At 273 K and 1 atm pressure, 1 mol of an ideal gas occupies 22.4 L. (Section 10.4) (b) Looking at Figure 18.1, we see that the temperature is lower at 85 km altitude than at 50 km. Does this mean that one mole of an ideal gas would occupy less volume at 85 km than at 50 km? Explain.

Video transcript

Hey everyone and welcome back at 273 Kelvin and one atmosphere pressure, one mole of an ideal gas occupies 22.4 L. In the figure below the temperature is lower at a 10 kilometer altitude than at 50 kilometers. Does this mean that one mole of an ideal gas would occupy less volume at 10 kilometers then at 50 kilometers. So we're given our charts, what we want to identify those would be our altitude. So we have 10 kilometers, 50 kilometers. Let's label those, let's say identify the corresponding temperatures. So if we have 10 kilometers, the temperature would be around 220 Kelvin at 50 we have around 270 Kelvin. What about pressures? Well, essentially at 50 kilometers, we have around 20 tour at 10 kilometers. We have around 200 tour. Now let's recall the ideal gas flow which states that PV equals an RT, therefore, volume is equal to N RT divided by P. What we notice is that if we keep the same number of moles, then volume is proportional to temperature divided by pressure. So first of all, for the first case, let's call it V 10, we will have nr multiplied by T divided by P, right. So at 10 kilometers, we have our temperature of 200 and 20. And we're going to divide that by pressure as we sat at 10 kilometers, that's 204. If we calculate the result, we essentially get a 1.1 nr and now V 50 we get the same sample. NR multiplied by. Now. What is the temperature? Well, it's 270 Kelvin, what is our pressure? We know that our pressure is 24. And in this case, we get 13.5 an hour. Now, what we can see from here is that the volume at 50 kilometers is greater than the volume at 10 kilometers. And it might seem that the answer is yes, right? Because the gas would occupy less volume at 10 kilometers than it does at 50 kilometers. However, it's not the case because the question implies that it's only dependent on temperature and it's actually also dependent on pressure. So even though that we coincidentally got the same conclusion as it is expected in by our question, in reality, it's not always the case because it also depends on pressure. So we can say that in actuality, the answer is no, right, because we got the answer that satisfies the question. But we have shown that the temperature is not only the, the temperature is not the only factor which affects it. So we're saying no, even though it is true for this case volume, the bands on C divided by pe ratio, not only on temperature. And that'd be our final answer. Coincidentally, we got a situation in which the answer is seems to be. Yes. Right. We got a conclusion that indeed a volume at 10 kilometers is less than the volume at 50 kilometers. But it's just a coincidence in actuality, volume will depend on both temperature and pressure. So we can say conclusively that the answer is no. Thank you for watching.