Coulombic force of repulsion/attraction between ions

[cookiemnstr510510]

Homework Statement

The ionic radius of the Ca²⁺ ion is 0.106nm. The ionic radius of the O^2- ion is 0.132nm.
a.Calculate the coulomb force of repulsion between nearest neighbor O^2- ions in CaO (which has the NaCl-type structure).
b. Calculate the colombia force of repulsion between nearest neighbor Ca²⁺ ions in CaO (which has the NaCl-type structure).
c. Calculate the coulomb force of attraction between Ca²⁺ ions and O^2- ions in CaO (which has the NaCl-type structure).

Homework Equations

F_c=-k(Z₁q₁)(Z₂q₂)/a²
k=constant=9x10⁹Nm²/C²
Z represents the valences of the two ions
a is the interatomic spacing
q is the magnitude of charge of the electron

The Attempt at a Solution

I believe I can do c:
a=0.106nm+0.132nm=0.238nm
F_c= - k(+2 x 1.602x10^-19c)(-2 x 1.602x10^-19c)/(0.238x10^-9m)² = 1.63x10^-8 N

I have a couple questions:
1. What is the significance of the problem telling us "which has the NaCl-type structure" in each part? Is this just telling us that CaO is bonded ionically?
2. I know that repulsive force(F_r)+attractive force(F_c)=0, therefore F_r=-F_c
So does this mean that I can calculate the attractive force between two nearest neighbor O^2- ions, then flip the sign and call it the repulsive force?
3. If this is true then are we saying there is an attractive force between two negatively charged things (O^2-'s? I realize within CaO the Ca²⁺ and O^2- have an attractive and repulsive force which equals zero (that is why they are held together within the molecule).

I guess I want to know if the same process can be used for part C on part A and B, and if so why?

Thanks!

 

[DrClaude]

1. What is the significance of the problem telling us "which has the NaCl-type structure" in each part? Is this just telling us that CaO is bonded ionically?

This is necessary to figure out the distance between two like ions. NaCl has a cubic structure. If the crystal structure had been different, then the distance between say two O^2- ions would not be the same.

2. I know that repulsive force(F_r)+attractive force(F_c)=0, therefore F_r=-F_c
So does this mean that I can calculate the attractive force between two nearest neighbor O^2- ions, then flip the sign and call it the repulsive force?

F_c is the Coulomb force, which is not necessarily an attractive force. Whether it will be attractive or repulsive depends on the sign of F_c.

3. If this is true then are we saying there is an attractive force between two negatively charged things (O^2-'s? I realize within CaO the Ca²⁺ and O^2- have an attractive and repulsive force which equals zero (that is why they are held together within the molecule).

You have to be careful here, as real bonding is much more complicated than simply calculating attractive and repulsive forces, since it is quantum mechanical in nature.

 

[cookiemnstr510510]

This is necessary to figure out the distance between two like ions. NaCl has a cubic structure. If the crystal structure had been different, then the distance between say two O^2- ions would not be the same.F_c is the Coulomb force, which is not necessarily an attractive force. Whether it will be attractive or repulsive depends on the sign of F_c.You have to be careful here, as real bonding is much more complicated than simply calculating attractive and repulsive forces, since it is quantum mechanical in nature.

thank you! Will respond tomorrow when I have more time to read it over

 

[cookiemnstr510510]

Okay, I am gathering from what you are saying is that F_c could either be a coulombic force of attraction or repulsion.
In the case of O^2-, a=0.132nm + 0.132nm=0.264nm=0.264x10^-9m
Z1=-2, Z2=-2, q=1.602x10^-19C
F_c=-(9x10⁹Nm²/C²)((-2)(1.602x10^-19C))((-2)(1.602x10^-19C))/((0.264x10^-9m)²)= -1.33x10^-8N would be the repulsive force between two nearest neighbor O^2- ions? Not asking to check my math, just wondering if this is the correct method to obtain the answer for the question.
Thanks!

 

[DrClaude]

Not asking to check my math, just wondering if this is the correct method to obtain the answer for the question.

Well, yes and no. Actually, I'm not sure how to disentangle the two here. The method is correct in that you are using the right formula for $F_c$, but incorrect in that you are not thinking properly about where the ions are sitting. Making a drawing might help.

 

[cookiemnstr510510]

Well, yes and no. Actually, I'm not sure how to disentangle the two here. The method is correct in that you are using the right formula for $F_c$, but incorrect in that you are not thinking properly about where the ions are sitting. Making a drawing might help.

hmm. okay. Does this have to do with the crystal lattice of CaO? If so since it is NaCl type it would also be FCC. In that case I know what FCC unit cells look like. But I am not sure where two nearest neighbor O^2-'s would lie. I haven't been taught how an actual compound would arrange itself within a unit cell.

 

[DrClaude]

hmm. okay. Does this have to do with the crystal lattice of CaO? If so since it is NaCl type it would also be FCC. In that case I know what FCC unit cells look like. But I am not sure where two nearest neighbor O^2-'s would lie. I haven't been taught how an actual compound would arrange itself within a unit cell.

Be careful: if you take only one type of ion, then the structure is FCC, but both ions together form a simple cubic structure. The link I gave in post #2 shows a picture of the structure, so you can use this to figure out the distance between two like ions.

 

[cookiemnstr510510]

ahhhh okay, this makes much more sense! thank you Dr. Claude