WEBVTT 00:00:00.030 --> 00:00:02.529 NARRATOR: The following content is provided under a Creative 00:00:02.529 --> 00:00:03.780 Commons license. 00:00:03.780 --> 00:00:06.020 Your support will help MIT OpenCourseWare 00:00:06.020 --> 00:00:10.090 continue to offer high quality educational resources for free. 00:00:10.090 --> 00:00:12.670 To make a donation or to view additional materials 00:00:12.670 --> 00:00:16.580 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.580 --> 00:00:17.257 at ocw.mit.edu. 00:00:26.290 --> 00:00:28.670 CATHERINE DRENNAN: There are five types of problems. 00:00:28.670 --> 00:00:30.880 We just did two. 00:00:30.880 --> 00:00:33.430 And now I'm going to convince you that salt and water 00:00:33.430 --> 00:00:39.600 problems are in fact the same as weak acid weak base problems. 00:00:39.600 --> 00:00:41.985 So we're going to move now to today's handout. 00:00:46.950 --> 00:00:53.340 So the pH of a salt solution is determined 00:00:53.340 --> 00:00:56.850 by what made that salt. So a salt 00:00:56.850 --> 00:01:01.290 is formed when you neutralize an acid with a base or a base 00:01:01.290 --> 00:01:03.660 with an acid. 00:01:03.660 --> 00:01:06.310 And so depending on what acid and which 00:01:06.310 --> 00:01:09.550 base were used and mixed together, 00:01:09.550 --> 00:01:13.050 the salt might have a different pH. 00:01:13.050 --> 00:01:18.930 So an example here if we had HCl and NaOH, 00:01:18.930 --> 00:01:22.635 that's going to give our friend table salt NaCl and water. 00:01:25.300 --> 00:01:29.300 The pH of the salt and water is not always neutral. 00:01:29.300 --> 00:01:32.980 In this case it would be, but it's not always neutral. 00:01:32.980 --> 00:01:35.450 It depends on the nature of the acid 00:01:35.450 --> 00:01:38.440 and the nature of the base that were mixed together 00:01:38.440 --> 00:01:42.960 to form that salt. So there are some rules 00:01:42.960 --> 00:01:46.130 to help you figure out whether something's 00:01:46.130 --> 00:01:49.700 going to be acidic or basic. 00:01:49.700 --> 00:01:54.790 And if you have a salt that contains 00:01:54.790 --> 00:01:57.330 a conjugate acid of a weak base, so it 00:01:57.330 --> 00:02:00.160 has a conjugate acid in it, it will 00:02:00.160 --> 00:02:03.630 produce an acidic solution. 00:02:03.630 --> 00:02:07.940 And if you have a salt that has small highly charged metal 00:02:07.940 --> 00:02:14.470 cations like iron plus 3, that will also be acidic. 00:02:14.470 --> 00:02:18.090 So we saw last time I had the prescription medicine 00:02:18.090 --> 00:02:21.615 for my daughter, which was iron sulfate, was highly acidic. 00:02:24.120 --> 00:02:27.620 So note that periodic table group 1 and group 00:02:27.620 --> 00:02:34.750 2 ions, lithium plus 1, calcium plus 2, sodium plus 1-- 00:02:34.750 --> 00:02:39.190 these are all going to be neutral 00:02:39.190 --> 00:02:43.710 and in fact, anything plus 1 neutral. 00:02:43.710 --> 00:02:48.150 And then salts that can take conjugate bases of weak acids 00:02:48.150 --> 00:02:50.840 will produce basic solution. 00:02:50.840 --> 00:02:52.710 So you're going to be asking yourself, 00:02:52.710 --> 00:02:56.560 does this solution have a conjugate acid of a weak base? 00:02:56.560 --> 00:02:59.280 Does it have a conjugate base of weak acid? 00:02:59.280 --> 00:03:03.122 Does it have group 1, group 2-- what's in there? 00:03:03.122 --> 00:03:05.080 And then you can think about whether it's going 00:03:05.080 --> 00:03:08.100 to be acidic, neutral or basic. 00:03:08.100 --> 00:03:11.180 So let's look at some examples. 00:03:11.180 --> 00:03:14.850 So we have a salt, NH4Cl. 00:03:14.850 --> 00:03:16.300 And we want to figure out is this 00:03:16.300 --> 00:03:19.360 going to produce an acidic solution, a neutral solution 00:03:19.360 --> 00:03:21.130 or a basic solution. 00:03:21.130 --> 00:03:25.110 So we need to think about what went in to making this salt. 00:03:25.110 --> 00:03:27.610 And we're going to break apart the salt and we're going 00:03:27.610 --> 00:03:33.340 to think about NH 4 plus and we're going to think about Cl-. 00:03:33.340 --> 00:03:37.380 So let's think about NH 4 plus first. 00:03:37.380 --> 00:03:41.230 And we're going to ask the question is NH 4 00:03:41.230 --> 00:03:43.680 plus a conjugate acid of a weak base 00:03:43.680 --> 00:03:46.970 and therefore, a weak acid itself? 