0:00:00.180,0:00:02.220 - [Instructor] I have about 3.21 grams 0:00:02.220,0:00:03.600 of sulfur powder over here. 0:00:03.600,0:00:08.370 My question to you is how many[br]atoms of sulfur are there? 0:00:08.370,0:00:10.560 At first, this question sounds ridiculous. 0:00:10.560,0:00:12.480 I mean, there's gonna be[br]lots and lots of atoms. 0:00:12.480,0:00:14.790 How in the world are[br]we going to count that? 0:00:14.790,0:00:18.210 That's what we're gonna[br]find out in this video. 0:00:18.210,0:00:21.180 We're gonna do that by[br]introducing the idea of mole. 0:00:21.180,0:00:22.380 So let's begin. 0:00:22.380,0:00:24.000 To come up with the idea of moles, 0:00:24.000,0:00:27.240 we first need a new unit of mass to deal 0:00:27.240,0:00:28.620 with the masses of atoms. 0:00:28.620,0:00:29.640 See, atoms are very tiny. 0:00:29.640,0:00:31.410 Their masses are going[br]to be incredibly tiny. 0:00:31.410,0:00:33.270 So kilograms and grams is going 0:00:33.270,0:00:35.250 to be very inconvenient to use. 0:00:35.250,0:00:39.180 So we come up with a new unit[br]called the atomic mass unit, 0:00:39.180,0:00:40.590 AMU or u. 0:00:40.590,0:00:42.420 It's a very tiny unit of mass. 0:00:42.420,0:00:45.960 Just like grams or kilograms,[br]it's a unit of mass. 0:00:45.960,0:00:48.413 But, of course, whenever[br]we learn about a new unit, 0:00:48.413,0:00:51.570 we need to ask ourselves,[br]"How big is that unit?" 0:00:51.570,0:00:54.840 What is the definition of[br]that unit? How big is 1u? 0:00:54.840,0:00:56.855 Well, here's how we define what a u is. 0:00:56.855,0:01:00.840 You take a single atom of carbon 12. 0:01:00.840,0:01:05.840 Now, its mass by definition is 12u. 0:01:06.270,0:01:07.770 This is not something[br]that we have measured. 0:01:07.770,0:01:09.330 This is something that we fixed. 0:01:09.330,0:01:13.920 We fixed the mass of a[br]carbon 12 atom to be two 12u. 0:01:13.920,0:01:15.720 Exactly. Okay? 0:01:15.720,0:01:17.820 Now, what is 1u? 0:01:17.820,0:01:20.309 Well, if the mass of a[br]carbon 12 atom is 12u, 0:01:20.309,0:01:25.309 1u is 1/12 of its mass, right? 0:01:25.320,0:01:30.320 So we define one atomic[br]mass unit, 1u as 1/12 0:01:31.050,0:01:35.670 of the mass of a single atom[br]of the carbon 12 isotope. 0:01:35.670,0:01:36.783 Does that make sense? 0:01:37.650,0:01:38.670 Well, I'm sure at this point 0:01:38.670,0:01:39.990 you may be having some questions, 0:01:39.990,0:01:43.920 like why did we decide to[br]use carbon as a reference 0:01:43.920,0:01:45.450 and not any other elements? 0:01:45.450,0:01:47.520 Well, it turns out that we[br]actually started with hydrogen 0:01:47.520,0:01:49.260 because it's one of the lightest elements. 0:01:49.260,0:01:50.580 Then we ran into some problems 0:01:50.580,0:01:52.560 and then we switched to oxygen 0:01:52.560,0:01:54.810 because again, it's extremely abundant. 0:01:54.810,0:01:56.400 Then again, we ran into[br]some other problems, 0:01:56.400,0:01:59.070 and then finally, we[br]decided to go with carbon, 0:01:59.070,0:02:00.720 which is also abundant. 0:02:00.720,0:02:02.400 We'll not delve into the histories 0:02:02.400,0:02:03.690 and details of what really happened, 0:02:03.690,0:02:06.330 but yeah, we have to choose[br]some element as a reference, 0:02:06.330,0:02:09.180 and we ended up choosing[br]carbon as a reference. 