ts3201f09b

# ts3201f09b - EMSE 201 Introduction to Materials Science...

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EMSE 201 — Introduction to Materials Science & Engineering 2 December 2009 Department of Materials Science and Engineering 1 of 5 Case Western Reserve University Name: S O L U T I O N Test #3 — 75 minutes; 100 points; 5 questions; 5 pages; 10% of course grade Partial credit will be given for correct set-ups and reasoning. Give units on numerical answers where ap- propriate and use the correct number of significant figures. Please write all answers on these pages; use the backs if needed. Constants : Wiedemann-Franz constant, £ = π 2 k B 2 /(3 q e 2 ) = 2.445 × 10 -8 W K -2 Boltzmann’s constant, k B = 1.381 × 10 -23 J K -1 = 8.620 × 10 -5 eV K -1 gas constant, R : 8.314 J mol -1 K -1 Charge on an electron, | q e | = 1.602 × 10 -19 C Faraday’s constant, F = 96,500 C mol –1 1) A cobalt electrode, immersed in a solution with [Co 2+ ] = 1.00 M, is connected by a metal wire to a nickel electrode in a solution with [Ni 2+ ] = 1.00 M. The solutions are separated by a membrane that lim- its their mixing. The temperature is 25 °C. Ni 2+ + 2e Ni V ° = –0.250 V Co 2+ + 2e Co V ° = –0.277 V a) (4 points) Write the net spontaneous electrochemical reaction for this galvanic cell. Which elec- trode is the anode? Which electrode is the cathode? Ni 2+ + Co Ni + Co 2+ ( 2 pts ). The nickel electrode is the cathode, as it is where the reduction reaction (i.e. of the nickel ions) occurs ( 1 pt ). The cobalt electrode is the anode, as it is where the oxidation reaction (i.e. of the co- balt metal) occurs ( 1 pt ). b) (2 points) Compute the voltage generated in this cell. V = Ni Co = -0.250 – (–0.277) volts = 0.027 volts c) (6 points) What concentration of the Co 2+ solution would be needed to make the voltage of this cell equal 0.000 volts, keeping all other conditions the same as described above? Nernst equation, Ni is M 2 , Co is M 1 ( 2 pts ): V = V Ni o V Co o RT nF ln Co 2 + Ni 2 + = 0.000 volts Values ( 2 pts ): 0 volts [ ] = 0.250 ( 0.277) 8.314 J mol 1 K 1 × 298 K [ ] 2 × 96,500 C mol 1 ln Co 2 + 1 M volts [ ] Solve for the cobalt concentration ( 2 pts ) [Co 2+ ] = exp(2.10) = 8.19 M d) (8 points) When the voltage of the cell in part c) stabilizes at 0.000 volts, the temperature is raised to 100 °C. Write the net spontaneous electrochemical reaction and compute the voltage for the cell under these conditions. V = 0.250 ( 0.277) 8.314 J mol 1 K 1 × 373 K [ ] 2 × 96,500 C mol 1 ln 8.19 M 1 M volts [ ] = 6.79 mV ( 5 pts ) The negative voltage shows that the direction of spontaneity has reversed : Ni + Co 2+ Ni 2+ + Co ( 3 pts ).

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EMSE 201 — Introduction to Materials Science & Engineering 2 December 2009 Department of Materials Science and Engineering 2 of 5 Case Western Reserve University 2) a) (15 points) Diamond has the highest thermal conductivity κ of all known materials. At room tem- perature, what are the primary thermal carriers in diamond? Discuss the materials characteristics of diamond that give it its high thermal conductivity.
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