00:03:46.970 --> 00:03:48.920 One way to answer this question is 00:03:48.920 --> 00:03:53.220 to look up the Ka for NH 4 plus, which happens 00:03:53.220 --> 00:03:56.670 to be 5.6 x 10 to the -10. 00:03:56.670 --> 00:04:01.890 You could also ask about the weak base that it came from. 00:04:01.890 --> 00:04:04.790 The weak base in this case, its conjugate base, 00:04:04.790 --> 00:04:08.380 is NH3 and ask if that's a weak base. 00:04:08.380 --> 00:04:11.936 So if you have something that is an acid here, 00:04:11.936 --> 00:04:13.560 you can think about what the base would 00:04:13.560 --> 00:04:15.480 be by removing H plus. 00:04:15.480 --> 00:04:20.029 If you remove H plus from NH 4 plus you get NH3. 00:04:20.029 --> 00:04:23.970 And you can say, is NH3 a weak base and look up a Kb. 00:04:23.970 --> 00:04:28.410 In this case, it's 1.8 x 10 to the minus 5. 00:04:28.410 --> 00:04:30.150 So what do you think? 00:04:30.150 --> 00:04:35.330 Is this a weak base and this a weak acid with those numbers? 00:04:39.760 --> 00:04:40.550 What do you think? 00:04:40.550 --> 00:04:42.080 Is that a weak acid? 00:04:42.080 --> 00:04:45.550 Is that a strong acid? 00:04:45.550 --> 00:04:47.410 So it's a weak acid. 00:04:47.410 --> 00:04:49.450 Is this a weak base? 00:04:49.450 --> 00:04:50.950 Yeah. 00:04:50.950 --> 00:04:55.400 So we can look also in this chart down here 00:04:55.400 --> 00:04:59.030 and so NH3 is a moderately weak base and NH 4 plus 00:04:59.030 --> 00:05:03.440 is a very weak base, but it is very weak acid, 00:05:03.440 --> 00:05:04.870 but it is a weak acid. 00:05:04.870 --> 00:05:07.980 So we do have a conjugate acid of a weak base. 00:05:07.980 --> 00:05:12.330 So it is acidic, not super acidic, but it is acidic. 00:05:12.330 --> 00:05:16.050 NH3 is a weak base and so we probably 00:05:16.050 --> 00:05:18.890 had NH3 as our base that was being added 00:05:18.890 --> 00:05:22.180 and it formed the conjugate acid in this. 00:05:22.180 --> 00:05:27.340 So then this would produce an acidic solution, 00:05:27.340 --> 00:05:29.900 because we have this conjugate acid that's formed. 00:05:29.900 --> 00:05:33.000 So from this part, just from the NH 4 plus, 00:05:33.000 --> 00:05:39.230 it should be acidic and now we can consider Cl-. 00:05:39.230 --> 00:05:43.070 So here we're asking the question is Cl-, 00:05:43.070 --> 00:05:46.570 a conjugate base of a weak acid and therefore, 00:05:46.570 --> 00:05:48.900 itself a weak base. 00:05:48.900 --> 00:05:52.110 And if you tried to look up the Kb of Cl-, 00:05:52.110 --> 00:05:54.490 you would not find it in any table. 00:05:54.490 --> 00:05:59.240 But you could find in a table its conjugate acid. 00:05:59.240 --> 00:06:03.660 So if you add H to Cl-, you get HCL, 00:06:03.660 --> 00:06:07.570 and so you could look up a Ka for that in the table and its 00:06:07.570 --> 00:06:09.510 times 10 to the 7. 00:06:09.510 --> 00:06:11.660 So is this a weak acid? 00:06:11.660 --> 00:06:12.350 AUDIENCE: No. 00:06:12.350 --> 00:06:14.450 CATHERINE DRENNAN: It's a strong acid. 00:06:14.450 --> 00:06:17.840 So it's not a weak acid, it's a strong acid. 00:06:17.840 --> 00:06:20.660 So is Cl- going to be basic? 00:06:23.530 --> 00:06:24.570 No. 00:06:24.570 --> 00:06:30.160 So it is not, it is not going to be a basic solution. 00:06:30.160 --> 00:06:34.700 If we look over here, we see HCl is a strong acid 00:06:34.700 --> 00:06:38.270 and so its conjugate base is ineffective in it's base. 00:06:38.270 --> 00:06:41.180 It just doesn't work as a base at all. 00:06:41.180 --> 00:06:42.900 So with a number of 10 to the seventh, 00:06:42.900 --> 00:06:44.240 it really goes to completion. 00:06:44.240 --> 00:06:46.800 It's a strong acid by our definition. 00:06:46.800 --> 00:06:50.740 And so Cl- is not going to do anything to the solution. 00:06:50.740 --> 00:06:54.210 It's not going to be useful as a weak base. 00:06:54.210 --> 00:06:56.610 So this solution is going to be neutral, 00:06:56.610 --> 00:06:59.740 or at least the part of the solution due to Cl- 00:06:59.740 --> 00:07:01.130 will be neutral. 00:07:01.130 --> 00:07:04.310 So here we have something that is acidic and something that's 00:07:04.310 --> 00:07:05.400 neutral. 00:07:05.400 --> 00:07:08.745 And so overall, the solution is acidic. 00:07:11.260 --> 00:07:13.560 So you need to break down the two parts. 