0:02:09.180,0:02:10.230 Another question you could be having 0:02:10.230,0:02:13.540 is why do we fix the mass of a[br]single atom of this carbon 12 0:02:13.540,0:02:15.030 to be 12u? 0:02:15.030,0:02:17.340 Why not any other number? Why 12? 0:02:17.340,0:02:18.570 Well, for that, you[br]can see that over here. 0:02:18.570,0:02:22.560 Carbon has how many[br]protons and neutrons in it? 0:02:22.560,0:02:26.040 Well, it has a total of, I mean, 0:02:26.040,0:02:28.110 it has six protons and six neutrons. 0:02:28.110,0:02:32.100 So it has a total of 12 protons[br]and neutrons, 12 particles. 0:02:32.100,0:02:34.170 I think of protons and[br]neutrons together over here 0:02:34.170,0:02:36.210 because they have pretty[br]much similar mass. 0:02:36.210,0:02:38.460 I mean, a neutron is[br]actually slightly heavier 0:02:38.460,0:02:40.440 than a proton, but for our purposes, 0:02:40.440,0:02:42.750 to get an intuition over[br]here, they're masses. 0:02:42.750,0:02:44.040 We can pretty much think of them 0:02:44.040,0:02:45.810 to be almost equal to each other. 0:02:45.810,0:02:49.590 So it has a total of 12 particles, right? 0:02:49.590,0:02:53.460 Now, by fixing the mass of[br]those 12 particles to be 12u, 0:02:53.460,0:02:54.300 look at what we are doing. 0:02:54.300,0:02:56.700 We are basically saying, "Hey, 0:02:56.700,0:02:59.430 let's fix the mass of a single proton 0:02:59.430,0:03:02.370 or a neutron to be about 1u. 0:03:02.370,0:03:04.740 That was the whole intention. Okay? 0:03:04.740,0:03:09.210 So you can also think 1u[br]is kind of a representation 0:03:09.210,0:03:13.110 of a mass of a single proton or a neutron, 0:03:13.110,0:03:16.410 but again, this is not exact[br]because masses of protons 0:03:16.410,0:03:19.800 and neutrons are not[br]exactly equal to each other. 0:03:19.800,0:03:22.890 So a proton and neutron[br]will have a mass very close 0:03:22.890,0:03:26.220 to 1u, but it's not exactly 1u, 0:03:26.220,0:03:29.010 but it's a good way to think[br]about what a u represents. 0:03:29.010,0:03:32.100 It represents sort of the[br]mass of a proton or neutron. 0:03:32.100,0:03:34.830 Anyways, now that we understand[br]this, here's a question. 0:03:34.830,0:03:38.130 What do you think is the[br]mass of a single atom 0:03:38.130,0:03:40.050 of oxygen 16 isotope? 0:03:40.050,0:03:41.220 A single atom of this, 0:03:41.220,0:03:44.073 what will be its mass[br]in u, atomic mass unit? 0:03:45.150,0:03:48.480 Well, it has a total of[br]16 particles, 16 protons 0:03:48.480,0:03:50.940 and neutrons together,[br]and since each particle, 0:03:50.940,0:03:52.920 each proton and neutron has a mass of 1u, 0:03:52.920,0:03:57.810 and there are total 16,[br]oxygen mass will be about 16u. 0:03:57.810,0:04:00.330 Again, you can see it's[br]not gonna be exactly 16u 0:04:00.330,0:04:03.510 because mass of each proton[br]and neutron is not exactly 1u, 0:04:03.510,0:04:05.460 but it's gonna be very close to that. 0:04:05.460,0:04:09.030 Similarly, if you take an[br]isotope of say chlorine, 0:04:09.030,0:04:11.310 a particular isotope, the most[br]abundant isotope of fluorine, 0:04:11.310,0:04:15.390 which has 35 protons and[br]neutrons together in it, 0:04:15.390,0:04:19.320 well, then its mass would be close to 35u. 0:04:19.320,0:04:20.640 Makes sense, right? 0:04:20.640,0:04:22.620 Okay, now, here's a question[br]we're gonna ask ourselves. 0:04:22.620,0:04:24.090 Let's go back to carbon. 0:04:24.090,0:04:27.390 Each carbon has a mass[br]of 12u, by definition. 