Unit 8: Thermodynamics/Electrochemistry Review Packet Thermodynamics AP CHEMISTRY 1.
A two bulbed flask contains four particles. What is the probability of finding all four particles in only one of the bulbs?
2.
Which of the following liquids is likely to have the highest value for S°?
1.
CH3OH
2.
C2H5OH
3.
H2O
4.
N2H4
5.
Hg
It is determined that for a particular process, ΔH = +185 kJ and ΔS = +1.80 J/K. At what temperature does the reaction
become spontaneous (watch units!)?
3.
4.
5.
6.
7.
Calculate ΔS° for the following reaction (using the information to the right):
2 NH3 → 3 H2 + N2.
Substance Sº J/(K mol)
NH3(g)
193
H2(g)
131
N2(g)
192
The lowest possible entropy achievable occurs:
1.
in a perfect crystal at 0 K
2.
only in the vapor phase
3.
when a liquid is converted to a solid
4.
only at very high temperatures
5.
at the completion of an endothermic reaction
In normal chemical storage, the element sulfur remains unreacted with oxygen in the atmosphere. However, it is possible for
sulfur and oxygen to react spontaneously to form gaseous sulfur dioxide. This is most likely to happen:
1.
only in the presence of a catalyst
2.
at very low temperatures
3.
combustion of methane
4.
rusting of iron
5.
oxidation of glucose
Which of the following statements are true for the reaction I2(g) → 2 I(g)
I. ΔH is positive
II. ΔH is negative
III. ΔS is positive
IV. ΔS is negative
V. The reaction is spontaneous at any temperature
8.
Determine ΔG° for the weak acid HC2H3O2 (acetic acid, Ka = 1.8 x 10-5) at 25°C.
9.
The standard free energy of formation of NaBr(s) is -347 kJ/mol. Calculate ΔG° for the reaction
2NaBr(s) → 2Na(s) + Br2(l)
10. The boiling point of compound X is 12.0°C, and the enthalpy of vaporization of compound X is 24.6 kJ/mol. What is the
entropy of vaporization for compound X?
Unit 8: Thermodynamics/Electrochemistry Review Packet AP CHEMISTRY 11. Which of the following samples of oxygen has the greatest positional entropy?
1.
1 mole of O2(s) at 15 K
2.
1 mole of O2(g) at 0.5 atm and 273 K
3.
1 mole of O2(g) at 1.0 atm and 273 K
4.
1 mole of O2(g) at 2.0 atm and 200 K
5.
1 mole of O2(g) at 2.0 atm and 273 K
12. For which of the following processes would ΔS° be expected to be most positive?
1.
Na+(aq) + Cl-(aq) → NaCl(s)
2.
C6H12O6(s) + 6 O2(g) → 6 CO2(g) + 6 H20(g)
3.
H+(aq) + OH-(aq) → H2O(l)
4.
Cl2(g) + H2(g) → 2 HCl(g)
5.
CO2(g) → CO2(s)
13. Which of the following statements is true?
1.
Exothermic reactions are always spontaneous
2.
The entropy of the universe is increasing
3.
A system at constant temperature cannot experience entropy changes
4.
In a spontaneous process, ΔG has a positive value
5.
For a process to be spontaneous, the number of moles of product must exceed the number of moles of reactant
14. At 25°, the free energy of formation of gaseous water is -229 kJ/mol. Calculate ΔG for the following reaction if the hydrogen
is supplied at 4.00 atm and the oxygen is supplied at 3.00 atm, while the water produced is at 1.00 atm pressure.
2H2 + O2 → 2H2O
15. Which of these processes occurs with a decrease in entropy?
1.
combustion of methane
2.
rusting of iron
3.
oxidation of glucose
4.
decomposition of liquid water
5.
