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Moving to another Question will save this response:Jestlon 23cublc unit cell, What is the density ofthe atomn Inyct} Jualeeth duefuecel 32. Potassium (K) metal; cry...

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Moving to another Question will save this response:Jestlon 23cublc unit cell, What is the density ofthe atomn Inyct} Jualeeth duefuecel 32. Potassium (K) metal; crystallizes in a body-centered (1A=1x10-8 cm; gram 6.022 x1023 amu) edge i5 5.31 A

Moving to another Question will save this response: Jestlon 23 cublc unit cell, What is the density ofthe atomn Inyct} Jualeeth duefuecel 32. Potassium (K) metal; crystallizes in a body-centered (1A=1x10-8 cm; gram 6.022 x1023 amu) edge i5 5.31 A



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An element crystallizes in a face centered cubic lattice and the edge of the unit cell is $0.559$ $\mathrm{nm}$. The density is $3.19 \mathrm{~g} / \mathrm{cm}^{3}$. What is the atomic weight? (a) $87.6$ (b) $79.9$ (c) $85.5$ (d) $83.9$

In this problem, we know that for BCC they had is equated. Also we know that um is equal to 10 30 multiplication AQ multiplication. Any by ted just putting the value. Yeah. So I can write it as .533 decide density multiplication, a cube at this point 351 multiplication And 24 -7. Hope you multiplication. A room that is. And in that age 6.022 multiplication 10 to depart 23. Bye Dad is too on solving it. I get the value of em Which is equal to 6.94. So according to the option here, option B. H. That a cancer.

Okay, So the first part of this question apart A is asking what type of unit cell is potassium. So I tried to break to him the picture that's shown in the textbook to illustrate a little bit of what's going on in that image. So what kind of units that we have here is called a body center cubic unit cell which we off in abbreviate by B C. C. And you know that you have a BCC body centred cubic UNIX cell when you have eight Adams around the edges and then you have one in the center, so total of nine in the centre one is connecting to all the rest. So that's what we have going on for part A, then for party were asked to find the density for potassium based on this unit cell and some information we're given. So first we wanted just set up what the density equation is. So we know what we're looking for when we set out to find this Ah, the answer to this problem. So we know that density is mass over volume. It's so left tackle is one part at a time. So for the mass we want the mass to be in grams because for density are standard. Unis are always going to be grams per centimeters cube. So I'll just put that over here just so you know what our final ending units are going to be. So to find the mass, we basically can take the molar mass of potassium, which we can know just by looking at a pure on a table. So molar mass, and then the molar mass is basically, ah, representation of how many grams or in one mole of an atom or a market or whatever you want. So that's great and all, but we just want from the mass of our like, one Adam here. So we just need to multiply this through by the number of moles, and then we'll be able to get just grams. Okay, so we haven't done any math here. We're just setting it all up purely then we can set up for how we're going to sell for volume. So like I said before, we won't volume to be in the units of centimeters cute. And the problem gives us that one edge of our cube. So let's take this for example as 533 PICO meters. So that's great. P. Caminos Air. Great. But we want to get those into centimeters before we continue any further because we want those to be our end units. So we know that to sell volume for a cube, we just can multiply the edges by themselves three times so it will be a to the power of three will give us our volume. So it's like this side times this side times this side so you can do your calculator, whatever to convert 5 33 into centimeters and out of PICO meters and you'll get something like 5.33 times 10 to the negative eighth. So I'll just in 1/2 i e negative eight neither center near. So the volume is just going to be this number raised to the third power. So now that we have all the set of done, we can start plugging in some numbers. So we go back to our general equation up here, we can start plugging things in, so we'll start with the top of the fraction. So we will cover Moeller mass. We get 39.9 roughly. And then we know that for the moles you're going to have to and that's going to be over of a god rose number, which is Ah, 6.2 to times 10 to the 23rd giver t so spring. But that in. And then we also have this while supplied by or a volume number here. So if you cube that, you're gonna go ahead and get this huge number, I'm not gonna write it all out. Ah, it would be something around 1.514 times 10 to the negative 22nd centimeters. Cute. So if you put this all into your calculator, then you should end up getting a number around 0.86 grams per centimeters cubed and naturally, the density that you should calculate based from this problem.

So you were given a body centered cubic cell as well as the density and the edge like that. So what we want to do is to determine the molar mass of the metal that's making up this lattice. So we always recommend doing for problems like this is comparing the units that you're given to the units you're trying to get to. In this case, we're trying to find molar Mass, so we're trying to finish with grams per mold. That's helpful for us because we can see that our density already has one of those units so we can start out with Our grams are numerator, which means that the only thing that we need to try to do is to get from the physical measurements of the dimensions of this cell and get it in terms of moles. The easiest way to do that is to take your distance measurements, factor those into the calculation to get it in terms of per unit cell and then use the number of atoms per unit cell to take you finally through avocados number and get two moles. So what I would recommend doing early on is taking the edge link value that they've given you, which is in terms of Nana meters and first converting that centimeters. So every nanometer is one times 10 to the negative seventh centimeter. We're told that the edge length is point 28664 Nana meters, which means that the edge length is going to be too 0.8664 times 10 to the negative eighth. Now we can take that value in Cuba and the reason we're doing this is because we're trying to get rid of the distance measurement of the cell and getting this term just in terms of the unit cell itself. Now the reason this is helpful because we also know that since we're giving, given the fact that it's ah, body centered cubic cell, we know that there's a net of two atoms within this unit self that helps us get rid of cell. And now that we have Adams of the Dominator, we're well on our way to converting this finally, two moles because we can now take Oh God Years number 6.22 times 10 to the 23rd Adam's promote. What you can see now is we're going to end up with a number that's in terms of grams per mole. It's always to do is execute this for action all the way across. What we find is that the molar mass of this compound is 55.84 grams for more.

Okay, so we know that volume is equal to length. Cute on, you know, like equals. 0.28 664 times 10 to the negative. Nine meters. Q. Okay, so we keep that. We get 2.3551 times 10 to the 29 meters. Cute. Oh, it's convert that to centimeters. It's 100 cube centimeter cube, which gives me 2.355 110 to the negative. 23 centimeters cube get. Since you know density, we can get the number of grams because you know that 7.8748 grams is one centimeter you for once in every accused incidence e that I give us 1.8546 times 10 to the negative. 22 grams. Okay, so the number of Adam's of metals units is too. Adam, um times on budget number 6.22 times 10 to the 23 for one more. Just give me 3.3212 times 10 to the 24 both of our Adam. Now calculated. More mask gets on our grams. 1.8546 times tented in the 22 grams over more than just 3.3212 times 10 tonight was formal that usually 55.84 grams.


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