - with Feedback and Hints MISSED THIS? Read Section 19.5 (Pages 860 - 863) ; Watch IWE 19.3 . Given the values of

,

, and

below, determine

.

Part A 124

,

260

,

300

.

Express your answer using three significant figures.

Hint 1. Calculate the entropy change of the surroundings Calculate the entropy change of the surroundings, in units of temperature ( ).

, using information from the heat of the system (

) and the

Express your answer using three significant figures. ANSWER: = -413

ANSWER: = -673

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Chapter 19 Workshop Activity - Entropy

Correct The entropy change of the universe ( the surroundings ( ). Since

) is the sum of the change in entropy of the system ( is given, calculate as shown in the hint above.

) and the change in entropy of

Part B 124

,

260

,

300

.

Express your answer using three significant figures.

Hint 1. Calculate the entropy change of the surroundings Calculate the entropy change of the surroundings, in units of temperature ( ).

, using information from the heat of the system (

) and the

Express your answer using three significant figures. ANSWER: = 413

ANSWER: = 673

Correct The

is given and

is calculated in the hint above.

Part C 124

,

260

,

300

.

Express your answer using three significant figures.

Hint 1. Calculate the entropy change of the surroundings Calculate the entropy change of the surroundings, in units of temperature ( ).

, using information from the heat of the system (

) and the

Express your answer using three significant figures. ANSWER: = 413

ANSWER: = 153

Correct The

is given and

is calculated in the hint above.

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Chapter 19 Workshop Activity - Entropy

Part D 124

,

260

,

545

.

Express your answer using two significant figures.

Hint 1. Calculate the entropy change of the surroundings Calculate the entropy change of the surroundings, in units of temperature ( ).

, using information from the heat of the system (

) and the

Express your answer using three significant figures. ANSWER: = 228

ANSWER: = -32

Correct The

is given and

calculated in the hint above.

Part E Predict whether or not the reactions above will be spontaneous. (Assume that all reactants and products are in their standard states.) Drag the appropriate items to their respective bins. ANSWER: Reset

Part B ( 260

124 , 300 )

,

Part C (

124 260

,

, 300

)

Part A (

124 ,

260

Help

, 300

) Part D (

124 260

,

, 545

)

Correct Any process where the entropy of the universe increases is spontaneous.

Exercise 19.32 - Enhanced - with Feedback MISSED THIS? Read Section 19.4 (Pages 856 - 860) ; Watch IWE 19.2 .

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Chapter 19 Workshop Activity - Entropy

Part A Calculate the change in entropy that occurs in the system when 1.16 normal boiling point (34.6 ). The heat of vaporization is 26.5

of diethyl ether (

) condenses from a gas to a liquid at its

.

Express your answer with the appropriate units. ANSWER: = -99.9

Correct The change in entropy of a system can be calculated using the following equation:

The enthalpy of vaporization is given as

The enthalpy of condensation is the same in magnitude but opposite in sign:

Converting the temperature from degrees Celsius to kelvins gives

Finally, substitute the quantities into the first equation to calculate the change in entropy for the system:

Exercise 19.34 - Enhanced - with Feedback MISSED THIS? Read Section 19.4 (Pages 856 - 860) ; Watch IWE 19.2 .

Part A Calculate the change in entropy that occurs in the system when 43.4 (56.1 ). The heat of vaporization is 29.1 .

of acetone (

) vaporizes from a liquid to a gas at its boiling point

Express your answer with the appropriate units. ANSWER: = 66.0

Correct The change in entropy of a system can be calculated using the following equation:

The enthalpy of vaporization is given as

Converting the temperature from degrees Celsius to kelvins gives

Finally, substituting these values into the first equation to calculate the change in entropy for the system gives

Interactive Worked Example: Calculating ΔS for a Change of State https://session.masteringchemistry.com/myct/assignmentPrintView?assignmentID=9839194

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Chapter 19 Workshop Activity - Entropy

First, launch the video below. You will be asked to use your knowledge of chemistry to predict the outcome of a demonstration. Then, close the video window and answer the related questions. You can watch the video again at any point to review.

Part A Calculate the change in entropy that occurs in the system when 27.0 of acetone .

of acetone condenses from a gas to a liquid at the normal boiling point

Express your answer in joules per kelvin to three significant figures. ANSWER: = -41.1

Correct Since condensation occurrs at the boiling point of acetone and the temperature is constant, the following equation can be used to calculate the entropy change of the system:

where is the heat exchanged with the surroundings in a reversible process, and can be calculated as:

is the temperature in

. Temperature in kelvins

The enthalpy of condensation is the same in value as the enthalpy of vaporization but has an opposite sign since it is the reverse process.