melting of ice
Additional Thermodynamics Practice Problems: 1. 2. Which of the following pairs is likely to have the highest positional probability per mole at a given temperature? a. solid or gaseous phosphorus b. CH4(g) or C4H10(g) Determine if the values for entropy in each of the following will produce a spontaneous process. Also, which of the following processes are endothermic (from the perspective of the system)? ΔSsys (J/K) ΔSsurr(J/K) Spontaneous or not? Endothermic or not? 25 45 35 -­‐20 45 -­‐65 3. Given the values for ΔH, ΔS, and T, determine whether each of the following sets represents spontaneous or nonspontaneous processes. ΔH (kJ) ΔS (J/K) T (K) Calculated ΔG Spontaneous 45 300 140 40 300 155 -­‐40 -­‐300 140 4. Predict the sign of ΔS° for each of the following reactions. a. CaCO3(s) à CaO(s) + CO2(g) b. N2O4(g) à 2 NO2(g) 5. Calculate ΔS° and ΔH° for each of the following reactions using Appendix C in your textbook. a. Cr2O3(s) + 2 Al(s) à Al2O3(s) + 2 Cr(s) b. C2H6(g) + O2(g) à CO2(g) + H2O(g) Unit 8: Thermodynamics/Electrochemistry Review Packet 6. 7. 8. 9. Using the values for ΔS° and ΔH° calculated in problem #5, determine ΔG° a. WITHOUT using Appendix C in the back of the book. b. using Appendix C. c. How do the different values of ΔG° compare to each other? Is ΔG° a state function? Given the following data: Equation 1: S(s) + ³⁄₂ O2(g) à SO3(g) Equation 2: 2 SO2(g) + O2(g) à 2 SO3(g) ΔG° = -­‐372 kJ ΔG° = -­‐142 kJ Calculate ΔG° for the equation: S(s) + O2(g) à SO2(g) Calculate ΔG° at 720K for the following reaction: Cgraphite(s) + H2O(g) à CO(g) + H2(g) Initial pressures are PH2O = 0.80 atm; PCO = 0.00015 atm; PH2 = 0.00025 atm. (Why is there no pressure for C?) Determine the direction of reaction for the equation in problem #8 if you are given the following initial pressures: PH2O = 0.68 atm; PCO = 0.23 atm; PH2 = 0.51 atm. 10. Calculate the equilibrium constant, K, for Cr2O3(s) + 2 Al(s) à Al2O3(s) + 2 Cr(s) at 25°C. ANSWERS TO Additional Thermodynamics Practice Problems 1. 2. a. gaseous phosphorus b. C4H10(g) ΔSsys (J/K) 25 35 45 3. 5. 6. 7. 8. 9. 10. ΔSsurr(J/K) 45 -­‐20 -­‐65 Spontaneous or not? Spontaneous (70 J/K) Spontaneous (15 J/K) Non-­‐spontaneous (-­‐20 J/K) Endothermic or not? Exo Endo Endo ΔH (kJ) 45 40 -­‐40 4. AP CHEMISTRY ΔS (J/K) 300 300 -­‐300 T (K) 140 155 140 Calculated ΔG 3 kJ -­‐7 kJ 82 kJ Spontaneous Nonspontaneous Spontaneous Nonspontaneous ΔS° is positive b. ΔS° is positive a. a. ΔS° = -­‐39.6 J/K ΔH° = -­‐530. kJ b. ΔS° = 1011 J/K ΔH° = -­‐2860 kJ a. ΔG° = -­‐537 kJ b. ΔG° = -­‐519 kJ c. They are close; ΔG° is a state function. ΔG° = -­‐301 kJ ΔG = ΔG° = -­‐RTln(Q) ΔG° = +92 kJ ΔG = -­‐9 kJ C is a solid, therefore no pressure ΔG = +8 kJ spontaneous in reverse direction 94
using ΔG° = -­‐RTln(K) K = 1.3 x 10 Unit 8: Thermodynamics/Electrochemistry Review Packet Electrochemistry 1.
AP CHEMISTRY 2.
The standard hydrogen electrode is assigned a potential of:
1.
zero volts
2.
-1.00 volts
3.
1.00 volts
4.
0.76 volts
A mole of electrons has a charge of 96,485 coulombs per mole of electrons. This quantity is known to chemists as:
3.
For the galvanic cell described below, the correct line notation is:
4.
o Cl2 + 2e- → 2Cl- (E0 = 1.36v)
o Cu+ + e- → Cu (E0 = 0.52v)
3.
Pt(s)|Cl2(g)|2Cl-(aq)||Cu(s)|Cu+(aq)
4.
Cu(s)|Cu+(aq)||Cl2(g)|2Cl-(aq)
5.
Pt(s)|Cu(s)|Cu+(aq)||Cl2(g)|2Cl-(aq)|Pt(s)
6.
Cu(s)|Cu+(aq)||Cl2(g)|2Cl-(aq)|Pt(s)
7.
Pt(s)|Cl2(g)|2Cl-(aq)||Cu(s)|Cu+(aq)|Pt(s)
The equilibrium constant (K) for the reaction below is approximately:
o
o
5.
Cl2 + 2e- → 2Cl- (E0 = 1.36v)
Cu+ + e- → Cu (E0 = 0.52v)
How many electrons are transferred in the following reaction?
2NaCl + 2H2SO4 + MnO2 → Na2SO4 + MnSO4 + 2H2O + Cl2
6.
