It turns out that the van der Waals constant b equals four
times...

Question

It turns out that the van der Waals constant b equals four 
times the total volume actually occupied by the molecules 
of a mole of gas. Using this figure, calculate the fraction of 
the volume in a container actually occupied by Ar atoms 
(b) at 20.27 MPa pressure and 0 °C. (Assume for 
simplicity that the ideal-gas equation still holds.)

Accepted Answer

Hi everyone for this problem, we're told that the volume occupied by the particle of gasses represents a quarter of the Vander wal's constant B. Incorporating this statement into the ideal gas law, calculate the fraction of the volume and a container actually occupied by neon Adams at 126.7. Kill a pascal pressure and 15°C. Okay, so this problem is asking us to calculate the fraction of the volume in a container occupied by neon Adams. Okay, so we want Moeller volume and molar volume is for the ideal gas law. When you write out the ideal gas law, P. V is equal to N. R. T. What we want is V over N. Okay, so for moller volume, we want to know V over N. Which tells us how many leaders there are per So we need to rearrange this ideal gas law to tell us what our molar volume is for our total volume and the volume of our neon Adams. So when we divide the molar volume of our neon Adams over the total volume, we'll be able to calculate that fraction of the volume. Okay, so our mission here is to first calculate our total volume and we need to rearrange the ideal gas law to do that. So we want V over end. So that means we need to divide both sides of our ideal gas law by P. And when we do that, we get V is equal to N. R. T over P. And we want V over N. So when we rearrange this even further, we'll get V over N. Is equal to R. T over P. All right, so let's go ahead and solve for our molar volume are total molar volume. Our our is our gas constant. So Let's write that over here. R. R. is equal to 0.08206. Leaders times A. T. M. Over mole times kelvin T. Is our temperature. Because our our constant has a temperature in Kelvin. We need to convert our 15°C to Kelvin. And the problem they tell us that The container is actually occupied by Neon atoms at 15°C. So to convert this to Kelvin, we add 273.15 And we get a temperature in Calvin of 288.15 Kelvin and then P represents our pressure for our constant. You see our pressure is an A. T. M. And then the problem they give us our pressure and 100 as 126.7 killer pascal. So we need to go from killer pascal's to A T. M. So first we need to convert killer pascal's to pascal And one killer pascal there is 1000 pascal's and to go from pascal to A T. M. The unit conversion is one A T. M. Is equal to 101, pascal. So our kill a pascal's cancel our pascal cancels. We have a final pressure and A. T. M. To be 1. A. T. M. Okay, so now we have everything that we need to solve for molar volume. Our total molar volume. So V over N. Is equal to 0. leaders times A. T. M. Over more times kelvin. This is times our temperature. 288. - 200 and Yes, Kelvin. And this is divided by our pressure. 1.25 A. T. M. Okay so we get a total molar volume of 18. leaders per Okay, so now that we know are total volume, we need to figure out our volume for our neon Adams. Okay. And so we need to Divide by four since the problem tells us a quarter of it is the volume occupied by the particle. Okay so we have, let's see here we have to use the Vander wall's constant for our neon atom. So that is a value. We need to look up. Okay, so let's move some things here to give us some space. Okay, so the Vander wal's constant B for neon. When we look up this value it's zero 01672 L per mole. And the problem tells us that The volume occupied by the particle of gasses represents a quarter of the Vander Wal's constant b. So we need to divide this value by four. Since it's a quarter of our Vander Wal's constant b. When we do that, we get zero 00418 liters per mole. So this is going to be the volume of our neon adam. Okay, So we said that we're going to divide our molar volume of neon by our total volume. So that's what we're going to do to get our final answer. So Our volume of our neon we just said is 0.00418 L per mole Divided by our total volume. We said is 18.9 L per mole. So once we do that calculation, we get final answer. Let me move some things over so we have some space. We get a final answer of 2.2, 1 times 10 to the -4. So this is going to be that fraction of the volume in the container. Okay, that's the end of this problem. I hope this was helpful

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