Chapter 19 Workshop Activity - Entropy

2021/3/15 Chapter 19 Workshop Activity - Entropy Chapter 19 Workshop Activity - Entropy Due: 12:00am on Thursday, May 13, 2021 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 1/20 2021/3/15 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: 2/20 2021/3/15 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: 3/20 2021/3/15 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. 4/20 2021/3/15 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 5/20 2021/3/15 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. 6/20 2021/3/15 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 . 7/20 2021/3/15 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 8/20 2021/3/15 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 9/20 2021/3/15 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. 10/20 2021/3/15 Chapter 19 Workshop Activity - Entropy Part B Liquid Boiling point ( ) Enthalpy of 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 pressure along with the other constituents of the air. The temperature at which the vapor pressure is equal to the atmospheric pressure is called the boiling point. 11/20 2021/3/15 Chapter 19 Workshop Activity - Entropy Hint 2. Identify the relationship between Trouton's rule and the boiling point Which of the following is the correct equation for the boiling point of a liquid? ANSWER: ANSWER: Boiling point of 2-methylheptane = 382 Correct The actual boiling point for 2-methylheptane is 390.6 , compared to your calculated value of 382 good estimate for the normal boiling point of the liquid in this case. . Trouton's rule gives you a Chapter 19 Multiple Choice Question 10 Part A An exothermic reaction is a process that ANSWER: has a positive and a positive . has a positive and a negative . has a negative and a positive . has a negative and a negative . Correct Exercise 19.40 - Enhanced - with Feedback MISSED THIS? Read Section 19.5 (Pages 860 - 863) ; Watch IWE 19.3 . A reaction has -129 and 322 . Part A At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings? Express your answer in kelvins. ANSWER: = 401 12/20 2021/3/15 Chapter 19 Workshop Activity - Entropy Correct The equation for the entropy of the surroundings provides insight into why exothermic processes have a tendency to be spontaneous at low temperatures: From the equation, it can be deduced that the entropy of the surroundings will increase with decreasing temperature. This means that at low temperatures, the entropy of the surroundings will be relatively large. Exercise 19.84 Determine the sign of for each of the following processes. Part A dry ice subliming ANSWER: Correct Part B dew forming ANSWER: Correct Part C the process in the figure ANSWER: Correct Exercise 19.99 Indicate the sign of for each process. 13/20 2021/3/15 Chapter 19 Workshop Activity - Entropy Part A ANSWER: >0 <0 =0 Correct Part B the electrolysis of to and at 298 ANSWER: >0 =0 <0 Correct Part C the growth of an oak tree from a little acorn ANSWER: >0 =0 <0 Correct Interactive Worked Example: Calculating Entropy Changes in the Surroundings 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 Consider the combustion of butane gas: , Calculate the entropy change in the surroundings when this reaction occurs at 25 . Express your answer in joules per kelvin to three significant figures. 14/20 2021/3/15 Chapter 19 Workshop Activity - Entropy ANSWER: = Part B Determine the sign of the entropy change for the system. ANSWER: Part C Complete previous part(s) For More Practice 19.3 - Enhanced - with Feedback A reaction has and . Part A At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings? Express the temperature to three significant figures and include the appropriate units. ANSWER: = For Practice 19.3 - Enhanced - with Feedback Consider the decomposition reaction of dichlorine monooxide to chlorine and oxygen gas: Part A Calculate the entropy change in the surroundings associated with this reaction occurring at 25 . Express the entropy change to three significant figures and include the appropriate units. ANSWER: = Part B Determine the sign of the entropy change for the system and the universe. Drag the appropriate items to their respective bins. ANSWER: 15/20 2021/3/15 Chapter 19 Workshop Activity - Entropy Reset sign of the enthalpy change for the universe Help sign of the entropy change for the system Part C Complete previous part(s) Chapter 19 Reading Question 1 Part A Which of the following is a correct statement? You did not open hints for this part. ANSWER: Nonspontaneous processes can be made spontaneous by the addition of a catalyst. Nonspontaneous processes are not possible. A spontaneous process occurs without outside intervention. Spontaneous processes occur rapidly. Exercise 19.27 - Enhanced - with Feedback MISSED THIS? Read Section 19.2 (Pages 848 - 850) . Part A Classify each of the following processes as spontaneous or nonspontaneous. Drag the appropriate processes to their respective bins. ANSWER: 16/20 2021/3/15 Chapter 19 Workshop Activity - Entropy the extraction of iron metal from iron ore the combustion of natural gas Reset Help Reset Help drawing heat energy from the ocean's surface to power a ship a hot drink cooling to room temperature Exercise 19.28 - Enhanced - with Feedback MISSED THIS? Read Section 19.2 (Pages 848 - 850) . Part A Which of the following processes are nonspontaneous? Drag the appropriate items to their respective bins. ANSWER: a bike going up a hill a meteor falling to Earth a ball rolling down a hill obtaining hydrogen gas from liquid water Part B Are the nonspontaneous processes impossible? ANSWER: 17/20 2021/3/15 Chapter 19 Workshop Activity - Entropy Nonspontaneous processes are impossible. Nonspontaneous processes are not impossible. Exercise 19.104 Calculate the entropy of each of the following states. Part A State (a). Express your answer as an integer. ANSWER: = Part B State (b). Express your answer using three significant figures. ANSWER: = Part C State (c). Express your answer using three significant figures. ANSWER: = Part D Rank order the states in order of increasing entropy. ANSWER: 18/20 2021/3/15 Chapter 19 Workshop Activity - Entropy (a) < (b) < (c) (a) < (c) < (b) (b) < (a) < (c) (b) < (c) < (a) (c) < (a) < (b) (c) < (b) < (a) Exercise 19.33 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 48.4 . of isopropyl alcohol freezes at its melting point ( 89.5 ). Express your answer in joules per kelvin to three significant figures. ANSWER: = Exercise 19.109 Given the data, calculate for each liquids. ( , where is in ) Compound Name Diethyl ether 34.6 26.5 Acetone 56.1 29.1 Benzene 79.8 30.8 Chloroform 60.8 29.4 Ethanol 77.8 38.6 Water 100 40.7 Part A Diethyl ether Express your answer with the appropriate units. ANSWER: = Part B Acetone Express your answer with the appropriate units. ANSWER: = Part C Benzene Express your answer with the appropriate units. ANSWER: 19/20 2021/3/15 Chapter 19 Workshop Activity - Entropy = Part D Chloroform Express your answer with the appropriate units. ANSWER: = Part E Ethanol Express your answer with the appropriate units. ANSWER: = Part F Water Express your answer with the appropriate units. ANSWER: = For Practice 19.2 - Enhanced - with Feedback Part A Calculate the change in entropy that occurs in the system when 29.0 boiling point (56.1 ). of acetone ( ) vaporizes from a liquid to a gas at its normal Express your answer using three significant figures. ANSWER: Score Summary: Your score on this assignment is 58.3%. You received 14 out of a possible total of 24 points. 20/20