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Barium metal crystallizes in a body-centered cubic lattice (the Ba atoms are at the lattice points only). The unit cell edge length is $502 \mathrm{pm}$, and the density of the metal is $3.50 \mathrm{g} / \mathrm{cm}^{3} .$ Using this information, calculate Avogadro's number. [Hint: First calculate the volume (in $\mathrm{cm}^{3}$ ) occupied by 1 mole of $\mathrm{Ba}$ atoms in the unit cells. Next calculate the volume (in $\mathrm{cm}^{3}$ ) occupied by one Ba atom in the unit cell. Assume that $68 \%$ of the unit cell is occupied by Ba atoms.

$6 \cdot 203 \times 10^{23}$

Chemistry 102

Chapter 11

Intermolecular Forces and Liquids and Solids

Liquids

Solids

Regine B.

December 4, 2020

Carleton College

Rice University

University of Kentucky

University of Toronto

Lectures

04:08

In physics, a solid is a state of matter characterized by rigidity and resistance to changes of shape or volume. Solid objects have a definite volume, they resist forces (such as pressure, tension and shear) in all directions, and they have a shape that does not change smoothly with time. The branch of physics that studies solids is called solid-state physics. The physical properties of solids are highly related to their chemical composition and structure. For example, the melting point of ice is significantly lowered if its crystal structure is disrupted.

03:07

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, a liquid is one of the four fundamental states of matter (the others being solid, gas and plasma). A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.

Barium metal crystallizes …

07:30

02:20

03:01

09:29

Barium metal has a body-ce…

01:00

Barium crystallizes in a b…

01:40

07:09

Metallic barium has a body…

04:07

Okay, The first thing we're gonna do is just draw out of the unit cells that we can see exactly what it is we're looking for in a BCC unit. So So in BCC, we've got lattice points in each of the corners and we have one Adam sitting right in the middle over here, so that gives us a total of two atoms in the cell. And this is an important point we're gonna come back to in a bit. So the question has told us to start by calculating Moeller volume and the atomic volume. So let's start by figuring out the volume Permal that we're working with. So this is just gonna be the molar mass that we're working with for barium times, the density. So if we look in our periodic table, we see that the molar mass of barium is 1 37 grand total, and in the question were given the density as being 3.5 grams per centimeter cubed. But we need to invert this in order to get the correct units of Centimeter Cube Permal. So let's just right one centimeter cubed per 3.5 grams and we can calculate this boat and we'll get a value of 39.23 centimeter cubed term mole. Now let's move on to the volume per Adam. So our atomic volume is going to be dependent on the size of unit cell that we're working with were given an edge as being 502 p commuters. So the volume of the unit cell is quite simple. We're just gonna cube the length of that edge so that 502 p commuters cubed Purcell. Now, the next thing you need to consider is how many atoms there are. Purcell. We're gonna multiply this value by in everyone sell the fact that we have to Adams, and that's going to get us r p commuters, Purcell. Now I want to draw your attention to something here and that is that in the question were given the value of 68% of the cell being occupied by Adams. However, we've already taken that into account by the fact that we're considering the fact that there are two atoms in the cell here. So that's actually a red herring. They've given us in the question to try and throw us off from the fact that that is an unnecessary value for calculating our answer. So if we go ahead and run this equation, we're going to see that this equals 63 0.25 times 10 to the sixth Pekka meters cubed per Adam. And if we do a quick unit conversion here, we see that this is equal to 6.3 to 5 times 10 to the negative, 23 centimetres cubed. Per now, the fact that we're seeing times 10 to the negative 23 is a very good sign because we know there is attended the negative 23 in avocados number. So how do we use these two values here together? Well, we know avocados number is in atoms per mole. So let's see how we can arrange these in such a way that we're gonna get avocados number. Well, we know that we've got Centimeters Cube on each side, so we just need to arrange these numbers and multiply them or divide them in such a way that we get this Adams on top. So for avocados number, we're going to see that we know we want Permal. So this the mole is already in Permal for us. And if we divide by Per Adam, that's gonna get us Adams on top, which is what we're looking for. So we see that we're gonna have V mole over the Adam and let's go ahead and substitute these values in. We had our 39.23 centimeters cube more divided by 6.3 to 5 times 10 to the negative. 23 centimetres cubed per adam centimeters. Cancel it on top and on bottom and we're left with Adam's per mole. And if we calculate that we're going to see here that avocados number is equal to 6.20 time. Tend to the negative. 23. Adams. Permal No, sorry. That should be positive. 23 Adams Permal. So, as you can see, this is a little off from the true value, which is 6.0 2/10 tenor of the times, 10 to the 23. But that's to be expected because this is, after all, an approximation that we're working with. And as we can see, we're right in that book park range that we would like to see for avocados. Number at 6.2 times 10 of the 23

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