1 00:00:00,000 --> 00:00:00,410 2 00:00:00,410 --> 00:00:04,299 In the last video we hopefully learned the intuition behind 3 00:00:04,299 --> 00:00:09,449 the ideal gas equation, that pressure times volume is equal 4 00:00:09,449 --> 00:00:16,539 to the number of molecules we have times some constant times 5 00:00:16,539 --> 00:00:17,619 the temperature. 6 00:00:17,620 --> 00:00:19,740 And that's all nice and it hopefully it makes sense to 7 00:00:19,739 --> 00:00:21,099 you how all of these fit together. 8 00:00:21,100 --> 00:00:23,350 That pressure should be inverse to volume and that's 9 00:00:23,350 --> 00:00:27,570 why you're multiplying both sides by each other. 10 00:00:27,570 --> 00:00:28,719 You could take volume and put it on 11 00:00:28,719 --> 00:00:29,519 this side of the equation. 12 00:00:29,519 --> 00:00:31,439 Or that pressure should be proportional to the number of 13 00:00:31,440 --> 00:00:33,060 particles and the temperature. 14 00:00:33,060 --> 00:00:36,280 But now let's apply it and actually do some problems. 15 00:00:36,280 --> 00:00:39,719 Because just knowing this isn't good enough. 16 00:00:39,719 --> 00:00:48,036 So let's say that I have a two liter container, or let's say 17 00:00:48,036 --> 00:01:03,170 a two liter balloon, containing hydrogen gas. 18 00:01:03,170 --> 00:01:06,250 And that's hydrogen as a diatomic molecule. 19 00:01:06,250 --> 00:01:08,569 So each molecule has two hydrogens in it. 20 00:01:08,569 --> 00:01:19,089 And let's say I'm measuring it at 30 degrees Celsius. 21 00:01:19,090 --> 00:01:20,480 My brain is really malfunctioning. 22 00:01:20,480 --> 00:01:26,480 23 00:01:26,480 --> 00:01:32,530 And let's say that the pressure on the outside of the 24 00:01:32,530 --> 00:01:35,560 balloon, we've measured at two atmospheres. 25 00:01:35,560 --> 00:01:39,000 26 00:01:39,000 --> 00:01:44,549 So my question to you is how many moles of 27 00:01:44,549 --> 00:01:45,799 hydrogen do we have? 28 00:01:45,799 --> 00:01:55,789 29 00:01:55,790 --> 00:01:59,020 So let's apply our ideal gas equation. 30 00:01:59,019 --> 00:02:02,439 And since we're dealing with liters and atmospheres, we 31 00:02:02,439 --> 00:02:03,569 have to make sure we use the right 32 00:02:03,569 --> 00:02:04,819 proportionality constant. 33 00:02:04,819 --> 00:02:07,369 34 00:02:07,370 --> 00:02:09,780 So our pressure is given in atmospheres. 35 00:02:09,780 --> 00:02:11,330 Let me write down all the units, actually. 36 00:02:11,330 --> 00:02:24,460 So we have 2 atmospheres times our volume is 2 liters, is 37 00:02:24,460 --> 00:02:26,020 equal to n. 38 00:02:26,020 --> 00:02:29,230 n is the number of particles we care about, and we care 39 00:02:29,229 --> 00:02:31,869 about it in moles, but let's just write n there for now. 40 00:02:31,870 --> 00:02:35,099 Is equal to n times R. 41 00:02:35,099 --> 00:02:38,900 42 00:02:38,900 --> 00:02:42,219 I'll do R in a second. 43 00:02:42,219 --> 00:02:43,870 Times T. 44 00:02:43,870 --> 00:02:46,700 Now you might be tempted to just put 30 degrees in there. 45 00:02:46,699 --> 00:02:49,219 But in all of these problems-- in fact in general, whenever 46 00:02:49,219 --> 00:02:53,039 you're doing any of these gas problems or thermodynamics 47 00:02:53,039 --> 00:02:56,159 problems, or any time you're doing math with temperature-- 48 00:02:56,159 --> 00:02:58,900 you should always convert into Kelvin. 