Problem 122
In an ionic crystal lattice each cation will be attracted by anions next to it and repulsed by cations near it. Consequently the coulomb potential leading to the lattice energy depends on the type of crystal. To get the total lattice energy you must sum all of the electrostatic interactions on a given ion. The general form of the electrostatic potential is where and are the charges on ions 1 and 2, is the distance between them in the crystal lattice. and e is the charge on the electron. (a) Consider the linear crystal shown below. The distance between the centers of adjacent spheres is R. Assume that the blue sphere and the green spheres are cations and that the red spheres are anions. Show that the total electrostatic energy is (b) In general, the electrostatic potential in a crystal can be written as where is a geometric constant, called the Madelung constant, for a particular crystal system under consideration. Now consider the NaCl crystal structure and let R be the distance between the centers of sodium and chloride ions. Show that by considering three layers of nearest neighbors to a central chloride ion, is given by (c) Carry out the same calculation for the CsCl structure. Are the Madelung constants the same?

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Chapter 15 Cont.: IR Spectroscopy * Three things to pay attention to for structure identification 1) Wave number 2) IR Active/ IR Inactive 3) Broad Peak or short peak: helps determine intermolecular types of associations IR Signal Shapes - O β H: signal will be narrower if alcohol is prepared in a solvent incapable of H-bonding - In a sample with an intermediate concentration, both narrow and broad signals may be observed - If there is no carbonyl group signal, it is definitely an alcohol - Secondary amine: broad w/ 1 sharp spike - Primary amine: broad with 2 sharp spikes - No signal for tertiary amines Using IR to distinguish between molecules - IR alone cannot determine structure - Some signals may be ambiguous - Functio

The answer to βIn an ionic crystal lattice each cation will be attracted by anions next to it and repulsed by cations near it. Consequently the coulomb potential leading to the lattice energy depends on the type of crystal. To get the total lattice energy you must sum all of the electrostatic interactions on a given ion. The general form of the electrostatic potential is where and are the charges on ions 1 and 2, is the distance between them in the crystal lattice. and e is the charge on the electron. (a) Consider the linear crystal shown below. The distance between the centers of adjacent spheres is R. Assume that the blue sphere and the green spheres are cations and that the red spheres are anions. Show that the total electrostatic energy is (b) In general, the electrostatic potential in a crystal can be written as where is a geometric constant, called the Madelung constant, for a particular crystal system under consideration. Now consider the NaCl crystal structure and let R be the distance between the centers of sodium and chloride ions. Show that by considering three layers of nearest neighbors to a central chloride ion, is given by (c) Carry out the same calculation for the CsCl structure. Are the Madelung constants the same?β is broken down into a number of easy to follow steps, and 213 words. This textbook survival guide was created for the textbook: General Chemistry: Principles and Modern Applications, edition: 10. General Chemistry: Principles and Modern Applications was written by and is associated to the ISBN: 9780132064521. This full solution covers the following key subjects: . This expansive textbook survival guide covers 28 chapters, and 3268 solutions. Since the solution to 122 from 12 chapter was answered, more than 233 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 122 from chapter: 12 was answered by , our top Chemistry solution expert on 12/23/17, 04:52PM.