00:07:13.560 --> 00:07:16.080 You had an acid and a base being mixed. 00:07:16.080 --> 00:07:25.810 Here we had HCl mixed with NH3 and formed this NH4 salt. 00:07:25.810 --> 00:07:30.160 And that's going to be acidic, because HCL was a weak acid 00:07:30.160 --> 00:07:32.120 and its conjugate is ineffective. 00:07:32.120 --> 00:07:34.220 Whereas, NH3 was a weak base. 00:07:34.220 --> 00:07:35.860 So it has a conjugate acid that's 00:07:35.860 --> 00:07:39.990 a weak acid, a very weak acid, but still a weak acid. 00:07:39.990 --> 00:07:40.810 All right. 00:07:40.810 --> 00:07:43.120 So that's how you think about these salt problems. 00:07:43.120 --> 00:07:45.860 So they really break down to weak acid and weak base 00:07:45.860 --> 00:07:46.810 problems. 00:07:46.810 --> 00:07:48.650 So why don't you give this one a try? 00:07:48.650 --> 00:07:52.578 [AUDIENCE MUMBLING] 00:07:58.930 --> 00:08:01.180 CATHERINE DRENNAN: All right, let's do 10 more seconds 00:08:01.180 --> 00:08:04.680 [AUDIENCE MUMBLING] 00:08:17.222 --> 00:08:18.680 CATHERINE DRENNAN: That is correct. 00:08:18.680 --> 00:08:20.690 All right, let's look at why that's correct. 00:08:23.340 --> 00:08:27.170 So it will produce a basic solution. 00:08:27.170 --> 00:08:31.210 So we're going to break it down to NA . 00:08:31.210 --> 00:08:33.110 That's one of the things in there. 00:08:33.110 --> 00:08:37.250 And we ask is NA a conjugate acid of a weak base? 00:08:37.250 --> 00:08:40.250 Is it going to be neutral, acidic or basic? 00:08:40.250 --> 00:08:44.070 And what's it going to be? 00:08:44.070 --> 00:08:45.380 It's going to be neutral. 00:08:45.380 --> 00:08:47.760 It is not a conjugate acid of a weak base. 00:08:47.760 --> 00:08:49.170 It's group 1. 00:08:49.170 --> 00:08:49.930 It'll be neutral. 00:08:52.860 --> 00:08:56.590 So this is not contributing to the pH. 00:08:56.590 --> 00:09:00.320 So let's look at the second part and look at CH3COO-. 00:09:02.990 --> 00:09:08.970 So we have-- this can be divided into Na+ and HC3OO-. 00:09:08.970 --> 00:09:13.080 And then we ask is this a conjugate base of a weak acid? 00:09:13.080 --> 00:09:15.370 Or we could ask the other question 00:09:15.370 --> 00:09:18.420 is this over here a weak acid? 00:09:18.420 --> 00:09:20.700 And the Ka for that was given. 00:09:20.700 --> 00:09:24.165 So is that a weak acid or a strong acid? 00:09:24.165 --> 00:09:28.710 Is it weak or strong? 00:09:28.710 --> 00:09:29.890 Weak, yes. 00:09:29.890 --> 00:09:30.970 So the answer is yes. 00:09:30.970 --> 00:09:37.130 It's weak and so it's conjugate base would also be a weak base. 00:09:37.130 --> 00:09:40.830 And so therefore, this will be acidic. 00:09:40.830 --> 00:09:44.650 So sometimes you'll be given Ka, sometimes you'll be given Kb's. 00:09:44.650 --> 00:09:46.220 If you're given either one of them 00:09:46.220 --> 00:09:47.750 you can answer the question. 00:09:47.750 --> 00:09:50.930 If you want, you can convert your Ka to your Kb. 00:09:50.930 --> 00:09:54.890 What would you use to convert Ka to Kb? 00:09:54.890 --> 00:09:56.450 Kw, right. 00:09:56.450 --> 00:09:58.950 But just with one of these pieces of information, 00:09:58.950 --> 00:10:02.200 you should be able to answer this question. 00:10:02.200 --> 00:10:05.380 So let's just look at the general rule now. 00:10:05.380 --> 00:10:08.570 You have a compound XY. 00:10:08.570 --> 00:10:12.480 That can be broken up into X and you'll 00:10:12.480 --> 00:10:17.110 ask yourself is X a conjugate acid of a weak base? 00:10:17.110 --> 00:10:19.490 If yes, then the solution will be acidic. 00:10:19.490 --> 00:10:22.270 If no, it will be neutral. 00:10:22.270 --> 00:10:24.790 For Y, you have Y-. 00:10:24.790 --> 00:10:27.750 Is Y- a conjugate base of a weak acid? 00:10:27.750 --> 00:10:32.260 If yes, then it's going to be add some basic nature to this. 00:10:32.260 --> 00:10:34.240 If no, neutral. 00:10:34.240 --> 00:10:36.610 And then over all, you say, if it's 00:10:36.610 --> 00:10:40.300 acidic plus neutral, that's acidic, basic plus 00:10:40.300 --> 00:10:43.520 neutral, basic, neutral plus neutral, neutral. 00:10:43.520 --> 00:10:45.840 And if I give you a question of something 00:10:45.840 --> 00:10:49.300 that is acidic and basic, you can answer the question 00:10:49.300 --> 00:10:50.940 without doing math, because it'll 00:10:50.940 --> 00:10:55.730 depend on the Ka of one thing and the Kb of the other thing. 