Thus,

can be calculated as:

± Entropy Changes in Physical Transformations Phase transitions are similar to chemical reactions in that they each have an associated entropy change. A phase transition involves the breaking or forming of intermolecular attractive forces. A change in entropy accompanies not only a variation in the temperature, pressure, or volume of a system but also a physical transformation such as the fusion, vaporization, or transition from one crystalline state into another. In the equilibrium between two phases, the exchange of heat can be carried out reversibly, and the quantity of heat is equal to the enthalpy change for the transition, . The associated change in entropy, , is given by the equation

where

is the transition temperature.

It has been observed that most organic liquids exhibit almost the same value for the entropy of vaporization. This observation is described by Trouton's rule and is useful for making predictions about liquids.

Part A https://session.masteringchemistry.com/myct/assignmentPrintView?assignmentID=9839194

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Chapter 19 Workshop Activity - Entropy

Predict whether each of the following transformations generally leads to an increase or decrease in the entropy of a system. Drag the appropriate transformations to their respective bins.

Hint 1. Definition of entropy Entropy is a measure of the amount of disorder in a system. The more disorder in a system, measured by the number of microstates available to each molecule or atom, the higher the entropy of the system. A microstate is one of the different accessible arrangements of the molecules for a particular state of the system. Hint 2. Identify the relative number of microstates Molecules have a certain amount of energy associated with their motion. This energy is constantly being redistributed among molecules during collisions, which allows them to access different energy levels and alter the arrangement of molecules. These arrangements of molecules in their respective physical state are known as microstates. The more arrangements of molecules available, the higher the number of microstates. Which of the following transformations generally results in an increase in the number of microstates available to the molecules or atoms? Check all that apply. ANSWER: Crystalline structure becomes amorphous. Solid melts to form a liquid. Dissolved particles precipitate. Gas condenses to form a liquid. More dense structure becomes less dense.

ANSWER:

Reset

to

to to

Higher density density

Help

to lower

(graphite) to

(diamond)

Correct The change in entropy is a measure of disorder in the system. When evaluating a change in entropy during a physical transformation from solid to liquid, liquid to gas, or solid to gas (and vice versa), the molecular state of the system should be taken into account. Physical transformations also involve a change in allotropic modifications, which are the result of the rearrangement of atoms in the molecule, resulting in a change in the molecular structure.

Trouton's rule Trouton's rule states that the entropy of vaporization is almost the same value, about 87-88

, for various types of liquids.

This implies that approximately the same amount of disorder is generated in the passage of one mole of a substance from liquid to gas, when comparisons are made at the normal boiling point.

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Chapter 19 Workshop Activity - Entropy

Part B Liquid

Boiling Enthalpy of point vaporization ( ) ( )

o-xylene

417.5

36.24

toluene

383.6

33.18

nonane

423.8

37.18

chloroform

334.2

29.24

ethanol

351.3

38.56

ammonia

239.6

23.35

Predict which of the following compounds follow Trouton's rule. Check all that apply.

Hint 1. Calculate the entropy of vaporization for a sample liquid 87

values determine whether a liquid follows Trouton's rule or not. When , then Trouton's rule is followed.

for a liquid approximately (within about 2%) equals

Calculate the entropy change for nonane. Express your answer in joules per kelvin per mole to three significant figures.

Hint 1. How to determine the change in entropy The change in entropy for any physical transformation is calculated by dividing the heat of transformation by the transition temperature in kelvins:

ANSWER: = 87.7

ANSWER: nonane o-xylene ammonia ethanol chloroform toluene

Correct During phase transitions from liquid to gas, there is always an increase in entropy for nonpolar liquids having higher molecular weights; the increase in entropy is approximately 87 . This is called Trouton's rule. In case of polar solvents (such as alcohols), however, Trouton's rule fails because of the additional attractive forces of hydrogen bonding.

Part C Estimate the normal boiling point of 2-methylheptane using Trouton's rule [estimating that is approximately 87-88 assuming that the enthalpy of vaporization, = 33.26 , remains relatively constant.

]

Express your answer in kelvins to three significant figures.

Hint 1. Definition of boiling point Molecular kinetic energy is greater at higher temperatures, so more molecules can escape the surface, and the saturated vapor pressure is correspondingly higher. If the liquid is open to the air, the vapor pressure is seen as a partial pressu...