49 00:02:58,900 --> 00:03:02,140 And just as a bit of review as to what Kelvin is, it's just a 50 00:03:02,139 --> 00:03:03,029 different scale. 51 00:03:03,030 --> 00:03:07,219 So for example, the lowest possible temperature that that 52 00:03:07,219 --> 00:03:10,379 can be achieved in the universe, when you think about 53 00:03:10,379 --> 00:03:14,620 it in Celsius, let me draw a little temperature scale here. 54 00:03:14,620 --> 00:03:16,120 So if that's the temperature scale. 55 00:03:16,120 --> 00:03:21,069 I'll draw two, one for Celsius and one for Kelvin. 56 00:03:21,069 --> 00:03:23,250 So the lowest possible temperature that can be 57 00:03:23,250 --> 00:03:29,969 achieved in the universe, and when we say the lowest 58 00:03:29,969 --> 00:03:33,849 possible temperature that means that the average kinetic 59 00:03:33,849 --> 00:03:36,479 energy of the molecules or the atoms are zero. 60 00:03:36,479 --> 00:03:37,979 They're just not moving. 61 00:03:37,979 --> 00:03:40,689 They're just stationary. 62 00:03:40,689 --> 00:03:49,900 So in Celsius, it's minus 273.15 degrees Celsius. 63 00:03:49,900 --> 00:03:53,909 So zero might be some place over here. 64 00:03:53,909 --> 00:03:55,729 Zero, that's where water freezes. 65 00:03:55,729 --> 00:03:59,619 And then 100 degrees, that's where water boils. 66 00:03:59,620 --> 00:04:03,560 And you can immediately see, the whole Celsius scale was 67 00:04:03,560 --> 00:04:05,530 made based on the freezing point and the 68 00:04:05,530 --> 00:04:08,229 boiling point of water. 69 00:04:08,229 --> 00:04:11,419 So look at this and you say, if I have something that's 5 70 00:04:11,419 --> 00:04:15,869 degrees and I have another thing that's 10 degrees, when 71 00:04:15,870 --> 00:04:18,079 you look at the Celsius scale, you're like, oh, maybe the 10 72 00:04:18,079 --> 00:04:20,088 degree thing it has twice as much energy as 73 00:04:20,088 --> 00:04:20,899 the 5 degree thing. 74 00:04:20,899 --> 00:04:22,370 It has twice the temperature. 75 00:04:22,370 --> 00:04:25,379 But when you look at it from the absolute distance to zero. 76 00:04:25,379 --> 00:04:28,750 77 00:04:28,750 --> 00:04:29,879 Let me see if I can draw this. 78 00:04:29,879 --> 00:04:33,969 So the 10 degree is all the way over here and the 5 degree 79 00:04:33,970 --> 00:04:36,050 is almost as far. 80 00:04:36,050 --> 00:04:39,629 So the 10 degrees Celsius is only a slight increment over 5 81 00:04:39,629 --> 00:04:42,089 degrees Celsius, if you were to divide the two. 82 00:04:42,089 --> 00:04:43,829 It's not twice as hot. 83 00:04:43,829 --> 00:04:45,659 And that's why they came up with the Kelvin scale. 84 00:04:45,660 --> 00:04:48,795 Because in the Kelvin scale, absolute zero is defined as 0. 85 00:04:48,795 --> 00:04:51,410 86 00:04:51,410 --> 00:04:56,520 So this right here is zero degrees Kelvin. 87 00:04:56,519 --> 00:04:58,509 And so zero degrees Kelvin is absolute zero. 88 00:04:58,509 --> 00:05:02,099 So what is zero degrees Celsius? 89 00:05:02,100 --> 00:05:03,870 And the increments are the same. 90 00:05:03,870 --> 00:05:06,350 One degree change in Celsius is one 91 00:05:06,350 --> 00:05:07,590 degree change in Kelvin. 92 00:05:07,589 --> 00:05:09,500 So at least they keep it, it's just a shift. 93 00:05:09,500 --> 00:05:14,620 So this is going to be plus 273 degrees Kelvin. 