Chapter 15 Concepts
Two 1.0-L flasks are connected by a stopcock with 1.5 moles of an ideal gas restrained in one flask. Determine the change in entropy (ΔSsys), when the stopcock is open and the gas is allowed to expand into both flasks at a constant temperature.
+8.6 J/K (Reason: ΔSsys = nR ln(Vfinal/Vinitial) = 1.5 mol × (8.314J/K⋅mol) × ln(2.0L/1.0L) = 8.6 J/K
Rank the following compounds in order of decreasing standard entropies. (Place the compound with the highest entropy at the top of the list).
1. C3H8 (g) 2. CH4 (g) 3. C3H8 (l) 4. CH4 (l)
Calculate the standard entropy change for the following reaction at 25°C. Use the values provided in the table below. 2CO2 (g) → 2CO (g) + O2 (g) Substance S°(J/K⋅mol) CO2 (g)= 213.6 CO (g)= 197.9 O2 (g)= 205.0
173.6 J/mol⋅K Reason: ΔS°rxn = [(2)(197.9 J/mol⋅K ) + 205 J/mol⋅K ] - (2)(213.6 J/mol⋅K)
Rotational Motional Energy
Atoms spin about an axis running through the center of mass of the molecule.
In which cases do the substance(s) on the left have a higher entropy than the substance(s) on the right? Select all that apply
C3H8 (g) vs. C2H6 (g) 2NO2 (g) vs. N2O4 (g)
When heat, q, is transferred from the system to the surroundings, the amount of energy that is dispersed is greater when the temperature is love. Which of the following options reflect this relationship (at constant pressure)? Select all that apply.
DeltaSsurr=-qsys/T DeltaSsurr=-deltaHsys/T
The combustion of glucose (shown below) is exothermic. C6H12O6 (s) + 6O2 (g) -> 6CO2 (g) + 6H2O (g) Does this reaction cause an increase or a decrease in entropy for the system and surroundings?
Increase in the entropy of the surroundings Increase in the entropy of the system
The dissolution of a molecular solute typically results in a(n) _____ entropy because the system's molecules and _____ are dispersed into a larger volume. (Assume that the solute is not an acid or a base)
Increase; energy
Entropy will generally increase when ______. (Select all the options that complete this sentence correctly.)
a solid sublimes a liquid evaporates a molecular substance dissolves in water
Mathematically entropy is defined by the equation S = k ln W. W represents the number of possible arrangements, where mathematically W = XN. X represents the number of _____ containing N _____.
cells; molecules, atoms, or particles
As temperature increases, entropy ______ due to a(n) ______ in the number of available energy states, and thus a(n) ______ in the number of possible arrangements of molecules within those energy states.
increases, increase, increase
The change in entropy for a system can be calculated using the equation below. Match each variable with the correct term. ΔSsys = nR ln Vfinal/Vinitial
n - number of moles R - ideal gas constant Vfinal - final volume Vinitial - initial volume
The equation ΔSsys = nR ln Vfinal/Vinitial is much more frequently used than the Boltzman equation ΔSsys = k ln Wfinal/Winitial because _____.
the number of microstates is difficult to determine for a real process
Transitional Motional Energy
The entire molecule moves through space.
A reaction that results in an overall increase in the number of gas molecules has a positive sign for deltaSrxn. Select the statement that correctly explains why.
The entropy of a substance in a gas phase is much higher than its entropy in the liquid or solid phase
True or false: The state with the largest number of possible arrangements has the greatest entropy.
True (Reason: The most probable state is the one with the largest number of energetically equivalent possible arrangements: S = k ln W)
In each of the following pairs, which species will have a greater value for standard entropy? (i) F (g) vs. H2O (g) (ii) H2O2 (l) vs. H2O2 (g)
(i) H2O (g) (ii) H2O2 (g)
In the following reaction, there is one species for which the standard entropy is not known. Use the given value for the change in entropy of the reaction and the values for standard entropy that are listed in the table below to solve for the missing standard entropy at 25°C. O2 (g) + 2MgF2 (s) → 2MgO (s) + 2F2 (g); ΔS°rxn = 140.76 J/mol⋅K Substance S° (J/K⋅mol) O2 (g) = 205.0 MgO (s) = 26.78 F2 (g) = 203.34
57.24 J/mol⋅K (Reason: Let S°[MgF2(s)] be x. 140.76 = 2(26.78) + 2(203.34) - [2x + 205.0] 140.76 = 253.96 - 2x 2x = 253.96 - 140.76 = 113.20 x = 57.24 J/mol⋅K)
Select all the options in which the first species of each pair has a higher standard entropy.
