For an Na+Cl- ion pair, attractive and repulsive energies EA and ER, respectively, depend on the...
For an Na+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 = 7.32 * (10^-6 / r^8)
For these expressions, energies are expressed in electron volts (eV) / Na+Cl- ion pair, and r is the distance in nanometers (nm). The net energy, EN, is the sum of the EA and ER.
a) Using graphical software (e.g. Matlab or Excel), create a single plot that shows EA, ER and EN superimposed. Extend your x-axis out to 1 nm. Print and paste the graph into your homework set. Label the axes, the three curves and use appropriate units.
b) Using your plot from part a, estimate the equilibrium spacing, r0, between Na+ and Cl-. Determine the magnitude of the bonding energy, Eo, between the two ions. Be sure to report r0 and E0 using the correct units.
c) Mathematically solve for r0 and E0. Use the Give-Find-Solve methodology.
d) REFLECT: Compare your answers in part b to part c.
Homework Answers
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For an Na+Cl- ion pair, attractive and repulsive energies EA and
ER, respectively, depend on the...
For a K+–Cl– ion pair, attractive and repulsive energies EA and ER, respectively, depend on the...
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...
10. For a Na +Cl-ion pair, attractive and repulsive energies Ea and ER, respectively depend on...
10. For a Na +Cl-ion pair, attractive and repulsive energies Ea and ER, respectively depend on the distance between the ions r, according to 7.32 × 10-6 EA 1.436 For these expressions, energies are expressed in electron volts per Na+ Cl- pair, and ance in nanometers. The net energy Ev is just the sum of the preceding two expressions. (a) Superimpose on a single plot EN,FR, and EA versus r up to 1.0 nm. (b) On the basis of this...
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3. Assuming atoms can be represented as hard spheres, the bonding energy between a sodium ion and a chloride ion pair can be represented by: 1.436 7.32x10-6 8 1 1 where U is energy per ion pair in eV...
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3. Assuming atoms can be represented as hard spheres, the bonding energy between a sodium ion...
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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
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energy EN is just the sum of the two expressions above (EN = EA +
ER). (a) Superimpose on a single plot...
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Answer to Problem 2.19
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2.16 Consider a hypothetical X-Y ion pair for which the equilibrium interionic spacing and bonding energy values are 0.38 nm and -6.13 eV, 2.14 The net potential energy between two adjacent ions, EN, may be represented by the sum of Equations 2.9 and 2.11; that is, B EN= (2.17) r Calculate the bonding energy Eo in terms of the parameters A, B, and n using the following procedure: 1. Differentiate EN with respect to r, and then set the resulting...
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