Calculate ΔG0 for the reaction:
o
o
Cl2 + 2e- → 2Cl- (E0 = 1.36v)
Cu+ + e- → Cu (E0 = 0.52v)
7.
In the electrolytic decomposition of water:
8.
2H2O → 2H2 + O2
0.
oxygen is formed at both the anode and the cathode
1.
hydrogen is formed at the cathode and oxygen is formed at the anode
2.
hydrogen is formed at both the anode and the cathode
3.
hydrogen is formed at the anode and oxygen is formed at the cathode
In the reaction below, the oxidizing agent is:
2NaCl + 2H2SO4 + MnO2 → Na2SO4 + MnSO4 + 2H2O + Cl2
Unit 8: Thermodynamics/Electrochemistry Review Packet 9.
AP CHEMISTRY The equation that represents a reaction that is not a redox reaction is:
1. 2H2 + O2 → 2H2O
2. Zn + CuSO4 → ZnSO4 + Cu
3. 2H2O2 → 2H2O + O2
4. H2O + CO2 → H2CO3
10. Which of the following would be the best reducing agent, and why?
0.
Na+
1.
Na
2.
F3.
O24.
Cl2
11. What value of E do you expect for
Pb(s) → Pb2+ + 2ein 0.015m Pb2+ solution? E0 = +0.13v
12.
This picture of an electrochemical cell can best be described as:
0.
a galvanic cell, but missing at least one essential component
1.
an electrolytic cell, but missing at least one essential component
2.
a complete electrolytic cell
3.
a complete galvanic cell
13. Two cells, one containing aqueous AgNO3 and the other containing CuSO4 are set up in series. In a given electrolysis that
results in depositing 1.25 g of silver in the first cell, how much copper should deposit simultaneously in the second cell?
14. Calculate the value of E0cell for a galvanic cell that contains the following half cells:
o
o
Cl2 + 2e- → 2Cl- (E0 = 1.36v)
Cu+ + e- → Cu (E0 = 0.52v)
15. The current in a given wire is 1.80 amp. How many coulombs will pass a given point on the wire in 1.36 minutes?
16. What is the oxidation state of S in H2SO3?
Unit 8: Thermodynamics/Electrochemistry Review Packet AP CHEMISTRY 17. Reduction potential is:
0.
an intensive property
1.
measured in amperes
2.
an extensive property
3.
always positive
18. With a current of 20 amps, how long would it take to generate 1.00 kilograms of aluminum by the reaction:
Al3+ + 3e- → Al(s)
19. In all electrochemical cells, the process that takes place at the anode is _________________ and the process that takes place
at the cathode is _________________.
20. If a constant current of 8.00 amperes is passed through a cell containing Zn2+ for 2.00 hours, how many grams of zinc will
plate out onto the cathode?
Additional Electrochemistry Practice Problems: For each of the following three reactions, write a balanced equation for the reaction in part (i) and answer the question about the reaction in part (ii). In part (i), coefficients should be in terms of lowest whole numbers. Assume that solutions are aqueous unless otherwise indicated. Represent substances in solutions as ions if the substances are extensively ionized. Omit formulas for any ions or molecules that are unchanged by the reaction. You may use the empty space at the bottom of the next page for scratch work, but only equations that are written in the answer boxes provided will be scored. 1. A solution of potassium iodide is electrolyzed. (i) Balanced equation: (ii) At which electrode is a gas released? ______________________________________________________________________________ 2. A solution of copper (II) sulfate is electrolyzed. (i) Balanced equation: (ii) What substance is the reducing agent? ______________________________________________________________________________ (ii – b) Calculate the mass of copper released by a current of 10A passing for 200 seconds through a Copper (II) sulfate solution. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Unit 8: Thermodynamics/Electrochemistry Review Packet AP CHEMISTRY 3. A solution containing tin (II) ions is added to acidified potassium dichromate solution. (i) Balanced equation: (ii)There is a color change during the reaction; which atom is most likely responsible? Explain. ______________________________________________________________________________ ____________________________________________________________