0:04:27.390,0:04:29.520 Now, how many carbon atoms do I need 0:04:29.520,0:04:33.330 to take together says[br]that the total mass of all 0:04:33.330,0:04:37.140 of those carbon atoms[br]together becomes 12 grams. 0:04:37.140,0:04:39.690 You can imagine it's going to be lots 0:04:39.690,0:04:40.800 and lots of atoms, right? 0:04:40.800,0:04:43.920 Because each atom has a very tiny mass 0:04:43.920,0:04:46.800 and we want together 12 grams. 0:04:46.800,0:04:48.930 So we probably need to take billions 0:04:48.930,0:04:50.430 and billions and billions of atoms. 0:04:50.430,0:04:52.800 But the big question is how[br]many atoms do I need to take 0:04:52.800,0:04:56.250 is that they all add up to[br]give me 12 grams of mass? 0:04:56.250,0:04:58.560 Well, it turns out we figured it out. 0:04:58.560,0:04:59.730 Again, we'll not get into the details 0:04:59.730,0:05:01.350 of how we figured it out, okay? 0:05:01.350,0:05:02.940 The history is actually[br]pretty interesting, 0:05:02.940,0:05:05.520 but again, we'll not talk[br]about that over here, 0:05:05.520,0:05:09.690 but we figured it out, and it[br]turns out to be this number. 0:05:09.690,0:05:12.240 You need to take about 6.022, 0:05:12.240,0:05:13.800 and there are some other[br]decimals over here, 0:05:13.800,0:05:17.623 some numbers here, times[br]10 to the power 23, 0:05:19.410,0:05:21.780 which is a huge number, okay? 0:05:21.780,0:05:24.930 If you take these many[br]carbon atoms together, 0:05:24.930,0:05:28.410 carbon 12 atoms together,[br]they will together have a mass 0:05:28.410,0:05:31.110 of 12 grams. 0:05:31.110,0:05:33.900 This number is what we[br]call the Avogadro number 0:05:33.900,0:05:36.630 named after the scientist Amedeo Avogadro 0:05:36.630,0:05:38.190 who worked a lot on this idea. 0:05:38.190,0:05:40.410 But anyways, you can[br]now see the significance 0:05:40.410,0:05:41.580 of this number. 0:05:41.580,0:05:46.020 I can now count the number[br]of atoms in a carbon isotope. 0:05:46.020,0:05:48.030 If you give me 12 grams of carbon, 0:05:48.030,0:05:51.750 I know it has these many[br]number of carbon atoms in it. 0:05:51.750,0:05:52.770 Carbon 12, okay? 0:05:52.770,0:05:54.930 These many number of[br]carbon 12 atoms in it. 0:05:54.930,0:05:57.060 If you give me 24 grams of carbon, 0:05:57.060,0:05:58.470 there must be twice the amount. 0:05:58.470,0:06:00.240 If you give me six grams of carbon, 0:06:00.240,0:06:01.890 then there must be half the amount. 0:06:01.890,0:06:03.990 You tell me the mass of[br]the carbon 12 isotope 0:06:03.990,0:06:05.130 that I'm holding in my hand, 0:06:05.130,0:06:07.410 and I can now use this number to tell you 0:06:07.410,0:06:09.210 how many atoms there are. 0:06:09.210,0:06:10.500 Beautiful, isn't it? 0:06:10.500,0:06:13.770 In other words, this becomes[br]the conversion factor 0:06:13.770,0:06:17.640 for our tiny unit of mass,[br]from our tiny unit of mass u 0:06:17.640,0:06:20.340 to our more familiar[br]big unit of mass, grams. 0:06:20.340,0:06:24.030 If you take u and you[br]multiply with this number, 0:06:24.030,0:06:26.250 you get grams. 0:06:26.250,0:06:29.880 And whenever you have an[br]Avogadro number of things 0:06:29.880,0:06:33.420 with you, we call it a mole. 0:06:33.420,0:06:35.880 Just like how when you[br]have 12 things with you, 0:06:35.880,0:06:38.250 we call it a dozen, these many things, 0:06:38.250,0:06:41.010 if you have together,[br]it could be anything. 