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One way to gain a physical understanding of $b$ in the van der Waals equation is to calculate the "excluded volume." Assume that the distance of closest approach between two similar atoms is the sum of their radii $(2 r) .$ (a) Calculate the volume around each atom into which the center of another atom cannot penetrate. (b) From your result in (a), calculate the excluded volume for 1 mole of the atoms, which is the constant $b$. How does this volume compare with the sum of the volumes of 1 mole of the atoms?

a. $$V_{\text {excluded }}=\frac{4}{3} \pi(2 r)^{3}=\frac{32}{3} \pi r^{3}=8\left(\frac{4}{3} \pi r^{3}\right)$$ b. $$V_{\text {cractuded }}=\frac{1}{2}\left(\frac{32}{3} \pi r^{3}\right)=\frac{16}{3} \pi r^{3}$$

Chemistry 101

Chapter 5

Gases

Rice University

University of Maryland - University College

University of Kentucky

Lectures

05:03

In physics, a gas is one of the three major states of matter (the others being liquid and solid). A gas is a fluid that does not support tensile stress, meaning that it is compressible. The word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont, based on the Greek word ("chaos"), the simplest of all the elemental forms of matter.

04:46

In physics, thermodynamics is the science of energy and its transformations. The three laws of thermodynamics state that energy can be exchanged between physical systems as heat and work; that the total energy of a system can be calculated by adding up all forms of energy in the system; that energy spontaneously flows from being localized to becoming dispersed, spread out, or uniform; and that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

03:16

One way to gain a physical…

02:20

Table 10.3 shows that the …

08:08

01:36

02:11

It turns out that the van …

06:32

in this question, we're going to be looking into the volume of atoms and we are going to be assuming that these are perfect spheres in such a way that the volume is equal to for over three multiplied by pi and radius. Ways to the power train are looking at this first scenario that we've been given. If we look zika, we can tell that the hugs fears of radius R. They cannot approach each other beyond air that is off to our so there is a sphere of radius to our that is surrounding each hemisphere from which the other hemispheres are excluded. So if we are to look at the volume of the excluded volume, a pair of molecules the volume of you take Yeah, this is going to be equal to for over three multiplied by pi and the radios that we're looking at here is to our cube. So this is going to give us three to over train multiplied by hi are. So if we factor out if we want to have following this expression so that we determine the ratios between these two volumes or how big the other is or better the other, what you can do here is to isolate such a way that we're going to end up with this volume of a sphere. So if we look at this information that we've been given for us to have a four right at the top. There, 32 is equal to eight multiplied by four. So we need to Factor out in eight Is going to be eight and we're going to have a 4/3 pi r cubed. This is still the following atmosphere. So this means that It is eight times the volume of individual one. Now looking at the next one, Looking at the next one, the result in part is for a pair of molecules. So let's look at the excluded volume molecule that is we have this and this is going to have Multiplied by two over the pie. Uh huh. Killed. So this is going to be equal to 16 divided by three. I are you so to convert from the excluded volume per molecule to excluded volume per more. All we have to do is to multiply by advocate rose number which is and a So the volume of the excluded the excluded volume pay more. This is going to be equal to one. Multiplied by in a multiplied by pi r. Yeah what we're trying to do here is remember one more of any substance. It contains the same number of molecules which is given by the advocate response. So what we heard here we heard excluded excluded the volume of the excluded excluded fallen pair molecule And we want basically molecule tool. No and this is where africa was constant. Came into play

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