Question #4 Part A (2007) An external direct-­‐current power supply is connected to two platinum electrodes immersed in a beaker containing 1.0 M CuSO4(aq) at 25˚C, as shown in the diagram above. As the cell operates, copper metal is deposited onto one electrode and O2(g) is produced at the other electrode. The two reduction half-­‐reactions for the overall reaction that occurs in the cell are shown in the table below. Half-­‐Reaction E0(V) O2(g) + 4 H+(aq) + 4 e-­‐ → 2 H2O(l) +1.23 Cu2+(aq) + 2 e-­‐ → Cu(s) +0.34 (a) On the diagram, indicate the direction of electron flow in the wire. (b) Write a balanced net ionic equation for the electrolysis reaction that occurs in the cell. (c) Predict the algebraic sign of ∆G˚ for the reaction. Justify your prediction. (d) Calculate the value of ∆G˚ for the reaction. An electric current of 1.50 amps passes through the cell for 40.0 minutes. (e) Calculate the mass, in grams, of the Cu(s) that is deposited on the electrode. (f) Calculate the dry volume, in liters measured at 25˚C and 1.16 atm, of the O2(g) that is produced. Unit 8: Thermodynamics/Electrochemistry Review Packet AP CHEMISTRY Question #5 (2008) Answer the following questions related to chemical reactions involving nitrogen monoxide, NO(g). The reaction between solid copper and nitric acid to form copper(II) ion, nitrogen monoxide gas, and water is represented by the following equation. 3 Cu(s) + 2 NO3-­‐(aq) + 8 H+(aq) → 3 Cu2+(aq) + 2 NO(g) + 4 H2O(l) E˚ = +0.62 V (a) Using the information above and in the table below, calculate the standard reduction potential, E˚, for the reduction of NO3-­‐ in acidic solution. Standard Reduction Potential, E0 Half-­‐Reaction Cu2+(aq) + 2 e-­‐ → Cu(s) +0.34 V NO3-­‐(aq) + 4 H+(aq) + 3 e-­‐ → NO(g) + 2 H2O(l) ? (b) Calculate the value of the standard free energy change, ∆G˚, for the overall reaction between solid copper and nitric acid. (c) Predict whether the value of the standard entropy change, ∆S˚, for the overall reaction is greater than 0, less than 0, or equal to 0. Justify your prediction. Nitrogen monoxide gas, a product of the reaction above, can react with oxygen to produce nitrogen dioxide gas, as represented below. 2 NO(g) + O2(g) → 2 NO2(g) Experiment Initial Concentration of Initial Concentration of O2 Initial Rate of Formation NO (mol L-­‐1) (mol L-­‐1) of NO2 (mol L-­‐1 s-­‐l) 1 0.0200 0.0300 8.52 × 10-­‐2 2 0.0200 0.0900 2.56 × 10-­‐1 3 0.0600 0.0300 7.67 × 10-­‐1 (d) Determine the order of the reaction with respect to each of the following reactants. Give details of your reasoning, clearly explaining or showing how you arrived at your answers. (i) NO (ii) O2 (e) Write the expression for the rate law for the reaction as determined from the experimental data. (f) Determine the value of the rate constant for the reaction, clearly indicating the units. Unit 8: Thermodynamics/Electrochemistry Review Packet AP CHEMISTRY Question #6 (2000) Answer the following questions that relate to electrochemical reactions. (a) Under standard conditions at 25°C, Zn(s) reacts with Co2+(aq) to produce Co(s). (i) Write the balanced equation for the oxidation half reaction. (ii) Write the balanced net-­‐ionic equation for the overall reaction. (iii) Calculate the standard potential, E°, for the overall reaction at 25°C. (b) At 25°C, H2O2 decomposes according to the following equation. 2 H2O2(aq) → 2 H2O(l) + O2(g) E° = 0.55 V (i) Determine the value of the standard free energy change, ΔG°, for the reaction at 25°C. (ii) Determine the value of the equilibrium constant, Keq, for the reaction at 25°C. (iii) The standard reduction potential, E°, for the half reaction O2(g) + 4 H+(aq) + 4 e-­‐ à 2 H2O(l) has a value of 1.23 V. Using this information in addition to the information given above, determine the value of the standard reduction potential, E° for the half reaction below. O2(g) + 2 H+(aq) + 2 e-­‐ → H2O2(aq) (c) In an electrolytic cell, Cu(s) is produced by the electrolysis of CuSO4(aq). Calculate the maximum mass of Cu(s) that can be deposited by a direct current of 100. amperes passed through 5.00 L of 2.00 M CuSO4(aq) for a period of 1.00 hour. ANSWERS To Additional Electrochemistry Practice Problems Answer to #1: -­‐