94 00:05:14,620 --> 00:05:18,670 And then 5 degrees would be plus 278; ' 10 degrees would 95 00:05:18,670 --> 00:05:21,259 be plus 283 Kelvin. 96 00:05:21,259 --> 00:05:23,789 And then you see that 5 and 10 degrees really aren't that 97 00:05:23,790 --> 00:05:24,900 different from each other. 98 00:05:24,899 --> 00:05:27,509 But in general, if you want to convert from Celsius to Kelvin 99 00:05:27,509 --> 00:05:30,349 you just add 273 degrees. 100 00:05:30,350 --> 00:05:34,590 So 30 degrees Celsius is what? 101 00:05:34,589 --> 00:05:36,739 Well, this 5 and 10 I drew too close to 100. 102 00:05:36,740 --> 00:05:38,400 But let's say it's sitting here. 103 00:05:38,399 --> 00:05:41,849 It would be 303 degrees Kelvin. 104 00:05:41,850 --> 00:05:48,379 105 00:05:48,379 --> 00:05:51,629 All right, so now for our temperature, that's what we 106 00:05:51,629 --> 00:05:52,250 were worried about. 107 00:05:52,250 --> 00:05:53,990 We wanted to put in the temperature there. 108 00:05:53,990 --> 00:05:59,819 So now we can put in our 303 degrees Kelvin. 109 00:05:59,819 --> 00:06:04,240 Now we have to figure out what constant to use here. 110 00:06:04,240 --> 00:06:05,480 And I've written a couple of down here. 111 00:06:05,480 --> 00:06:08,950 Remember, we're dealing with atmospheres and liters. 112 00:06:08,949 --> 00:06:14,079 So I wrote down a couple of versions of R right here. 113 00:06:14,079 --> 00:06:16,529 Let's see we're dealing with atmospheres and liters. 114 00:06:16,529 --> 00:06:17,959 And in the denominator we're always dealing with mole and 115 00:06:17,959 --> 00:06:19,060 Kelvin no matter what. 116 00:06:19,060 --> 00:06:20,280 So those are always going to be there. 117 00:06:20,279 --> 00:06:22,639 So we should use this proportionality constant. 118 00:06:22,639 --> 00:06:28,620 R is equal to 0.082 liter atmospheres per mole Kelvin. 119 00:06:28,620 --> 00:06:31,209 Let me write that down. 120 00:06:31,209 --> 00:06:33,870 So let me rewrite our whole equation actually. 121 00:06:33,870 --> 00:06:41,420 So I have 2 atmospheres times 2 liters is equal to n times, 122 00:06:41,420 --> 00:06:51,290 I have a bad memory, 0.082 liter atmospheres per mole 123 00:06:51,290 --> 00:06:57,750 Kelvin, times 303 degrees Kelvin. 124 00:06:57,750 --> 00:06:59,350 So let's see what we can do. 125 00:06:59,350 --> 00:07:01,939 Let's see if all of the units work out. 126 00:07:01,939 --> 00:07:04,519 So we can always, when you do dimensional analysis, you can 127 00:07:04,519 --> 00:07:06,339 treat units like numbers. 128 00:07:06,339 --> 00:07:09,769 So if you divide both sides of this equation by atmospheres, 129 00:07:09,769 --> 00:07:11,719 the atmospheres cancel out. 130 00:07:11,720 --> 00:07:14,260 Divide both sides of this equation by liters, liters 131 00:07:14,259 --> 00:07:15,230 cancel out. 132 00:07:15,230 --> 00:07:17,400 You have a Kelvin in the numerator, Kelvin in the 133 00:07:17,399 --> 00:07:20,199 denominator, that cancels out. 134 00:07:20,199 --> 00:07:26,199 And so we have 2 times 2 is equal to n 135 00:07:26,199 --> 00:07:34,909 times 0.082 times 303. 136 00:07:34,910 --> 00:07:39,740 And then we have just a per mole and a 1 over the mole. 137 00:07:39,740 --> 00:07:43,030 So to solve for n, or the number of moles, what we do is 138 00:07:43,029 --> 00:07:47,569 we divide both sides of this equation by all of this stuff. 