0:06:41.010,0:06:42.510 It could be these many atoms. 0:06:42.510,0:06:44.730 Then we'll call it a mole of atoms, 0:06:44.730,0:06:46.410 or it could be these many babies. 0:06:46.410,0:06:48.960 Then we'll say we have a mole of babies. 0:06:48.960,0:06:51.180 It's a ridiculous number[br]but you get the idea. 0:06:51.180,0:06:55.080 And this word mole actually[br]comes from the Latin molecule, 0:06:55.080,0:06:58.590 which translates to a very[br]tiny amount of something. 0:06:58.590,0:07:00.540 But anyways, what is a mole? 0:07:00.540,0:07:03.060 A mole represents Avogadro number, 0:07:03.060,0:07:04.710 these many number of things. 0:07:04.710,0:07:08.910 It could be number of atoms,[br]molecules, particles, anything. 0:07:08.910,0:07:10.620 And what's so special about this number? 0:07:10.620,0:07:12.900 It's a conversion factor[br]from the tiny unit 0:07:12.900,0:07:14.400 of mass u to grams. 0:07:14.400,0:07:16.230 You take this number,[br]multiply it by this number, 0:07:16.230,0:07:19.020 and you will now get it in grams. 0:07:19.020,0:07:20.910 Okay, now, let's see[br]if you understand this. 0:07:20.910,0:07:24.000 What do you think would[br]be the mass of one mole 0:07:24.000,0:07:26.730 of oxygen 16 atoms? 0:07:26.730,0:07:30.780 If I had an Avogadro number[br]of oxygen 16 atoms together, 0:07:30.780,0:07:33.230 what do you think collectively[br]would its mass be? 0:07:34.560,0:07:36.210 Well, an Avogadro number 0:07:36.210,0:07:39.480 of 12us will give me a mass of 12 grams. 0:07:39.480,0:07:41.610 So an Avogadro number of 16us 0:07:41.610,0:07:44.820 will give me me a mass of 16 grams. 0:07:44.820,0:07:47.610 That's what we mean by a[br]conversion factor, okay? 0:07:47.610,0:07:50.550 It works for any atom which has any mass. 0:07:50.550,0:07:51.990 You just multiply it by this, 0:07:51.990,0:07:55.680 and now you'll get the mass in grams. 0:07:55.680,0:07:59.310 Similarly, if I had an[br]Avogadro number of chlorine 35, 0:07:59.310,0:08:02.760 if I had one more of[br]chlorine 35 atoms with me, 0:08:02.760,0:08:06.480 then it'll have 35 grams of mass. 0:08:06.480,0:08:07.440 Make sense? 0:08:07.440,0:08:09.600 And so another way to talk about all 0:08:09.600,0:08:10.860 of these things, whatever I just said now, 0:08:10.860,0:08:13.530 another way to talk about[br]this is we say the molar mass 0:08:13.530,0:08:16.350 of carbon 12 is 12 grams. 0:08:16.350,0:08:21.030 Carbon 12 has a mass of 12 grams per mole. 0:08:21.030,0:08:22.140 Makes sense, right? 0:08:22.140,0:08:26.910 We would say oxygen 16 will[br]have 16 grams per mole. 0:08:26.910,0:08:28.320 I mention oxygen 16 0:08:28.320,0:08:30.540 because remember, there[br]are other isotopes as well. 0:08:30.540,0:08:32.790 Different isotopes will[br]have different masses, 0:08:32.790,0:08:35.100 so their molar mass would be different. 0:08:35.100,0:08:39.270 So oxygen 16 isotope has a molar mass 0:08:39.270,0:08:41.820 of 16 grams per mole, 0:08:41.820,0:08:45.300 and chlorine 35 has a molar mass 0:08:45.300,0:08:47.850 of 35 grams per mole, okay? 0:08:47.850,0:08:49.950 Same thing, whatever I[br]just said, a technical way 0:08:49.950,0:08:52.320 of stating the same thing over here. 0:08:52.320,0:08:53.820 All right, the last thing we need to do 0:08:53.820,0:08:55.980 to make this more practical is to remember 0:08:55.980,0:08:58.560 that over here we considered pure cases. 