-­‐ (i) 2 I + 2 H2O -­‐-­‐> I2 + H2 + 2 OH
(ii) Potassium is being reduced into its metallic solid form. Iodine is being oxidized into its gaseous elemental form. In a voltaic cell, oxidation occurs at the anode, but here we are forcing the reaction by electrolysis. In electrolysis, the oxidation occurs at the cathode. So, the gas would appear at the cathode. Answer to #2: 2+
+
(i) 2 Cu + 2 H2O -­‐-­‐> 2 Cu + O2 + 4 H (ii) H2O (remember this is electrolysis and the reaction is forced. That is why H2O is the reducing agent even though it appears to be the weaker reducing agent on you standard reduction potential sheet.) (ii – b) Charge = Amps x seconds (Q=It) = 10 C/s x 200 s = 2000 coulombs Number of Faradays = 2000 C / 96500 C/mol = 0.0207 Faradays (or moles of e ) The reaction occurring at the cathode is: Therefore: 2 Faradays (moles of e ) will produce 1 mole of copper -­‐
2+
-­‐
Cu (aq) + 2e Cu(s) -­‐
Hence 0.0207 Faradays will produce 0.0207/2 moles of copper = 0.0104 moles of Cu Therefore the mass of copper produced = 0.0104 mol x 63.5 g/mol = 0.658 grams Cu Answer to #3: 2+ +
2-­‐ 4+
3+
(i) 3 Sn + 14 H + Cr2O7 → 3 Sn + 2 Cr + 7 H2O (ii) The chromium changes in oxidation state and is a transition metal; most transition metal compounds are colored and the color changes with oxidation state. Answer to #4: (a) from the right to the left (b) 2+
+
2 Cu (aq) + 2 H2O(l) → 2 Cu(s) + O2(g) + 4 H (aq) Unit 8: Thermodynamics/Electrochemistry Review Packet (c) +, a non-­‐spontaneous reaction that requires the input of energy to take place (d) E˚ = +0.34v + (–1.23v) = –0.89v; ∆G˚ = –nℑE˚ = –(4)(96500)(–0.89) = 343540 J = 340 kJ (e) (1.50amps)(2400 sec) = 3600 coul.; 3600 coul. × 1 mol e × 1 mol Cu × 63.55 g = 1.19 g Cu 96500 coul 2 mol e- 1 mol Cu
1.19 g Cu = 0.187 mol Cu; using a 2:1 ratio from equation in part (b), this gives 0.00933 mol O2 (f) AP CHEMISTRY Liatm
V = nRT = (0.00933 mol)(0.0821 mol i K )(298 K) = 0.197 L O2 P
1.16 atm
Answer to #5: (a) X + (-­‐0.34V) = +0.62 V; X = +0.96 V (b) (c) (d) ∆G˚ = –nℑE˚ = -­‐(6)(96500)(0.62) = -­‐358980 J = -­‐360 kJ greater than 0; solid copper is changing to an aqueous ion, an increase in entropy and aqueous nitrate is changing into a gas, also and increase in entropy. (i) second order with respect to NO; using experiments 1 & 3, k O n = rate [ ]
2
0.0852
0.767
; m = 2 =
m
[0.200]
[0.600]m
(ii) first order with respect to O2; using experiments 1 & 2, 0.0852
0.256 ; n = 1 =
[0.0300]n [0.0900]n
k[NO]m =
[NO]m
rate [O 2 ]n
2
(e) rate = k [NO] [O2] -­‐1 -­‐1
-­‐1 2
-­‐1
(f) 0.0852 mol L s = k (0.200 mol L ) (0.0300 mol L ) 2
-­‐2 -­‐1
k = 7100 L mol s Answer to #6: (a) (i) Zn(s) – 2 e-­‐ → Zn2+(aq) (ii) Zn(s) + Co2+(aq) → Zn2+(aq) + Co(s) (iii) oxid: Zn(s) – 2 e-­‐ → Zn2+(aq) Co2+(aq)+ 2 e-­‐ → Co(s) E° = +0.76V red: (b) (i) ΔG° = –nℑE° = –(2)(96500)(0.55) = –106 kJ Δ
(ii) Keq = e– G/RT = e–(–106150/(8.31)(298)) = 4.13 x 1018 (iii) 2 H2O(l) + O2(g) → 2 H2O2(aq) O2(g) + 4 H+(aq) + 4 e-­‐ → 2 H2O(l) E° = 1.23 V __________________________________________________ 2 O2(g) + 4 H+(aq) + 4 e-­‐ → 2 H2O2(aq) E° = 0.68 V divide the equation by 2 but keep the E° the same. 3600 sec
1 coul.
1 mol e-­‐
1 mol Cu 63.55 g Cu
1.00 hr x x 100. amp x x x x = 119 g Cu 1 hr
1amp•sec 96500 coul. 2 mol e-­‐ 1 mol Cu
(c) E° = –0.28V +0.48V E° = –0.55 V