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hs09201f10

# hs09201f10 - EMSE 201 Introduction to Materials Science...

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EMSE 201 – Introduction to Materials Science & Engineering Fall 2010 Case Western Reserve University 1 of 4 Case School of Engineering Solution to Homework #9 Explain how answers were obtained. Give appropriate units for all numerical answers. 1) (6 points) C&R problem 16.2 a) Compute the voltage at 25°C of an electrochemical cell consisting of pure lead immersed in a 5 × 10 –2 M solution of Pb 2+ ions, and pure tin in a 0.25 M solution of Sn 2+ ions. b) Write the spontaneous electrochemical reaction. Solution (modified from the publisher’s solution manual; used with permission) a) Since tin is lower in the standard emf series (Table 16.1), we will begin by assuming that tin is oxidized and lead is reduced, as Sn + Pb 2+ Sn 2+ + Pb (1) and with Sn as M 1 (the metal that gets oxidized) and Pb as M 2 (the metal that gets reduced), Equation 16.20 takes the form Δ V = ( V Pb V Sn ) 0.0592 2 log Sn 2+ Pb 2+ (2 pts) = 0.126 V ( 0.136 V) [ ] 0.0592 2 log 0.25 5 × 10 2 = – 0.011 V (2 pts) since, from Table 16.1, the standard potentials for Pb and Sn are –0.126 and –0.136, respectively. b) Since the V is negative, the spontaneous cell direction is just the reverse of eq. 1 above, i.e. Sn 2+ + Pb Sn + Pb 2+ (2 pts) This problem underscores the importance of keeping straight which metal is M 1 (the one in your starting reaction that gets oxidized) and which is M 2 (the one that gets reduced). It's also essential to keep track of the signs. With our starting assumption (eq. 1), the first term in the Nernst equation is then slightly positive — so far, so good. But the concentration of the Pb solution is more dilute than that of the Sn solution, which would favor the opposite reaction (Pb oxidized, Sn reduced). The second term in the Nernst eq'n will be negative, in fact more negative than the first part is positive. The resulting voltage is negative, telling us that our original assumption (Pb reduced, Sn oxidized) was incorrect. 2) (6 points) An electrochemical cell is constructed such that on one side a pure Zn electrode is in contact with a solution containing Zn 2+ ions at a concentration of 10 –2 M. The other cell half consists of a pure Pb electrode immersed in a solution of Pb 2+

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