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Thermodynamics (Entropy and Free Energy)
1. Define entropy and list the variables or conditions that you must consider when comparing the entropy of two
substances, or when trying to determine the relative change in entropy.
2. Does entropy increase or decrease with increase in temperature? Explain.
3. Work on this part with your partner, one of you first going over Part A, explaining your answers to the other person,
and then that person going over Part B.
A. which member of the following pairs has the
B. which member of the following pairs has
greater amount of entropy.
the lesser predicted amount of entropy.
CO2 (g) or CO2 (s)
H2O (l) or H2O (s)
PbS (s) or PbF2(s)
FeCl2 (s) or FeCl3(s)
Fe(s) at 25˚C or Fe(s) at 100˚C
H2(g) in a 1 L vessel or H2(g) in a 2 L vessel
4. For each of the following reactions, indicate whether the entropy of the system will increase or decrease, and explain
why. If you cannot tell just by inspecting the equation, explain why.
a. CH3OH(l) --> CH3OH(g)
b. N2O4(g) --> 2NO2(g)
c. CO(g) + H2O(g) --> CO2(g) + H2(g)
d. 2KClO3(s) --> 2KCl(s) + 3O2 (g)
e. 2NH3(g) + H2SO4(aq) --> (NH4)2SO4(aq)
5. Predict which of the following reactions has a positive entropy change.
i)
2 N2(g) + O2(g) 2 N2O(g)
ii)
CaCO3(s)  CaO(s) + CO2(g)
iii)
Zn(s) + 2 HCl(aq)  ZnCl2(aq) + H2(g)
6. Predict which of the following reactions has a negative entropy change.
i) 2 HgO(s)  2 Hg (l) + O2 (g)
ii) Ba2+(aq) + SO42-(aq) --> BaSO4(s)
iii)
2H2O2(l)  2 H2O (l) + O2 (g)
7. True or false? All exothermic reactions are spontaneous?
8. Which variable can tell you if a process is spontaneous without exception?
a. Hrxn
b. Srxn
c. Hsurr
d. Ssurr
e. Stot
9. Circle the correct words: Nature tends towards (higher or lower) energy and more (order or disorder)?
10. Which of the following reactions will have the most positive ΔHo ?
a. N2(g) → 2 N(g) b. F2(g) → 2 F(g)
c. O2(g) → 2 O(g)
d. The reactions all have the same ΔHo .
11. Which state of matter has the highest entropy?
12. Predict whether the entropy change will be positive or negative for the following:
a. H2O (g)  H2O (l)
b. C6H12O6(s)  2C2H5OH(l) + 2CO2(g)
c. 2NH3(g) + CO2(g)  H2O(l) + NH2CONH2(aq) d. NaCl(s)  NaCl(aq)
e. Cu(s) (100oC)  Cu(s) (25oC)
e. 2NH3(g) N2(g) + 3H2(g)
13. If a process is endothermic and the process creates more order than existed before, the process is:
a. always spontaneous b. never spontaneous c. spontaneous at high T d. spontaneous at low T
14. Which of the following substances has the greatest entropy per mole?
Thermodynamics (Entropy and Free Energy)
a. O2(g)
b. N2(g)
c. CO(g)
d. CO2(g)
e. C4H10(g)
15. Which of the following reactions will have an increase in entropy? Choose all that apply.
a. SO3(g) → 2SO2(g) + O2(g)
b. H2O(l) → H2O(s)
c. Br2(l) → Br2(g)
d. H2O2(l) → H2O(l) + ½ O2(g)
16. Using the data below, calculate ΔSorxn for the following reaction: 4 Cr(s) + 3 O2(g) → 2 Cr2O3(s)
a. 548.1 J/K
Substance Δ S, J/K·mol
b. 147.7 J/K
Cr(s)
23.77
c. -147.7 J/K
O2(g)
205.138
d. -548.1 J/K
Cr2O3(s) 81.2
17. Calculate the standard entropy change, ΔS, for the following reaction at 25 °C: 4Al(s) + 3O2(g)  2Al2O3(s)
S[Al(s)] = 28.32
J
K × mol
S[O2(g)] = 205
J
K × mol
S[Al2O3(s)] = 51.0
J
K × mol
18. Joseph Priestly prepared oxygen by heating according to the reaction HgO(l) → Hg(l) + ½O2, for which ΔHo = 90.84
kJ/mol and ΔSo = 108 J/K.mol. Which of the following statements is true for this reaction?
a. spontaneous only at low temperatures.
b. spontaneous at all temperatures.
o
c. ΔG becomes less favorable as temperature increases.
d. spontaneous only at high temperatures.
o
e. The reaction is at equilibrium at 25 C and 1 atm pressure.
19. For : H2O2(g) → H2O(l) + 1/2 O2(g) where, ΔHo = -106 kJ/mol; ΔSo = 58 J/K : Is H2O2(g) stable?
a. Yes, under all conditions.
b. Yes, if the temperature is low enough.
c. Yes, if the rate of decomposition is low.
d. Yes, if the O-O bond energy is greater than the O-H bond energy.
e. no
Calculate the standard free energy change, ΔG, for the following at 25 C:
MgO(s) + C(graphite)  Mg(s) + CO(g)
ΔH = 491.18 kJ
ΔS = 197.67 J/K
b. Is this reaction spontaneous at 25 C? If not, at what temperature can we make this reaction spontaneous?
