exam q u etion ~ exchange Cold Fusion as the Subject of a Final Exam in Honors General Chemistry Norbert 1.Porile Pwdwt University W. Lafayelte. IN 47907
T h e topics covered in the second semester of the Honors General Chemistry course at Purdue University include electrochemistry, crystal structure, and nuclear chemistry. Thus, the recent announcement of the discovery of electrochemically induced cold fusion provided a topic of current interest that could serve as a focus for much of the material taught in the course. T h e two-hour final exam was accordingly devoted t o the above topics within the context of the then-iust-~uhlishedreDort hv Fleischmann and Pons.' It was i o p e d that, in addition testing the students' knowledge and understanding of the material, such a n exam would give them a fairly detailed understanding of a highly puhlicized current scientific tmic. In decidineon this t v ~ of e final exam, we were aided by t h e fact that the texthook for the course2 covers nuclear chemistry in sufficient detail to permit a discussion of Coulomb barrier tunneling, without which the significance of cold fusion cannot he appreciated. I n o r e ~ a r a t i o nfor the final. the students were told to review t i e material on electroihemistry, crystal structure, and nuclear chemistrv. T h a t and their eeneral knowledee of chemistry would sufElce a s preparation. As hackgrounld on the specific topic, a lecture was devoted to nuclear fusion. T h e topics covered included fusion in the Sun, thermonuclea r weapons, controlled fusion, including both magnetic and inertial confinement, muon-catalyzed fusion, and electrochemical fusion.
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The Questions University of Utah chemists recently claimed that they at room temhad achieved nuclear fusion of deuterium (?H) perature inside an electrolytic cell. In essence, their experiwhere D ment involved the electrolysis of heavy water (D20, = 'H) in a cell containine a olatinum ( P t ) anode and a palladium (Pd) cathode. likuterium, whieh is known to be very soluble in palladium, is formed and diffuses into the metal lattice. T h e Utah chemists suggest that the deuterium atoms become so tightly packed in the P d lattice that their nuclei can undergo~unnelingand thereby fuse. This exam explores various aspects of this novel phenomein senon. It is suggested that you answer the quence.
' Fleischmann, M.; Pons, S. J. Electroanal. Chem. 1989, 261,301..
Porile, N. T. Modwn Universify Chemistry;Harcourt Brace Jovanovich: San Diego, 1987.
932
Journal of Chemical Education
edited- bv: JOHNJ. ALEXANDER University of Cincinnati Cmcin~ti.Ohio 45221
1. The electrolysisof D2O was wried out in the presence of 0.1 M
deuterated lithium hydroxide, LiOD. (a) What is the function of the LiOD? (b) Write balanced half-equations for the reactions occurring at the anode and cathode. (c) Sketch an electrolytic cell for the reaction. Label the anode and cathode, and show the direction of electron flow in the external circuit. 2. It is believed that deuterium diffusesinto palladium in the form of atomic deuterium. The D atoms occupy octahedral sites in the Pdlattice.' In order for fusion to be possible, the D atomsmust be exceedingly close to each other. Thus, a minimum requirement for fusion is that at least two D atoms he able to fit into a given odahedral site. To determine whether this is possible, answer questions (a)-(d). (a) I'd crystallizes in acubicclosest packed (CCP) lattice, witha lattice parameterao = 3.891 A. What is the atomic radius of Pd, expressed in A? (b) Calculat~thevolumeofempty spaceina Pd unit cell, i.e., the volume of all the octahedral and tetrahedral sites in the unit cell. Express your answer in A3. (The volume of a sphere is 41 3d . 1 (c) Calculate the volume of an octahedral site. (Assume that the
ratio of the volume of an octahedral and a tetrahedral site can be obtained from the radius ratio rule, i.e., it is equal to (0.414/0.225)3. Express your answer in A3. (d) The atomic radius of D is 0.37 A. Will two D atoms fit in an octahedral site? Show how you arrive at your answer. 3. The Utah group proposed that the observed process wsa nuclear fusion because of the observation of neutrons and tritium (3H), which are formed, respectively,in the two known fusion reactions between two deuterium atoms. (a) Write equations for the two nuclearreactiona that lead to the formation of these produets (each reaction forms two products). (b) Use the table of nudidic masses given below to calculate for each of the above reactions the energy liberated in the fusion of two deuterium atoms. Express your answer in MeV. Mas (u) Nuclide M ~ D (u) S NuclMe 1.0086654 =HB 3.0160299 1.0078252 'He 4.0026036 % 2.0141022 Ti 6.015126 'H 3.0160494 'Li 7.016005 4. Nudear fusion at room temperature is such a startling concept because the thermal kinetic energy of deuterium atom at this temperature is so much lower than the Coulomb barrier between them. (a) Calculate the Coulomb barrier between two deuterons (i.e., nuclei of deuterium atoms). Express your answer in keV. (b) Conventional attempts to achieve controlled fusion involve the confiement of deuterium atoms at a temperature of about 108K. What is the mean thermal energy of a deuteron at this temperature? Express your answer in keV. (c) The probability that two deuterons can tunnel through the n