A gas at 250oC vs. the same gas at 100oC A more complex substance vs. a simpler substance in the same phase, if their molar masses are similar
Entropy will generally increase when ______. (Select all the options that complete this sentence correctly.)
A liquid evaporates A molecular substance dissolves in water A standard sublimes
Which of the following changes would result in an increase in the entropy of the system? Select all that apply.
An ice cube melts at 273K A crystal of sodium chloride is heated from 275K to 290K A tire is punctured, releasing the gas trapped inside.
Vibrational Motional Energy
Atoms in the molecule move relative to one another.
Which of the following must be known in order to assess the spontaneity of a chemical reaction or physical process at a particular set of conditions? Select all that apply.
Change in enthalpy Change in entropy
Which of the following must be known in order to assess the spontaneity of a chemical reaction or physical process at a particular set of conditions? Select all that apply.
Change in entropy, change in enthalpy
Which of the following options correctly explain why the equation S = k ln W is rarely used to calculate the change in entropy of a system? How is ΔS determined?
It is difficult to determine the number of different possible arrangements (W). Tabulated standard entropy values are used to calculate entropy changes instead.
The _____ entropy of a substance is its absolute entropy at 1 atm.
Standard
Which of the following types of energy are forms of motional energy? Select all that apply.
Transitional Vibrational Rotational
Which of the following statements correctly explain the increase in entropy that occurs when substance changes from solid to liquid, or liquid to gas? Select all that apply.
The number of possible arrangements of the particles increases. The energy of the particles increases during these phase changes.
Which phase change will have a more dramatic increase in entropy? Select the statement that best explains why.
The mobility of the particles increases much more when this phase change occurs. Vaporization of a substance
Which of the following options correctly show how to calculate the entropy change of a system? Select all that apply.
ΔSsys= nR ln Vfinal/Vinitial; ΔSsys = k ln Wfinal - k ln Winitial
If we know that the entropy change for the surroundings is x J/K, and the system absorbed y kJ of heat during that reaction, what is the temperature at which this occurred (in K)?
1000y/x
What quantity is a measure of how spread out or dispersed a system's energy is?
Entropy
In each of the following pairs, which species will have a greater value for standard entropy? (i) F (g) vs. H2O (g) (ii) H2O2 (l) vs. H2O2 (g)
(ii) H2O2 (g) (i) H2O (g)
What is the change in entropy (ΔSsys), for the expansion of 0.10 mole of an ideal gas from 2.0 L to 3.0 L at constant temperature?
+0.34 J/K (Reason: Reason: ΔSsys = nR ln Vfinal/Vinitial = 0.10 mol × (8.314J/K⋅mol) × (ln 3.0L/2.0L) = 0.34 J/K
Calcite the entropy change of the surroundings in J/mol•K when 30kJ of heat is released by the system at 27oC.
+100 (Reason: remember to convert kJ to J. 30000/300=100)
Which of the following reactions/processes have a negative sign for deltaSrxn? Select all that apply.
4Fe (s) + 3O2 (g) -> 2Fe2O3 (s) C2H6O (l) -> C2H6O (s)
Which of the following is an application of the second law of thermodynamics?
A gas expands because matter tends to spread out.
Which of the following familiar processes is/are spontaneous? Select all that apply.
A teaspoon of table salt dissolving in 1 L of boiling water A ball rolling down a hill
Which of the following changes are favored in a spontaneous process?
An increase in entropy An overall decrease in energy
A particular process that results in a decrease in the entropy of the system. If this process is spontaneous, what must be true about the trophy change of the surroundings?
DeltaSsurr > -deltaSsys
The _____ of a system is a measure of the ways in which the energy of the system can be dispersed.
Entropy
The second law of thermodynamics states that the total _____ of the universe with _____ for any spontaneous process
Entropy; increase
Which of the following statements correctly describe general trends in standard entropy? Select all that apply.
For two monatomic species, the one with the larger molar mass will have a higher standard entropy. For elements with two allotropic forms, the one that is more mobile will have a greater value for standard entropy.
