Question

5) For a Kt-Ch ion pair, attractive and repulsive energies EA and ER, respectively, depend on the distance between the ions r, according to 1.436 5.8 x 106 For these expressions, energies are expressed in electron volts (eV) per K+-Cl-pair, and r is the distance in nanometers (nm). The net energy Es is just the sum of the two expressions above (Ev = EA + ER). (a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm (the plot must be printed using a computer software program (excel, matlab.etc) OR hand-drawn on graph paper with labels). (b) On the basis of this plot, determine the equilibrium spacing ro between the K* and Ch ions, and the magnitude of the bonding energy Eo between the two ons (c) Mathematically determine the ro and Eo values (Hint: at equilibrium distance ro. the first derivative of the EN is zero).

For a K+–Cl– ion pair, attractive and repulsive energies EA and ER, respectively, depend on the distance between the ions r, according to EA = − 1.436 r ER = 5.8 × 10−6 r 9 For these expressions, energies are expressed in electron volts (eV) per K+–Cl– pair, and r is the distance in nanometers (nm). The net energy EN is just the sum of the two expressions above (EN = EA + ER). (a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm (the plot must be printed using a computer software program (excel, matlab, etc) OR hand-drawn on graph paper with labels). (b) On the basis of this plot, determine the equilibrium spacing r0 between the K+ and Cl– ions, and the magnitude of the bonding energy E0 between the two ions. (c) Mathematically determine the r0 and E0 values (Hint: at equilibrium distance r0, the first derivative of the EN is zero).

Answer 1

a) b) From this plot r_0 = 0.28 nm E_0 = -4.6 ev c) from Equation for E_N, A = 1.436 B = 5.86 times 10^-6 n = 9 Thus, r_0 = (A/nB)^1/(1 - n) = [1.436/(8) (5.86 times 10^-6)]^1/(1 - 9) = 0.279 nm and E_0 = -A/(A/nB)^1/(1 - n) + B/(A/nB)^n/(1 - n) = -1.436/[1.436/(9) (5.86 times 10^-6)]^1/(1 - 9) + 5.86 times 10^-6/[1.436/(9) (5.86 times 10^-6)]^9/(1 - 9) = -4.57 ev.