0:08:58.560,0:09:01.410 I took a pure carbon 12 isotopes 0:09:01.410,0:09:03.480 where every single atom was carbon 12, 0:09:03.480,0:09:05.370 or I took a pure chlorine isotope 0:09:05.370,0:09:08.190 where every single atom was chlorine 35, 0:09:08.190,0:09:09.840 but in reality, that's not the case. 0:09:09.840,0:09:11.640 If I take a chunk of chlorine, 0:09:11.640,0:09:13.290 a lot of it will be chlorine 35, 0:09:13.290,0:09:15.870 but there'll be some[br]other isotopes as well. 0:09:15.870,0:09:18.540 Like, another abundant[br]isotope next to chlorine 35 0:09:18.540,0:09:20.670 is chlorine 37. 0:09:20.670,0:09:23.220 And that sounds really[br]complicated, but what's important 0:09:23.220,0:09:25.320 and powerful is that that[br]doesn't matter to us. 0:09:25.320,0:09:27.300 This whole idea still works. Okay? 0:09:27.300,0:09:28.170 Here's what I mean. 0:09:28.170,0:09:29.310 Let me take an example. 0:09:29.310,0:09:32.430 If you look at our periodic table, 0:09:32.430,0:09:35.340 and you can see that the atomic[br]mass of chlorine is given 0:09:35.340,0:09:36.960 to be not 35. 0:09:36.960,0:09:38.670 It's 35.45. 0:09:38.670,0:09:41.377 So significant deviation from 35. Why? 0:09:41.377,0:09:43.860 Because this also accounts for the fact 0:09:43.860,0:09:45.090 that if you take a chunk of chlorine, 0:09:45.090,0:09:48.570 it'll also contain a lot[br]of chlorine 37 in it. 0:09:48.570,0:09:50.460 So what we do is sort[br]of like take an average. 0:09:50.460,0:09:52.710 This is a weighted average, we say, 0:09:52.710,0:09:55.800 so this is the average[br]atomic mass of chlorine. 0:09:55.800,0:09:57.210 So since I know the average atomic mass 0:09:57.210,0:10:01.320 of chlorine is 35.45, if I[br]now take one mole of chlorine, 0:10:01.320,0:10:04.230 not pure as it exists[br]as a mixture in nature, 0:10:04.230,0:10:09.230 then one mole will have[br]a mass of 35.45 grams. 0:10:09.600,0:10:10.800 That's it. 0:10:10.800,0:10:14.250 Similarly, if I take one mole of carbon, 0:10:14.250,0:10:16.740 which, you know, it's not exactly 12 grams 0:10:16.740,0:10:21.210 because there are other[br]isotopes, it'll be 12.01 grams. 0:10:21.210,0:10:24.120 You see what I mean? A mole[br]is a conversion factor. 0:10:24.120,0:10:28.890 Take one mole of anything,[br]it'll be this number in grams. 0:10:28.890,0:10:31.890 And so now we can try and[br]answer our original question. 0:10:31.890,0:10:35.460 We asked ourselves, if you[br]have 3.21 grams of sulfur, 0:10:35.460,0:10:37.020 how many atoms there are? 0:10:37.020,0:10:38.225 Why don't you pause the video 0:10:38.225,0:10:41.520 and see if you can now answer[br]this question yourself. 0:10:41.520,0:10:43.260 If I take one mole of sulfur, 0:10:43.260,0:10:46.650 if I take Avogadro number of sulfur atoms, 0:10:46.650,0:10:51.570 it'll have a mass of 32.1[br]grams, roughly 32.1 grams. 0:10:51.570,0:10:54.780 So 32.1 grams represents[br]one mole of sulfur. 0:10:54.780,0:10:56.040 But how much sulfur do I have? 0:10:56.040,0:10:59.190 I have not 32.1, I have 3.21 grams, 0:10:59.190,0:11:02.327 which is just 1/10 of a mole. 0:11:02.327,0:11:05.220 That's why I took 3.21 to just[br]keep the calculation simpler. 0:11:05.220,0:11:07.590 We can do it in our head.[br]This is 1/10 of a mole. 0:11:07.590,0:11:09.360 So how many atoms you must be having? 0:11:09.360,0:11:13.680 1/10 of a mole, so 1/10[br]of the Avogadro number. 