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I would like to make sure my work on the practice final exam iscorrect. I need a detailed explanation. Thanks!

a)The cations in CsCl form a body-centered unit cell. Determine thenumber of both cations and anions per unit cell.

b)Given the density of CsCl is 3.99 g/cm3, calculate thevolume of the unit cell in cm3.

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Nelly Stracke
Nelly StrackeLv2
29 Sep 2019

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I would like to make sure my work on the practice final exam iscorrect. I need a detailed explanation. Thanks!

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This is what I did but need help might be wrong

I have an ionic solid, let's say Na+ I- in a face centered cubicstructure. I would like to find out the radius of Na+.

As givens, I have the radius of I- as 216.0 picometers and thedensity of the NaI molecule as 3.667 g/cm3.

Knowing that both Na and I form a face centered cubic structure,the total number of atoms is 4+4=8.

I can get the mass of the unit cell by taking the molar mass ofthe molecule (149.9g/mol)*(1/6.02e23)*(8atoms/unit cell)=1.99e-21grams/unit cell.

From this, knowing the density and mass, I can get the volume bydividing 1.99e-21g/cell / 3.667g/cm3, giving me a volume of5.427e-22cm3/cell.

From the volume, I can get the length of a side of the unit cellby taking the cube root, givine me a length of 8.157e-8.

Here's where I'm not sure how to proceed. Knowing what thearrangement of atoms is, it would seem that the length of any sidewould contain one atom in the center, and a half of an atom on eachside, giving a length equal to 4*radius (2 * radius of Na) + (2 *radius of I). Since the radius of I- was given as 216.0pm, to findthe other radius, I would just set this equation up:

2r+(2*216.0)=8.157e-8 (or 815.7pm) and solve for r.

Doing this, I'm not getting the right answer, and can't figureout where I'm going wrong. I'm sure it's something simple, butwould love some help.

Thanks!

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