1 00:00:00,000 --> 00:00:00,770 2 00:00:00,770 --> 00:00:04,470 Let's do a few more examples with the ideal gas equation. 3 00:00:04,469 --> 00:00:08,649 So we have pressure times volume is equal to the number 4 00:00:08,650 --> 00:00:13,480 of molecules we have in moles times the ideal gas constant 5 00:00:13,480 --> 00:00:15,365 times temperature in Kelvin. 6 00:00:15,365 --> 00:00:18,550 And I just got a comment on one of the videos saying it 7 00:00:18,550 --> 00:00:21,800 made sense except for the fact that R seems kind of like this 8 00:00:21,800 --> 00:00:24,679 mysterious thing in here. 9 00:00:24,679 --> 00:00:26,839 And the way you think about R-- let me rearrange this a 10 00:00:26,839 --> 00:00:27,129 little bit. 11 00:00:27,129 --> 00:00:28,879 Let me write it as pressure times volume is 12 00:00:28,879 --> 00:00:33,560 equal to R times nT. 13 00:00:33,560 --> 00:00:35,365 So we've established, or hopefully we've established, 14 00:00:35,365 --> 00:00:38,100 the intuition that the pressure times the volume 15 00:00:38,100 --> 00:00:41,590 should be proportional to essentially the total energy 16 00:00:41,590 --> 00:00:42,900 we have in the system. 17 00:00:42,899 --> 00:00:47,579 Temperature is average energy, or energy per molecule, and 18 00:00:47,579 --> 00:00:49,619 this is the total number molecules we had. 19 00:00:49,619 --> 00:00:55,039 What R is, the ideal gas constant is, when you multiply 20 00:00:55,039 --> 00:00:58,670 moles times Kelvin, you get mole Kelvin. 21 00:00:58,670 --> 00:01:02,310 And with pressure times volume, it's force per area 22 00:01:02,310 --> 00:01:03,130 times the volume. 23 00:01:03,130 --> 00:01:07,100 You get force times distance, or force times one dimension 24 00:01:07,099 --> 00:01:10,969 of distance, which is joules, so this is in joules. 25 00:01:10,969 --> 00:01:14,319 So what the ideal gas constant essentially does is it 26 00:01:14,319 --> 00:01:17,629 converts-- we know that this is proportional to this, but 27 00:01:17,629 --> 00:01:21,709 it sets the exact constant of proportionality and it also 28 00:01:21,709 --> 00:01:25,009 makes sure we get the units right, so that's all it is. 29 00:01:25,010 --> 00:01:27,540 It just helps us translate from a world dealing with 30 00:01:27,540 --> 00:01:31,270 moles and Kelvins to a world of dealing with, well, in this 31 00:01:31,269 --> 00:01:37,489 case, atmospheres and liters, or bars and meters cubed, or 32 00:01:37,489 --> 00:01:38,949 kilopascals and meters cubed. 33 00:01:38,950 --> 00:01:41,659 But no matter what the units of the pressure and the volume 34 00:01:41,659 --> 00:01:43,939 are, the whole unit of pressure times volume is going 35 00:01:43,939 --> 00:01:44,939 to be joules. 36 00:01:44,939 --> 00:01:47,009 So it's just a translation between the two and we know 37 00:01:47,010 --> 00:01:48,550 that they're proportional. 38 00:01:48,549 --> 00:01:50,719 Now, with that said, let's do some more problems. 39 00:01:50,719 --> 00:01:56,519 So let's say we want to know how many grams of oxygen. 40 00:01:56,519 --> 00:01:59,039 So we want to know grams of O2. 41 00:01:59,040 --> 00:02:02,690 42 00:02:02,689 --> 00:02:10,250 So how many grams of O2 are in a 300-milliliter container 43 00:02:10,250 --> 00:02:14,750 that has a pressure of 12 atmospheres and the 44 00:02:14,750 --> 00:02:19,125 temperature is 10 degrees Celsius? 45 00:02:19,125 --> 00:02:21,860 46 00:02:21,860 --> 00:02:25,330 Well, we've already broken out our ideal gas equation. 