00:10:55.730 --> 00:10:58.760 And you'll have to see which one's a stronger acid 00:10:58.760 --> 00:11:01.420 and which one's a stronger base. 00:11:01.420 --> 00:11:04.290 And so you can't just simply answer the question. 00:11:04.290 --> 00:11:06.950 Now you may note, that I did mention 00:11:06.950 --> 00:11:08.520 that problem set 7 is long. 00:11:08.520 --> 00:11:11.110 It takes a long time to do these problems. 00:11:11.110 --> 00:11:13.930 And so on the exam, writing a fair exam when the problems 00:11:13.930 --> 00:11:15.570 take a long time to do is hard. 00:11:15.570 --> 00:11:17.190 But these are short little things. 00:11:17.190 --> 00:11:20.690 I could ask you to predict the pH of salt by just thinking 00:11:20.690 --> 00:11:24.290 about things and looking up some Kb's and some Ka's. 00:11:24.290 --> 00:11:26.870 So these are good short questions on the exam. 00:11:26.870 --> 00:11:28.950 So I'm probably not going to give you one 00:11:28.950 --> 00:11:31.060 if it's supposed to be a short question that 00:11:31.060 --> 00:11:34.280 is an acid and a base mixed together, because then you'd 00:11:34.280 --> 00:11:35.430 have to do some math. 00:11:35.430 --> 00:11:37.930 So keep that in mind. 00:11:37.930 --> 00:11:41.070 All right, so salts, salt and water problems, 00:11:41.070 --> 00:11:43.770 are really just weak acid in water or weak base 00:11:43.770 --> 00:11:47.410 in water problems, which you already know how to do. 00:11:47.410 --> 00:11:49.575 So we're going to move on now to buffers. 00:11:52.590 --> 00:11:55.210 Buffers. 00:11:55.210 --> 00:12:00.960 So a buffer is a solution that maintains approximately 00:12:00.960 --> 00:12:06.000 a constant pH, there'll be a little range of pH can change, 00:12:06.000 --> 00:12:09.440 but the buffer tries to keep the pH constant. 00:12:09.440 --> 00:12:13.570 You use a buffer to keep pH constant. 00:12:13.570 --> 00:12:14.810 Why is this important? 00:12:14.810 --> 00:12:18.820 Well, buffers are very important in biology. 00:12:18.820 --> 00:12:21.390 We all work at a constant pH. 00:12:21.390 --> 00:12:24.560 Living things need to be at a constant pH, 00:12:24.560 --> 00:12:26.800 but a lot of times chemical processes 00:12:26.800 --> 00:12:29.560 also need to be at a constant pH. 00:12:29.560 --> 00:12:34.800 And here's just one example of why buffers are important. 00:12:34.800 --> 00:12:36.850 We're looking for alternative energy. 00:12:36.850 --> 00:12:39.160 We're trying to develop alternative energy. 00:12:39.160 --> 00:12:41.770 There's this idea of creating fuel cells that 00:12:41.770 --> 00:12:43.070 employ microbes. 00:12:43.070 --> 00:12:46.350 These little red circles are microbes here. 00:12:46.350 --> 00:12:49.350 There are microbes like shewanella 00:12:49.350 --> 00:12:53.390 that will live, adhere, to electrodes. 00:12:53.390 --> 00:12:57.460 Will live on surfaces of electrodes, metal electrodes. 00:12:57.460 --> 00:13:00.640 And they will eat things like sugar and organics. 00:13:00.640 --> 00:13:03.640 And they will respirate electrons 00:13:03.640 --> 00:13:05.640 into the metal electrodes. 00:13:05.640 --> 00:13:09.530 So the electrons go in and you create an electric current 00:13:09.530 --> 00:13:12.120 and you can do-- have a fuel cell. 00:13:12.120 --> 00:13:14.870 So it's a way of generating an electric current. 00:13:14.870 --> 00:13:17.980 And then people have other ideas that some like some microbes 00:13:17.980 --> 00:13:20.690 live in electrodes, other microbes like moorella 00:13:20.690 --> 00:13:24.480 thermoaceticum, they live on carbon dioxide. 00:13:24.480 --> 00:13:27.530 They convert carbon dioxide to things like acetyl CoA, which 00:13:27.530 --> 00:13:28.490 is a fuel. 00:13:28.490 --> 00:13:31.910 So you throw those in there and then you like pump in CO2 00:13:31.910 --> 00:13:33.890 and you make electric current. 00:13:33.890 --> 00:13:36.980 So there's a lot of great ideas of using microbes. 00:13:36.980 --> 00:13:39.560 So some of my research relates to understanding 00:13:39.560 --> 00:13:41.252 the fundamentals of these pathways. 00:13:41.252 --> 00:13:42.710 And every once in a while I venture 00:13:42.710 --> 00:13:45.920 to hear one of these big energy talks 00:13:45.920 --> 00:13:49.580 about how is the development coming of these ideas. 