Question

IIA 2. Calculate the net number of Na$^+$ and Cl$^-$ ions belonging to this cell. Na$^+$ SHOW WORK: Cl$^-$ 3. What is the ratio of positive to negative ions in a unit cell of NaCl? Is this expected? Explain. 4. What are the coordination numbers of the Na$^+$ and Cl$^-$ ions? (How many Na$^+$ ions are around each Cl$^-$ ion, and vice versa?) Na$^+$ Cl$^-$ 5. Calculate the shortest distance between two Na$^+$ ions and the shortest distance between two Cl$^-$ ions in terms of the unit cell edge length ($a_o$). Na$^+$ Cl$^-$ 6. Now build the NaCl unit cell by placing the sodium ions at the positions of the face-centered cubic unit structure, and the chloride ions in the "holes". (Essentially, this switches the positions of the Na$^+$ and Cl$^-$ ions.) What translation along the body diagonal ($d_o$) of this cell would interchange the positions of the Na$^+$ and Cl$^-$ ions? 

          IIA 2. Calculate the net number of Na$^+$ and Cl$^-$ ions belonging to this cell.
Na$^+$ 
SHOW WORK:
Cl$^-$
3. What is the ratio of positive to negative ions in a unit cell of NaCl?
Is this expected? Explain.
4. What are the coordination numbers of the Na$^+$ and Cl$^-$ ions? (How many Na$^+$ ions are
around each Cl$^-$ ion, and vice versa?)
Na$^+$ 
Cl$^-$
5. Calculate the shortest distance between two Na$^+$ ions and the shortest distance between
two Cl$^-$ ions in terms of the unit cell edge length ($a_o$).
Na$^+$ 
Cl$^-$
6. Now build the NaCl unit cell by placing the sodium ions at the positions of the face-centered
cubic unit structure, and the chloride ions in the "holes". (Essentially, this switches the
positions of the Na$^+$ and Cl$^-$ ions.) What translation along the body diagonal ($d_o$) of this
cell would interchange the positions of the Na$^+$ and Cl$^-$ ions?
Show more…
IIA 2. Calculate the net number of Na^+ and Cl^- ions belonging to this cell. Na^+ SHOW WORK: Cl^- 3. What is the ratio of positive to negative ions in a unit cell of NaCl? Is this expected? Explain. 4. What are the coordination numbers of the Na^+ and Cl^- ions? (How many Na^+ ions are around each Cl^- ion, and vice versa?) Na^+ Cl^- 5. Calculate the shortest distance between two Na^+ ions and the shortest distance between two Cl^- ions in terms of the unit cell edge length (ao). Na^+ Cl^- 6. Now build the NaCl unit cell by placing the sodium ions at the positions of the face-centered cubic unit structure, and the chloride ions in the "holes". (Essentially, this switches the positions of the Na^+ and Cl^- ions.) What translation along the body diagonal (do) of this cell would interchange the positions of the Na^+ and Cl^- ions?

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Chemistry: Structure and Properties
Chemistry: Structure and Properties
Nivaldo Tro 2nd Edition
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IIA 2. Calculate the net number of Na^(1+) and Cl^(1-) ions belonging to this cell. Na^(1+) Cl^(1-) SHOW WORK: 3. What is the ratio of positive to negative ions in a unit cell of NaCl? Is this expected? Explain. 4. What are the coordination numbers of the Na^(1+) and Cl^(1-) ions? (How many Na^(1+) ions are around each Cl^(1-) ion, and vice versa?) Na^(14) Cl^(1-) Calculate the shortest distance between two Na^(1+) ions and the shortest distance between two Cl^(1-) ions in terms of the unit cell edge length (a_(0)). Na^(1-1) Cl^(1-) Now build the NaCl unit cell by placing the sodium ions at the positions of the face-centered cubic unit structure, and the chloride ions in the "holes". (Essentially, this switches the positions of the Na^(1+) and Cl^(1-) ions.) What translation along the body diagonal (d_(b)) of this cell would interchange the positions of the Na^(1+) and Cl^(1-) ions? Na1* Cl1- SHOW WORK: 3. What is the ratio of positive to negative ions in a unit cell of NaCl? Toewiad cnenoss Is this expected? Explain bso 4. What are the coordination numbers of the Na1* and Cl ions? How many Na1* ions are around each Cl ion, and vice versa?) Na1+ lnor ysndolomia 5. Calculate the shortest distance between two Na1+ ions and the shortest distance between two Cl- ions in terms of the unit cell edge length a. Na1+ Cl1- 6. Now build the NaCl unit cell by placing the sodium ions at the positions of the face-centered cubic unit structure, and the chloride ions in the "holes". Essentially, this switches the cell would interchange the positions of the Na and Cl ions?
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Transcript

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00:01 Here, we want to find two positive numbers whose sum is 41 and product is as large as possible.
00:07 So let's say we have x and y, and we add them together to get 41.
00:12 That's what we call the constraint.
00:14 It's what has to always be true.
00:16 And generally speaking, you're going to find your constraint and then solve for one of the variables.
00:20 Say y.
00:21 So y is going to be 41 minus x.
00:24 And we'll save that and use it later.
00:26 Next, we need to find the objective function.
00:29 That's the function that we want to maximize or maximize.
00:31 Minimize.
00:32 It doesn't matter.
00:33 So in this case, that's the area, which is x times y.
00:37 So now we want to use that objective function to get rid of one of the variables...
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