47 00:02:25,330 --> 00:02:28,350 Let's see, pressure is 12 atmospheres. 48 00:02:28,349 --> 00:02:31,370 So we can say 12. 49 00:02:31,370 --> 00:02:32,689 I'll keep the units there. 50 00:02:32,689 --> 00:02:35,840 12 atmospheres times the volume. 51 00:02:35,840 --> 00:02:38,310 The volume should be in liters, so this is 300 52 00:02:38,310 --> 00:02:43,330 milliliters, or 300 thousandths or 3 tenths. 53 00:02:43,330 --> 00:02:45,435 So that's 0.3 liters. 54 00:02:45,435 --> 00:02:48,599 55 00:02:48,599 --> 00:02:53,069 300 one thousandths of a liter is 0.3 liters. 56 00:02:53,069 --> 00:02:56,819 And that is equal to the number of moles we have of 57 00:02:56,819 --> 00:02:58,169 this, and that's what we need to figure out. 58 00:02:58,169 --> 00:03:00,179 If we know the number of moles, we know the number of 59 00:03:00,180 --> 00:03:04,360 grams. So this is equal to n times R. 60 00:03:04,360 --> 00:03:05,860 Now which R should we use? 61 00:03:05,860 --> 00:03:08,610 We're dealing with liters and atmospheres. 62 00:03:08,610 --> 00:03:10,860 We'll deal with this one. 63 00:03:10,860 --> 00:03:14,260 Liters, atmospheres, mole-Kelvin, 0.082. 64 00:03:14,259 --> 00:03:16,379 Times 0.082. 65 00:03:16,379 --> 00:03:17,419 And what's our temperature? 66 00:03:17,419 --> 00:03:18,989 It's 10 degrees Celsius. 67 00:03:18,990 --> 00:03:21,000 We always have to do everything in Kelvin. 68 00:03:21,000 --> 00:03:25,680 So it's 283 degrees Kelvin. 69 00:03:25,680 --> 00:03:28,200 So all we have to solve for is n. 70 00:03:28,199 --> 00:03:30,759 We just have to divide both sides of this equation by this 71 00:03:30,759 --> 00:03:37,469 right here, and so we have n is equal to 12 atmospheres-- 72 00:03:37,469 --> 00:03:42,680 I'm just swapping the sides-- times 0.3 liters divided by 73 00:03:42,680 --> 00:03:49,080 0.082 times 283 degrees. 74 00:03:49,080 --> 00:03:50,900 Our answer will be in moles. 75 00:03:50,900 --> 00:03:54,280 And if you want to verify that, you can plug in all the 76 00:03:54,280 --> 00:03:58,469 units and use units for the ideal gas constant. 77 00:03:58,469 --> 00:04:03,930 The number of moles we're dealing with, so it's 12 times 78 00:04:03,930 --> 00:04:11,860 0.3 divided by 0.082 divided by 283 is 79 00:04:11,860 --> 00:04:23,020 equal to 0.155 moles. 80 00:04:23,019 --> 00:04:31,339 Now how many grams are in one mole of an oxygen molecule? 81 00:04:31,339 --> 00:04:39,609 So one mole of O2, well, we know oxygen's atomic mass. 82 00:04:39,610 --> 00:04:40,770 It's 16. 83 00:04:40,769 --> 00:04:45,539 One molecule of oxygen, of gaseous oxygen, has two atoms 84 00:04:45,540 --> 00:04:52,930 in it, so it has an atomic mass of 32. 85 00:04:52,930 --> 00:04:57,459 So it's molar mass, it's mass per mole, is going to be 32 86 00:04:57,459 --> 00:04:58,659 grams. 87 00:04:58,660 --> 00:04:59,680 Now we don't have one mole. 88 00:04:59,680 --> 00:05:02,129 We have 0.155 moles. 89 00:05:02,129 --> 00:05:06,949 So to figure out how many grams we have, we multiply 32 90 00:05:06,949 --> 00:05:21,689 grams per mole times 0.155 moles, and 91 00:05:21,689 --> 00:05:23,310 we'll get our answer. 92 00:05:23,310 --> 00:05:24,550 So let's do that. 93 00:05:24,550 --> 00:05:35,990 So we have 32 times 0.155 is equal to 4.96 grams, or 94 00:05:35,990 --> 00:05:42,730 roughly 5 grams. So we have approximately 5 grams of 95 00:05:42,730 --> 00:05:44,970 molecular oxygen. 96 00:05:44,970 --> 00:05:45,811