00:13:49.580 --> 00:13:53.480 And so I heard one talk and I was listening I wanted to know 00:13:53.480 --> 00:13:54.727 is this really working? 00:13:54.727 --> 00:13:56.060 Are people getting this to work? 00:13:56.060 --> 00:13:57.300 What's the status? 00:13:57.300 --> 00:13:59.760 And they talked about a lot of technical difficulties 00:13:59.760 --> 00:14:01.870 of getting it to work, but they had 00:14:01.870 --> 00:14:04.520 discovered something amazing. 00:14:04.520 --> 00:14:08.970 Something that might really change the ability to do this. 00:14:08.970 --> 00:14:11.340 And it turned out that when you're 00:14:11.340 --> 00:14:13.280 generating all this negative charge 00:14:13.280 --> 00:14:16.490 you need to have positive charge around, like H plus, 00:14:16.490 --> 00:14:17.670 for example. 00:14:17.670 --> 00:14:20.150 And so you need to have protons, but it 00:14:20.150 --> 00:14:23.020 mattered, the concentration of those protons. 00:14:23.020 --> 00:14:26.060 And they kind of had to be kept constant 00:14:26.060 --> 00:14:29.230 and they discovered buffers. 00:14:32.170 --> 00:14:33.510 Fifty minutes of my life. 00:14:33.510 --> 00:14:35.330 This was a talk at MIT. 00:14:35.330 --> 00:14:40.320 The person discovered buffers. 00:14:40.320 --> 00:14:43.200 I just felt like writing a letter to Washington saying, 00:14:43.200 --> 00:14:45.690 can I have their research dollars because I already 00:14:45.690 --> 00:14:47.440 know about buffers. 00:14:47.440 --> 00:14:49.280 I don't need to do a big research 00:14:49.280 --> 00:14:53.760 project to discover that buffers keep things at constant pH. 00:14:53.760 --> 00:14:56.130 And that when you're using living organisms 00:14:56.130 --> 00:15:00.000 and doing experiments and doing reactions, pH matters. 00:15:00.000 --> 00:15:01.150 I already knew that. 00:15:01.150 --> 00:15:04.480 Everyone who takes 5.111 already knows that. 00:15:04.480 --> 00:15:07.070 And so this is part of the reason I'm teaching you this. 00:15:07.070 --> 00:15:10.884 Because some of you will not go on and study chemistry. 00:15:10.884 --> 00:15:12.050 You'll be doing engineering. 00:15:12.050 --> 00:15:13.300 You'll be doing alternative energy. 00:15:13.300 --> 00:15:14.674 Doing all sorts of things and you 00:15:14.674 --> 00:15:17.380 can be the person in the room that raises your hand to go, 00:15:17.380 --> 00:15:19.480 it's called a buffer. 00:15:19.480 --> 00:15:24.310 And that is going to change the speed of that research. 00:15:24.310 --> 00:15:25.920 They're just like right away they're 00:15:25.920 --> 00:15:27.540 going to be using buffers. 00:15:27.540 --> 00:15:29.350 And when you do Problem Set 7, you're 00:15:29.350 --> 00:15:30.860 going to know how to make a buffer. 00:15:30.860 --> 00:15:32.980 So you cannot only raise your hand and say, 00:15:32.980 --> 00:15:36.270 it's called the buffer, you can tell people how to make 00:15:36.270 --> 00:15:39.160 a buffer to use in their experiments. 00:15:39.160 --> 00:15:42.500 So this is why the material in teaching was really important. 00:15:42.500 --> 00:15:44.410 I go out there and I hear these talks 00:15:44.410 --> 00:15:47.120 of people who are trying to do these innovative things, 00:15:47.120 --> 00:15:49.260 but they're lacking the fundamental chemistry 00:15:49.260 --> 00:15:51.780 knowledge that's hindering their ability to do it. 00:15:51.780 --> 00:15:54.040 So I want all of you to have this knowledge 00:15:54.040 --> 00:15:55.640 whether you study chemistry anymore 00:15:55.640 --> 00:15:58.270 or not, so that you can be the person who 00:15:58.270 --> 00:16:00.770 brings the case of chemical principles 00:16:00.770 --> 00:16:02.710 into the design process. 00:16:02.710 --> 00:16:04.842 And I care a lot about alternative energy. 00:16:04.842 --> 00:16:06.800 It's going to be super important in the future. 00:16:06.800 --> 00:16:09.580 I care that we don't destroy our planet going 00:16:09.580 --> 00:16:11.350 after some forms of energy. 00:16:11.350 --> 00:16:14.390 And this idea of using microbes is a great one, 00:16:14.390 --> 00:16:16.230 but we just need people who know how 00:16:16.230 --> 00:16:19.140 to work with them to get it to go right. 00:16:19.140 --> 00:16:21.380 All right, so buffers. 00:16:21.380 --> 00:16:22.850 What are buffers? 