20.a.
21.
Calculate Horxn, Sorxn and Gorxn for Mg(s) + O2(g)  MgO(s)) at 250C (Hint – balance the rxn)
o
H MgO = -601.7 kJ/mol , SoMgO = 26.9 J/K , SoMg = 32.7 J/K , SoO2 = 205.0 J/K
22. From # 21 the results for Horxn means (exothermic or endothermic), the results for Sorxn means (disorder or
order) increased, and Gorxn means (products or reactants) are favored under standard conditions.
23. The standard enthalpy of formation equation for NH3(g) is:
a) N(g) + 3H(g)  NH3(g)
b) N2(g) + 3H2(g)  2NH3(g)
c) 1/2N2(l) + 3/2H2(g)  NH3(g)
d) 1/2N2(g) + 3/2H2(g)  NH3(g)
24. Calculate H °rxn for the following reaction at 25 °C.
°
°
H f [NO(g)] = 90.3 kJ H f [H2O(g)] = -241.8 kJ
mol
mol
4NH3(g) + 5O2(g)  4NO(g) + 6H2O(g)
°
H f [NH3(g)] = -45.9 kJ
mol
25. Calculate G rxn at 25 C for this reaction: 2 NaHCO3(s) g  Na2CO3(s) + CO2(g) + H2O(g).
Given: Horxn = 128.9 kJ/mol and Sorxn = 321 J/molK
o
o
Thermodynamics (Entropy and Free Energy)
ANSWERS:
1. Entropy is the degree of chaos or disorder in a system. When comparing the relative
entropy you must consider the temperature, the physical state, and the molecular complexity.
2. Entropy increases with increasing temperature.An increase in temperature corresponds to an
increase in the average kinetic energy of the molecules.This means they are moving around
more and have more disorder
B. lesser predicted amount of entropy.
3. A. greater predicted amount of entropy.
CO2 (g) or CO2 (s)
H2O (l) or H2O (s)
PbS (s) or PbF2(s)
FeCl2 (s) or FeCl3(s)
Fe(s) at 25˚C or Fe(s) at 100˚C
H2(g) in a 2 L vessel
4.a.
Increase, gases have more freedom of motion
b.
Increase, there are more moles of gas produced in this rxn
c.
Can’t tell. The molecular complexity of CO to CO2 goes up, but the molecular complexity of
H2O (to H2) goes down. There are the same # of moles of gas on each side of the equation.
e.
Increase, you are forming a gas.
f.
Decrease, you are losing gas and you have a decrease in the number of molecules.
5. Predict which of the following reactions has a positive entropy change.
I. negative or more organized 3 total moles to 2
ii)& iii)making a gas!
6. Predict which of the following reactions has a negative entropy change.
i. 2 HgO(s)  2 Hg(l) + O2(g)
ii. Ba2+ (aq) + SO4 (aq)  BaSO4(s) making a solid from liquid (more organized)
iii. 2H2O2(l)  2 H2O(l) + O2(g)
7. True or false? All exothermic reactions are spontaneous? _ false _
8. a. Hrxn
b. Srxn
c. Hsurr
d. Ssurr
e. Stot
9. Circle the correct words: Nature tends towards (higher or lower) energy and more (order or disorder)?
10.
a. N2(g) → 2 N(g) Notice that all reactions are 1 mol of a diatomic gas going to 2 mol of a monoatomic gas,
i.e., the bonds between the two atoms are broken. This is a tricky question and really relates to CHM151 knowledge, i.e.,
a single bond is weaker than a double bond is weaker than a triple bond. If a triple bond is the strongest bond, it takes
more energy to break it. N2 has a triple bond, O2 has a double bond, and F2 has a single bond.
11.
Which state of matter has the highest entropy? ___ gas _____
12.
a. S= -ve
b.S__+__ c.S___-__
d. S___+_ S___-_f.
S___+_
14.
If a process is endothermic and the process creates more order than existed before, the process is:
a. always spontaneous b. never spontaneous c. spontaneous at high T d. spontaneous at low T
15. e. C4H10(g)
Thermodynamics (Entropy and Free Energy)
All choices are gases and, assuming they are all at the same temperature, the largest molecule will have the highest
entropy because of the greater possible movement of atoms within each molecule.
16. Which of the following reactions will have an increase in entropy? Choose all that apply.
a. SO3(g) → 2SO2(g) + O2(g) ΔS > 0 because 1 mol gas produces 3 mol gas
b. H2O(l) → H2O(s)
ΔS < 0 because liquid turns into solid
c. Br2(l) → Br2(g)
ΔS > 0 because liquid turns to gas
d. H2O2(l) → H2O(l) + ½ O2(g) ΔS > 0 because 1 mol liquid produces 1 mol liquid + ½ mol gas
16. Using the data below, calculate ΔSorxn for the following reaction:
4 Cr(s) + 3 O2(g) → 2 Cr2O3(s)
a. 548.1 J/K
Substance Δ S, J/K·mol
b. 147.7 J/K
Cr(s)
23.77
c. -147.7 J/K
O2(g)
205.138
d. -548.1 J/K
Cr2O3(s) 81.2
e. None of the above.