Which of the following reactions/processes are predicted to have a positive value for deltaSrxn? Select all that apply
H2CO3 (aq) -> H2O (l) + CO2 (g) N2O4 (g) -> 2NO2 (g
Which of the following familiar processes is/are spontaneous under the conditions stated? Select all that apply.
Ice melting at room temperature Iron rusting at room temperature
Which of the following correctly reflect that relationships between deltaSsurr, deltaHsys, and T? Select all that apply.
If deltaHsys is positive, deltaSsurr will be negative. DeltaSsurr is inversely proportional to temperature
For a chemical reaction, ΔSorxn = ΣnSo(_____)-ΣnSo(_____)
Products; reactants
Match each symbol in the equation S = k ln W correctly with its definition.
S - entropy k - Boltzmann Constant (1.38x10^-23 J/K) ln - natural log W - number of possible arrangements
What is the entropy of a system in which there is only one microstate?
S=0
Two unknown reactions (A and B) are analyzed. It is found that reaction A is exothermic, while reaction B is endothermic. Which of these reactions is spontaneous?
Spontaneity cannot be determined from the given information.
Given the balanced chemical equation CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (g) select the equation that should be used to calculate the total entropy change. (The physical state of the substances has been omitted to simplify the equation, but remember that the physical state of a substance has a significant effect on its entropy.)
S°[CO2] + 2(S°[H2O]) - S°[CH4] - 2(S°[O2]) (Reason: Correct - the total entropy of the reactants is subtracted from the products)
Which of the following processes or changes will lead to a decrease in entropy? Select all that apply.
Temperature decrease (Reason: A decrease in temperature results in a decrease in molecular motion and consequently a decrease in entropy) Condensation (Reason: A liquid has a lower entropy than a gas of the same substance)
Which of the following processes of changes will lead to a decrease in entropy?
Temperature decrease (Reason: a decrease in temperature results in a decrease in molecular motion and consequently a decrease in entropy) Condensation (Reason: a liquid had a lower entropy than a gas of the same substance)
Which of the following statements correctly explain the increase in entropy that occurs when substance changes from solid to liquid, or liquid to gas? Select all that apply
The energy of the particles increases during these phase changes. The number of possible arrangements of the particles increases.
An atom of hydrogen is bound to a metal surface (but free to move across it) with 10 possible sites of attachment. What would be the effect of increasing the size of the metal surface to 20 possible sites?
The entropy would increase, but it would be less than double the original entropy. (Reason: Correct. ln20/ln10 = 1.3; the entropy increases to 130% the original value)
Which statements correctly describe the changes that occur when an ionic solid dissolved in water? Select all that apply
The mobility of H2O molecules in such a solution is reduced since they are arranged in a specific way around the dissolved ions. When highly charged ions dissolve, the entropy of the system generally decreases The dissolution of ions with low charged typically results in an increase in the entropy of the system
Which of the following statements correctly describe why the process depicted in the illustration is spontaneous? Select all that apply. (The change is occurring from left to right in the illustration, and the system remains at constant temperature.)
The process is spontaneous due to the dispersal of the system's energy over a larger volume. The process is spontaneous due to an increase in entropy.
Which of the following statements correctly reflect the relationship between the spontaneity of a reaction and the sign of ΔH? Select all that apply.
The sign of ΔH alone is not sufficient evidence to determine the spontaneity of a process. A negative value of ΔH favors spontaneity.
Which of the following options correctly describe standard entropy? Select all that apply.
The units of standard entropy are J/mol⋅K The standard entropy of a substance is its absolute entropy at 1 atm.
What effect does increasing the temperature of a gas have on its entropy, and why?
There is an increase in the entropy of the system as temperature increases The kinetic energy of the particles in the system increases
True or false: If a process occurs spontaneously in one direction under a certain set of conditions, it does not occur spontaneously in the opposite direction under the same conditions.
True
In order to assess the spontaneity of a chemical reaction or physical process both the change in _____ and _____ associated with the reaction or process must be known.
enthalpy; entropy
The entropy of gaseous molecules is _____ the entropy of these molecules in a condensed phase. Therefore, reactions producing a greater number of gas molecules typically result in a positive change in entropy.
greater than
Four particles initially in one flask are allowed to also expand into a second flask. Select the correct value(s) for the number of microstates (W) and change in entropy of the system. Recall that W = X^N where X is the number of cells and N is the number of particles. Select all that apply.
ΔSsys = k ln 2^4 Winitial = 2^4 = 16 microstates