00:16:22.850 --> 00:16:26.620 You've got to know about buffers. 00:16:26.620 --> 00:16:28.940 A buffer consists, an acid buffer, 00:16:28.940 --> 00:16:32.030 consists of a weak acid in its conjugate base. 00:16:32.030 --> 00:16:34.420 They're often supplied as a salt, 00:16:34.420 --> 00:16:37.450 which means you have a counter ion that comes with it, 00:16:37.450 --> 00:16:40.620 like sodium plus or Cl-. 00:16:40.620 --> 00:16:44.400 And it buffers on the acidic side of neutral. 00:16:44.400 --> 00:16:48.050 A base buffer or a basic buffer has a weak base 00:16:48.050 --> 00:16:51.880 in its conjugate acid, often supplied as a salt, 00:16:51.880 --> 00:16:55.340 and it buffers on the basic side of neutral. 00:16:55.340 --> 00:17:01.030 So the key to a buffer is that it has a conjugate acid. 00:17:01.030 --> 00:17:02.770 It has NHA. 00:17:02.770 --> 00:17:05.410 But it also has the conjugate base. 00:17:05.410 --> 00:17:07.400 It has A-. 00:17:07.400 --> 00:17:11.770 If it just has HA, it's a weak acid. 00:17:11.770 --> 00:17:13.530 That's not a buffer, that's a weak acid. 00:17:13.530 --> 00:17:18.930 If you just have A-, you just have your base. 00:17:18.930 --> 00:17:20.410 That's not a buffer. 00:17:20.410 --> 00:17:27.869 You need to be both an acid and a base, a base and an acid, 00:17:27.869 --> 00:17:31.990 an acid and a base. 00:17:31.990 --> 00:17:34.380 On the exam people do buffer problems 00:17:34.380 --> 00:17:36.730 and they just have one, they don't have the other. 00:17:36.730 --> 00:17:38.290 That's not a buffer. 00:17:38.290 --> 00:17:40.120 And I'm going to write on your little exam, 00:17:40.120 --> 00:17:42.410 remember me twirling around the room. 00:17:42.410 --> 00:17:44.300 It was an acid and a base. 00:17:44.300 --> 00:17:45.930 I don't think you can ever forget this. 00:17:45.930 --> 00:17:49.050 This will be in your brain forever. 00:17:49.050 --> 00:17:51.660 Buffer has an acid and a conjugate base, 00:17:51.660 --> 00:17:54.480 a conjugate base and a conjugate acid. 00:17:54.480 --> 00:17:55.985 OK, let's look at some examples. 00:17:59.010 --> 00:18:04.230 So if you mix acetic acid and acetate salt, 00:18:04.230 --> 00:18:08.470 it's conjugate base supplied in the form of a salt. 00:18:08.470 --> 00:18:10.690 So here we have the acetic acid. 00:18:10.690 --> 00:18:13.980 Here we have the acetate, the conjugate base 00:18:13.980 --> 00:18:15.230 often will be supplied. 00:18:15.230 --> 00:18:18.550 There are probably going to be some NA around. 00:18:18.550 --> 00:18:20.660 And you get this dynamic equilibrium. 00:18:20.660 --> 00:18:25.350 It goes forward, it goes back, it goes forward, it goes back. 00:18:25.350 --> 00:18:28.340 So when you have this, if you added 00:18:28.340 --> 00:18:34.420 a strong acid to this solution, you put in more acid into this. 00:18:34.420 --> 00:18:38.620 And you had equal amounts of this and this, 00:18:38.620 --> 00:18:40.390 then you're conjugate base is going 00:18:40.390 --> 00:18:43.680 to react with the strong acid. 00:18:43.680 --> 00:18:48.680 And you're going to go in the back direction. 00:18:48.680 --> 00:18:52.640 And you're going to neutralize that acid that was added 00:18:52.640 --> 00:18:54.930 and the pH should stay more or less the same 00:18:54.930 --> 00:18:58.840 if you did a good job making your buffer. 00:18:58.840 --> 00:19:04.000 So the buffer can respond to the changes in pH 00:19:04.000 --> 00:19:06.450 by shifts in different directions 00:19:06.450 --> 00:19:10.930 to use up the extra added acid or the other way, 00:19:10.930 --> 00:19:12.740 the extra added base. 00:19:12.740 --> 00:19:17.870 So in this case, the acid that's added is effectively removed 00:19:17.870 --> 00:19:21.570 and the pH stays the same. 00:19:21.570 --> 00:19:26.830 So a buffer can respond to add acid. 00:19:26.830 --> 00:19:30.160 A buffer can also respond to added base. 00:19:30.160 --> 00:19:33.200 If you add a base, a strong base or any kind 00:19:33.200 --> 00:19:37.250 of base, and in this case hydroxide ion, 00:19:37.250 --> 00:19:40.640 would then remove a proton from the weak acid 00:19:40.640 --> 00:19:44.300 from the acetic acid forming water and some more 00:19:44.300 --> 00:19:46.890 of the conjugate base. 00:19:46.890 --> 00:19:50.510 And it's effectively removed as well 00:19:50.510 --> 00:19:54.360 and those OH ions are effectively removed. 