0:11:13.680,0:11:16.020 So the answer would be[br]the Avogadro number, 0:11:16.020,0:11:18.540 which is 6.02 times 10 to the power 23 0:11:18.540,0:11:20.160 divided by 10, 1/10 of it. 0:11:20.160,0:11:23.283 So it'll be 6.02 times 10 to the power 22. 0:11:24.180,0:11:25.650 Okay, here's our final question. 0:11:25.650,0:11:27.802 If I take one mole of carbon dioxide, 0:11:27.802,0:11:29.550 what do you think will its mass be? 0:11:29.550,0:11:33.030 What is the molar mass of[br]one mole of carbon dioxide? 0:11:33.030,0:11:36.243 Can you pause the video and[br]try to think about this? 0:11:37.500,0:11:39.300 Okay, let's do this step by step. 0:11:39.300,0:11:42.000 I know if I have one[br]mole of carbon dioxide, 0:11:42.000,0:11:47.000 then it must be having an[br]Avogadro number of molecules 0:11:47.070,0:11:48.960 of carbon dioxide, right? 0:11:48.960,0:11:51.660 Remember, if I had half a mole[br]of carbon dioxide, it means 0:11:51.660,0:11:54.090 that I would have half the Avogadro number 0:11:54.090,0:11:55.110 of carbon dioxide. 0:11:55.110,0:11:56.100 Makes sense, right? Okay. 0:11:56.100,0:11:57.840 Anyways, now comes the question 0:11:57.840,0:11:59.640 how many carbon atoms must be there 0:11:59.640,0:12:01.170 and how many oxygen atoms must be there? 0:12:01.170,0:12:02.070 What do you think? 0:12:03.000,0:12:05.520 Well, a single carbon dioxide molecule 0:12:05.520,0:12:07.440 has one atom of carbon. 0:12:07.440,0:12:10.860 If I have five molecules[br]of carbon dioxide, 0:12:10.860,0:12:13.260 I have five carbon atoms, 0:12:13.260,0:12:14.790 which means if I have these many molecules 0:12:14.790,0:12:18.210 of carbon dioxide, I should[br]have exactly that many amount 0:12:18.210,0:12:20.910 of carbon atoms, meaning I have one mole 0:12:20.910,0:12:22.440 of carbon atoms with me. 0:12:22.440,0:12:25.290 Okay, what about the[br]number of oxygen atoms? 0:12:25.290,0:12:30.290 Well, each carbon dioxide[br]molecule has atoms of oxygen. 0:12:30.480,0:12:33.120 And so if I had five,[br]for example, molecules 0:12:33.120,0:12:36.180 of carbon dioxide, I would[br]have twice the amount, 0:12:36.180,0:12:38.220 10 atoms of oxygen. 0:12:38.220,0:12:40.470 And therefore, if I have[br]these many molecules 0:12:40.470,0:12:43.533 of carbon dioxide, I would[br]have twice the amount, 0:12:44.790,0:12:48.810 which means I have two moles[br]of oxygen atoms with me. 0:12:48.810,0:12:50.400 And I can now look at the periodic table 0:12:50.400,0:12:52.950 to find the mass of one mole of carbon. 0:12:52.950,0:12:57.420 It's 12.0107 grams, 0:12:57.420,0:12:58.560 and for oxygen, 0:12:58.560,0:13:02.490 it would be 15.9994 grams. 0:13:02.490,0:13:04.440 That would be the mass[br]of one mole of oxygen. 0:13:04.440,0:13:06.300 But then we have to multiply it by two 0:13:06.300,0:13:08.340 because over here, we have two moles. 0:13:08.340,0:13:11.610 Simplifying this will[br]give me the molar mass 0:13:11.610,0:13:12.870 of carbon dioxide. 0:13:12.870,0:13:16.680 So one mole of carbon dioxide[br]will have this much mass. 0:13:16.680,0:13:18.840 Or we can also say that[br]carbon dioxide has a mass 0:13:18.840,0:13:23.160 of 44.0095 grams per mole. 0:13:23.160,0:13:24.930 Same thing. It's the same thing, okay? 0:13:24.930,0:13:26.520 They all mean the same thing. 0:13:26.520,0:13:27.510 Of course, we can round it off 0:13:27.510,0:13:29.410 and we are actually doing a numerical.