139 00:07:47,569 --> 00:07:53,719 So we get 2 times 2 is 4. 140 00:07:53,720 --> 00:08:01,260 4 divided by 0.082 divided by 303. 141 00:08:01,259 --> 00:08:03,110 I'm just taking this and putting it on the left-hand 142 00:08:03,110 --> 00:08:04,870 side, dividing both sides by it. 143 00:08:04,870 --> 00:08:07,665 And when you divide by a per mole, if you put a 1 over a 144 00:08:07,665 --> 00:08:08,890 mole here, that's the same thing as 145 00:08:08,889 --> 00:08:10,139 multiplying by a mole. 146 00:08:10,139 --> 00:08:14,009 147 00:08:14,009 --> 00:08:15,339 So it's good, the units all worked out. 148 00:08:15,339 --> 00:08:17,459 We're getting n in terms of moles. 149 00:08:17,459 --> 00:08:19,889 And so we just have to get the calculator out and figure out 150 00:08:19,889 --> 00:08:22,099 how many moles we're dealing with. 151 00:08:22,100 --> 00:08:28,590 So we have 4 divided by 0.082 divided by 152 00:08:28,589 --> 00:08:33,079 303 is equal to 0.16. 153 00:08:33,080 --> 00:08:34,960 If we wanted to go more digits, .161, 154 00:08:34,960 --> 00:08:36,500 but we'll just round. 155 00:08:36,500 --> 00:08:45,429 So this is equal to 0.16 moles of H2. 156 00:08:45,429 --> 00:08:51,009 I am telling you actually here, the exact number of 157 00:08:51,009 --> 00:08:52,279 hydrogen molecules. 158 00:08:52,279 --> 00:08:55,839 But if you wanted a number, you'd just multiply this times 159 00:08:55,840 --> 00:08:58,810 6.02 times 10 to the 23 and then you would have a number 160 00:08:58,809 --> 00:09:00,929 in kind of the traditional sense. 161 00:09:00,929 --> 00:09:03,989 And of course, if you wanted to know what is the mass of 162 00:09:03,990 --> 00:09:10,600 the hydrogen you have. You'd say, OK well one mole of H2 163 00:09:10,600 --> 00:09:11,850 has a mass of what? 164 00:09:11,850 --> 00:09:14,680 165 00:09:14,679 --> 00:09:18,549 The mass of one hydrogen is one atomic mass unit. 166 00:09:18,549 --> 00:09:21,250 The mass of two hydrogen when it's in its molecular form, is 167 00:09:21,250 --> 00:09:23,580 two atomic mass units. 168 00:09:23,580 --> 00:09:27,650 So a mole of it is going to be 2 grams. 169 00:09:27,649 --> 00:09:30,269 So in this case, we have 0.16 moles. 170 00:09:30,269 --> 00:09:34,490 So if we wanted to convert that to grams, this in the 171 00:09:34,490 --> 00:09:41,310 case of these hydrogen gas molecules would be 0.32 grams. 172 00:09:41,309 --> 00:09:45,099 And I just multiplied it by 2 because each mole is 2 grams. 173 00:09:45,100 --> 00:09:46,509 Anyway, I hope you found that useful. 174 00:09:46,509 --> 00:09:48,069 I'm going to do a bunch more of these problems. 175 00:09:48,070 --> 00:09:51,420 Because I think the math is pretty straightforward here. 176 00:09:51,419 --> 00:09:54,319 The thing that always makes it daunting, I think, is the 177 00:09:54,320 --> 00:09:56,610 units and making sure you're using the right units. 178 00:09:56,610 --> 00:09:58,990 What is they are using meters cubed instead of liters, or 179 00:09:58,990 --> 00:10:01,039 kilopascals instead of atmospheres. 180 00:10:01,039 --> 00:10:03,419 So I'll try to do a bunch of examples where we use all the 181 00:10:03,419 --> 00:10:05,819 different units and you're able to pick our constants 182 00:10:05,820 --> 00:10:07,070 appropriately. 183 00:10:07,070 --> 00:10:07,410