00:19:54.360 --> 00:19:56.930 And again, if you did a good job designing this buffer, 00:19:56.930 --> 00:19:59.490 the pH should stay constant. 00:19:59.490 --> 00:20:01.830 So that's why you need the conjugate acid 00:20:01.830 --> 00:20:03.370 and the conjugate base. 00:20:03.370 --> 00:20:06.980 You need the acid to react with the base that's added 00:20:06.980 --> 00:20:08.560 and keep the pH constant. 00:20:08.560 --> 00:20:11.660 You need the base to react with the acid that's added 00:20:11.660 --> 00:20:13.490 and keep the pH constant. 00:20:13.490 --> 00:20:18.000 If you just have one, it's not going to be a buffer. 00:20:18.000 --> 00:20:19.020 So buffer action. 00:20:19.020 --> 00:20:24.350 Again, weak acid transfers, its protons, it's H plus, to OH 00:20:24.350 --> 00:20:26.440 supplied by the base. 00:20:26.440 --> 00:20:30.910 So here we have added base and it's 00:20:30.910 --> 00:20:36.510 going to be reacted with the acid to be neutralized. 00:20:36.510 --> 00:20:40.621 The conjugate base, A-, can accept protons from a supplied 00:20:40.621 --> 00:20:41.120 acid. 00:20:41.120 --> 00:20:43.730 If you add an acid, it will take those 00:20:43.730 --> 00:20:46.390 and will neutralize the acid that's added. 00:20:49.000 --> 00:20:53.880 So let's think about what type of acids and conjugate bases 00:20:53.880 --> 00:20:56.470 are going to work to make a good buffer. 00:20:56.470 --> 00:20:59.060 A strong acid in its conjugate base 00:20:59.060 --> 00:21:01.060 does not make a good buffer. 00:21:01.060 --> 00:21:02.270 Why don't you tell me why. 00:21:28.790 --> 00:21:32.000 Yeah, so 67%. 00:21:32.000 --> 00:21:37.970 So it's really about the fact that the conjugate base 00:21:37.970 --> 00:21:40.640 of a strong acid is really not a base at all. 00:21:40.640 --> 00:21:42.510 It's ineffective as a base. 00:21:42.510 --> 00:21:45.060 And that's why it's not going to work. 00:21:45.060 --> 00:21:48.360 Buffer solution has to be in a dynamic equilibrium. 00:21:48.360 --> 00:21:50.950 You have to be able to push it both ways, otherwise, 00:21:50.950 --> 00:21:52.340 it's not going to work. 00:21:52.340 --> 00:21:57.580 So a conjugate base of a strong acid is ineffective as a base. 00:21:57.580 --> 00:22:00.710 And so if you added acid, it won't be neutralized 00:22:00.710 --> 00:22:02.250 and the pH will change. 00:22:02.250 --> 00:22:06.370 So you need to have something that works as a conjugate base. 00:22:06.370 --> 00:22:08.650 Something that's able to interact 00:22:08.650 --> 00:22:12.010 with the hydro ion or the acid that's added and take 00:22:12.010 --> 00:22:14.100 its proton to neutralize it. 00:22:14.100 --> 00:22:17.130 If this doesn't happen, the pH will be affected. 00:22:17.130 --> 00:22:20.880 So you need to have weak acids and weak bases in your buffers. 00:22:20.880 --> 00:22:24.410 They could be moderately weak or very weak or whatever, 00:22:24.410 --> 00:22:27.520 but you have to have a conjugate set that's 00:22:27.520 --> 00:22:31.100 going to be able to push both directions where the acid can 00:22:31.100 --> 00:22:34.000 interact with the added base and the base can interact 00:22:34.000 --> 00:22:35.810 with the added acid. 00:22:35.810 --> 00:22:37.780 All right, so all of this is really 00:22:37.780 --> 00:22:41.490 the same for a basic buffer. 00:22:41.490 --> 00:22:45.420 So we can look at an example here of ammonia 00:22:45.420 --> 00:22:49.720 plus water going to ammonium ion and hydroxide ion. 00:22:49.720 --> 00:22:52.180 And we can think about the same things. 00:22:52.180 --> 00:22:57.050 When you add a strong acid, the base will accept the protons 00:22:57.050 --> 00:23:01.640 and make more of your conjugate acid. 00:23:01.640 --> 00:23:04.660 When a strong base is added, the conjugate acid 00:23:04.660 --> 00:23:06.390 will donate its proton. 00:23:06.390 --> 00:23:11.050 And it will form NH3 again, that conjugate base, and water 00:23:11.050 --> 00:23:13.740 and the pH will stay the same. 00:23:13.740 --> 00:23:16.900 So it's the same idea, the only real difference 00:23:16.900 --> 00:23:19.460 between an acidic buffer and a basic buffer 00:23:19.460 --> 00:23:24.120 is whether it pH's in the acidic range or in the basic range. 