ΔS°rxn = [ 2 x 81.2 ] – [ ( 4 x 23.77 ) + ( 3 x 205.138 ) ] = -548.1 J/K
17. Calculate the standard entropy change, ΔS, for the following reaction at 25 °C:
4Al(s) + 3O2(g)  2Al2O3(s)
S[Al(s)] = 28.32
æ
è
S °rxn = (2) ç 51.0
J
K × mol
S[O2(g)] = 205
J
J
S[Al2O3(s)] = 51.0
K × mol
K × mol
J ö
J ö
J ö
J
æ
æ
÷ - (4) ç 28.32
÷ - (3) ç 205
÷ = -626
K × mol ø
K × mol ø
K × mol ø
K × mol
è
è
*note that entropy decreases as expected based on decrease in #molecules of gas
18. In 1774 Joseph Priestly prepared oxygen by heating mercury(II) oxide according to the reaction HgO(l) → Hg(l) +
½O2, for which ΔHo = 90.84 kJ/mol and ΔSo = 108 J/K.mol. Which of the following statements is true for this reaction?
a. The reaction is spontaneous only at low temperatures.
b. The reaction is spontaneous at all temperatures.
c. ΔGo becomes less favorable as temperature increases.
d. The reaction is spontaneous only at high temperatures.
e. The reaction is at equilibrium at 25 oC and 1 atm pressure.
Plug the enthalpy and entropy values into ΔGo = ΔHo − TΔSo and you’ll find that ΔGo < 0 only when the temperature is
above approximately 841 K ( 568 °C ); anything lower than this temperature makes ΔGo > 0 ( non-spontaneous).
19. H2O2(g) → H2O(l) + 1/2 O2(g) , ΔHo = -106 kJ/mol; ΔSo = 58 J/K
Is H2O2(g) stable?
a. Yes, under all conditions.
b. Yes, if the temperature is low enough.
c. Yes, if the rate of decomposition is low.
d. Yes, if the O-O bond energy is greater than the O-H bond energy.
e. No.
Thermodynamics (Entropy and Free Energy)
Note that ΔHo is negative and ΔSo is positive. ΔGo will always be negative (even when T = 0 K). Therefore, the
decomposition of hydrogen peroxide will always be spontaneous and hence never stable.
20. a. G = H - TS
æ
è
G = 491.18 kJ - (298 K) ç197.67
J ö æ 1 kJ ö
÷ = + 432.27 kJ
֍
K ø çè 1000 J ÷ø
bNo, it is not spontaneous at 25 C (G is a large positive value)
Set G = 0:
T=
0 = H - TS
491.18 kJ
= 2484.8 K
J öæ 1 kJ ö
æ
÷
ç197.67 ÷çç
K øè 1000 kJ ÷ø
è

T=
DH
DS
 This is T at equilibrium, spont at T > 2484.8 K
21. Calculate Horxn, Sorxn and Gorxn for 2 Mg(s) + O2(g)  2 MgO(s)) (Hint – balance the rxn)
Horxn = [ 2(-601.7)] – [0] = -1203.4 kJ
Sorxn = [ 2(26.9)] – [ 2(32.7) + 1(205.0) ] = -216.6 J/K
Gorxn = [ 2(-569.4) ] – [0] = -1138.8 kJ
22. From # 21 the results for Horxn means (exothermic or endothermic), the results for Sorxn means (disorder or order)
increased, and Gorxn means (products or reactants) are favored under standard conditions.
23.The standard enthalpy of formation equation for NH3(g) is:
a) N(g) + 3H(g)  NH3(g)
b) N2(g) + 3H2(g)  2NH3(g)
c) 1 N2(l) + 3 H2(g)  NH3(g)
d) 1 N2(g) + 3 H2(g)  NH3(g)
2
2
2
2
24. Calculate H °rxn for the following reaction at 25 °C.
4NH3(g) + 5O2(g)  4NO(g) + 6H2O(g)
°
H f
°
[NO(g)] = 90.3 kJ H f [H2O(g)] = -241.8
= (4)(90.3
mol
kJ )
mol
+ (6)(-241.8 kJ ) - [(4)(-45.9
mol
kJ )
mol
kJ
mol
°
H f [NH3(g)] = -45.9 kJ
mol
+ (5)(0)] = -906.0 kJ / mol
25. Calculate Gorxn at 25oC for this reaction: 2 NaHCO3(s) g  Na2CO3(s) + CO2(g) + H2O(g). Given: Horxn = 128.9
kJ/mol and Sorxn = 321 J/molK
Gorxn = 128.9 kJ/mol – (298 K)(0.321 kJ/molK) = 33.2 kJ/mol