% ionic character = {1 exp 0.25 X 2

Transcription

1 Pactice Poblems Set I MIME6 P1. Calculate the faction of bonding of MgO that is ionic (use the figue below). : % ionic chaacte = {1 exp.5 X A X } 1 Electonegativities of Mg and O ae 1. and 3.5 espectively. ionic component: {1 exp } 1 = 73.4% P. Conside the atomic bonding in the following mateials, MgO NiAl SiC Whose bonding is diectional? : SiC P3. Conside thee mateials, A, and C. The atomic bonding enegies within these mateials ae denoted as E A (), E (), and E C () espectively with being the atomic sepaation. Denoting the coesponding equilibium atomic sepaation (i.e., the sepaation at which de / d ) within these mateials as have df df df d d d A, de with F d,, and A C E( ) EA( ) EC ( ) Please ange the values of Young s modulus (Y) and melting tempeatue (T m ) fo these mateials. : Y Y Y T T T A C m m m C, espectively, we 1

2 Pactice Poblems Set I MIME6 P4. The net potential enegy between two adjacent ions, E N, may be epesented as follows, E N = A n Calculate the bonding enegy E in tems of the paametes A,, and n using the following pocedue: (E.1) a. Diffeentiate E N with espect to, and then set the esulting expession equal to zeo, since the cuve of E N vesus is a minimum at E. b. Solve fo in tems of A,, and n, which yields, the equilibium inteionic spacing. c. Detemine the expession fo E by substitution of into Equation (E.1). (a) Diffeentiation of Equation.11 yields (b) (c) den d den A n = d (1 + 1) ( n + 1) 1/(1 - n) A = n A E = E( ) = + A A n n 1/(1 - n) n/(1 - n) P5. Fo a K + Cl ion pai, attactive and epulsive enegies E A and E R, espectively, depend on the distance between the ions, accoding to E A , E R 9 6 Fo these expessions, enegies ae expessed in electon volts pe K + Cl pai, and is the distance in nanometes. The net enegy E N is just the sum of the two expessions above. (a) Supeimpose on a single plot E N, E R, and E A vesus up to 1. nm. (b) On the basis of this plot, detemine (i) the equilibium spacing between the K + and Cl ions, and (ii) the magnitude of the bonding enegy E between the two ions. (c) Mathematically detemine the and E values using the solutions to Poblem 1 and compae these with the gaphical esults fom pat (b).

3 Pactice Poblems Set I MIME6 (a) Cuves of E A, E R, and E N ae shown on the plot below. (b) Fom this plot =.8 nm, E = 4.6 ev (c) Using the solutions in Poblem #1,.79 nm E? 4.57 ev P6. The net potential enegy E N between two adjacent ions is sometimes epesented by the expession E N C Dexp in which is the inteionic sepaation and C, D, and ρ ae constants whose values depend on the specific mateial. (a) Deive an expession fo the bonding enegy E in tems of the equilibium inteionic sepaation and the constants D and ρ using the following pocedue: 1). Diffeentiate E N with espect to and set the esulting expession equal to zeo. ). Solve fo C in tems of D, ρ, and. 3). Detemine the expession fo E by substitution fo C in Equation (E.3). (b) Deive anothe expession fo E in tems of, C, and ρ using a pocedue analogous to the one in pat (a). (E.3) 3

4 Pactice Poblems Set I MIME6 (a) de/d = C De De / ( / ) C = Substitution into Equation (E.3) yields an expession fo E as = ( / ) 1 E De (b) ( / ) C e C D =, E = 1 P7. Make a plot of bonding enegy vesus melting tempeatue fo the metals listed in the Table below. Using this plot, appoximate the bonding enegy fo coppe, which has a melting tempeatue of 184C. : elow is plotted the bonding enegy vesus melting tempeatue fo these fou metals. Fom this plot, the bonding enegy fo coppe (melting tempeatue of 184C) should be appoximately 3.6 ev. 4

5 Pactice Poblems Set I MIME6 P8. What type(s) of bonding would be expected fo each of the following mateials: bass (a coppe-zinc alloy), ubbe, baium sulfide (as), solid xenon, bonze, nylon, and aluminum phosphide (AlP)? a. Fo bass, the bonding is metallic since it is a metal alloy. b. Fo ubbe, the bonding is covalent with some van de Waals. (Rubbe is composed pimaily of cabon and hydogen atoms.) c. Fo as, the bonding is pedominantly ionic (but with some covalent chaacte) on the basis of the elative positions of a and S in the peiodic table. d. Fo solid xenon, the bonding is van de Waals since xenon is an inet gas. e. Fo bonze, the bonding is metallic since it is a metal alloy (composed of coppe and tin). f. Fo nylon, the bonding is covalent with pehaps some van de Waals. (Nylon is composed pimaily of cabon and hydogen.) g. Fo AlP the bonding is pedominantly covalent (but with some ionic chaacte) on the basis of the elative positions of Al and P in the peiodic table. 5