'H
Coulomb barrier between them is approximately equal to erp -lRIEI1 2, where B is the barrier and E is the kinetic enerm. What is the tunneling probability of deuterons with the energy calculated in (h)? (d) What is the tunneling probability of deutrons with 10 times the mean thermal kinetic energy at room temperature (300 K)? (These energetic deuterons lying in the tail of the Maxwell-Boltmann distribution are the Likeliest to fuse at such a low temperature. The very small probability you calculate is the reason that, in the absence of as-yet-unknown forces squeezing the deuterium atoms together, room temperature fusion is so unexpected.) Note: Your calculator will probably show an answer of zero, because the number is smaller than 5. The Utah group has reported that the process occurring in the palladiumelenrode liberates more energy than issupplied to the electrolytic cell, another indication of a novel process. (a) In one experiment, a potential drop of 1.54 V is used lu drive a 0.266 A current through the cell. How much energy is supplied m the cell in exactly 1 b? (1 J = 1 V X 1 C.) Express your answer in kJ. (b) Haw many Dz molecules are generated in the electrolysis of Dt0 under these conditions? (c) The procass occurringin the palladium is observed to generate 45% more energy than is supplied to the cell for the conditions described ahove. Assuming that all the energy eiven off is the result of fusion. determine the fraction of the deuterium produced in the eleetrulysis that undergoes fusion. Awmw that '15% of the fuaions involve the reaction producing neutrons and 75%involve the reaction producing tritium. (Note: To answer these questions you must use your answers to 3h, 58, and 5h. If you were unahle to answer these questions or if your answers differ by more than a factor of 2 from the answers below, use the following approximate values: 3b: neutron reaction, E = 3.50 MeV; tritium reaction, E = 5.00 MeV. 5a: 1.00 kJ, 5b: 4.W X lozL.) (d) On the basis of (c), calculate the number of neutrons that should be emitted per second. (Note: If you were unable to answer 5c, or if your answer differs by more than a factor of 5 from the following, use 2.0 X 1015 for the number of Dz undereoine - fusion.) (e) The actual number of neutrons emitted per second, as determined by the Utah group, is 4 X 104/s.Assuming that fusion in Pd occurs via the reactions considered in 3a, what conclusions can you draw? 6. It has been proposed by some scientists that most of the energy given off by the palladium is actually due to a chemical reaction. Others have postulated a different type of fusion reaction. (a) A likely chemical reaction is the formation of Dz from deut& rium atoms in the palladium lattice, 2D(g) Dz(g). How manv. Dn- molecules would have to be nroduced to vield ths observed energy outputhur lap determmed in fir)? The standard enthalpy of fi~rmatronof DlgJ I< AHP = 219 76 k.l/ mol. Note: If you cannot answer 5e, or if your answer differs by more than a factor of 2 from the following value, use E = 2.06 kJ for the energy produced per hour. (b) Given your answer to 5b, how plausible is the above explanation? (c) It has also been proposed that some unexpected process in the Pd electrode permits the occurrence of the fusion reaetlon. 2H + 2H -'He. which does not occur with aienificant probability between free deuterium atoms. Since this process does not involve the emission of neutrons or the formation of tritium, it offers s way of reconciling the conflicting results on energy production and neutron emission. Assuming that d the observed energy is due to the above reaction, determine the number of 4Heatoms that would have to be formed
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in one hour for the conditions described in 5. Use the data in 3h. (Note: Use the approximate value given in 6a for the energy output if you were unable to answer 5e to within a fador of 2 of the value given in 6a.) (d) What experiment could be performed to test the proposal given in (c)? (e) The reaction 2H ZH 4Hewould he a much cleaner and safer source of energy than the known fusion reactions of deuterium. Explain why. I . (a) On the hasis of your answers to the preceding questions, do you believe that cold fusion bas really been ohserved? Explain. (b) DO you believe this exam is a fair test of your knowledge of the material? Has it taught you anything about cold fusion?
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T h e following constants and conversion factors were provided: N. = 6.022 X 1OZ3/mol 1MeV = lo3keV = 106eV F = 96,485 Clmol 1eV = 1.602 X 10-l9J R = 8.314 Jlmol K 1u = 931.5 MeV = 1.661X kg k = 1.381 X 10V3J/K 1 A = 10-lorn
Answers (Because of the length of the questions worked out, solutions are not given here but are available on request from the author.)
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5. 6.
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Oz(g) + 2DzO(L) 4e-eathode: 2DzO(l) + 2e-- Dz(g) 20D-. (a) 1.378A; (h) 15.01A3;(c) 2.85 A3; (d) yes, because of 0.42 A3