00:23:24.120 --> 00:23:26.580 But the buffers work the same way. 00:23:26.580 --> 00:23:31.470 So I can redraw this picture to have our different symbols 00:23:31.470 --> 00:23:33.950 on it, but the idea is the same. 00:23:33.950 --> 00:23:37.910 The weak base will take the proton supplied 00:23:37.910 --> 00:23:41.640 by the acid and the conjugate acid 00:23:41.640 --> 00:23:50.410 BH is going to probate the OHH- and again keep the pH constant. 00:23:50.410 --> 00:23:53.530 So the idea again of the buffer then 00:23:53.530 --> 00:23:57.590 is that a buffer is a mixture of weak conjugate acids and bases. 00:23:57.590 --> 00:23:59.780 Again, they're weak because its partner 00:23:59.780 --> 00:24:02.335 needs to be effective as an asset or a base. 00:24:02.335 --> 00:24:04.350 It can't be ineffective. 00:24:04.350 --> 00:24:07.380 Weak acid base mixtures that stabilize pH 00:24:07.380 --> 00:24:12.170 by providing a source or a sink for protons. 00:24:12.170 --> 00:24:15.260 It either adds protons or takes protons away. 00:24:15.260 --> 00:24:17.370 It can respond to add acid. 00:24:17.370 --> 00:24:20.580 It can respond to add base. 00:24:20.580 --> 00:24:26.730 So again, pH is important and buffering is important. 00:24:26.730 --> 00:24:30.150 Our body has its own buffering system. 00:24:30.150 --> 00:24:34.170 So we have carbonic acid and bicarbonate buffering 00:24:34.170 --> 00:24:35.990 agents in our blood. 00:24:35.990 --> 00:24:39.300 And our blood has to be kept in a sort of neutral range 00:24:39.300 --> 00:24:40.340 over here. 00:24:40.340 --> 00:24:44.710 If it gets too acidic, that is very unhealthy for us, 00:24:44.710 --> 00:24:47.250 leading to some pretty severe symptoms 00:24:47.250 --> 00:24:49.450 and too much leads to death. 00:24:49.450 --> 00:24:51.980 If it's too basic, that's really bad. 00:24:51.980 --> 00:24:54.170 Also, we have death and notice these are not 00:24:54.170 --> 00:24:56.210 all that far away. 00:24:56.210 --> 00:24:58.750 There are a number of different medical conditions 00:24:58.750 --> 00:25:01.640 that can affect the pH, diabetes, 00:25:01.640 --> 00:25:03.540 there are metabolic diseases. 00:25:03.540 --> 00:25:08.890 Something else that is under your control, hydration, 00:25:08.890 --> 00:25:11.600 you need to drink enough water. 00:25:11.600 --> 00:25:15.580 And as the weather gets colder in Boston, 00:25:15.580 --> 00:25:18.195 people so often stop drinking as much water 00:25:18.195 --> 00:25:20.210 or start drinking like hot beverages, 00:25:20.210 --> 00:25:21.930 which don't hydrate as well. 00:25:21.930 --> 00:25:23.440 So keep hydrated. 00:25:23.440 --> 00:25:27.000 If you're not hydrated, if it's gets really bad, 00:25:27.000 --> 00:25:30.090 it can start affecting the pH of your blood, which is really not 00:25:30.090 --> 00:25:30.880 good. 00:25:30.880 --> 00:25:34.660 So buffering, very important. 00:25:34.660 --> 00:25:38.930 All right, so let's do a sample buffer problem. 00:25:38.930 --> 00:25:41.500 So sample buffer problem-- and this is important. 00:25:41.500 --> 00:25:43.960 I actually know of at least one professor 00:25:43.960 --> 00:25:45.900 that if you want to do a UROP with them 00:25:45.900 --> 00:25:47.510 or come to their office and they're 00:25:47.510 --> 00:25:52.870 going to say, write down how you would design a buffer for me 00:25:52.870 --> 00:25:55.190 and do those calculations. 00:25:55.190 --> 00:25:58.220 So I can tell you later who that is, maybe I won't, I 00:25:58.220 --> 00:25:59.150 don't know. 00:25:59.150 --> 00:26:01.280 But this is one of the tasks that someone 00:26:01.280 --> 00:26:04.550 uses to see if they want you as a UROP. 00:26:04.550 --> 00:26:09.480 OK, so here we have one mol of formic acid 00:26:09.480 --> 00:26:13.430 and 0.5 mols of the conjugate base supplied 00:26:13.430 --> 00:26:16.570 in the form of a salt with sodium ions. 00:26:16.570 --> 00:26:18.820 And those are added to water and diluted 00:26:18.820 --> 00:26:22.760 to a total final concentration of one liter. 00:26:22.760 --> 00:26:27.920 And you're given the Ka and told to calculate the pH. 00:26:27.920 --> 00:26:32.660 So the first step is to write out the equation. 00:26:32.660 --> 00:26:36.370 So we have an acid and water going 00:26:36.370 --> 00:26:41.540 to hydronium ions and a conjugate base over here. 00:26:41.540 --> 00:26:44.580 And we want to think about what's there now 00:26:44.580 --> 00:26:48.290 and what's at equilibrium. 00:26:48.290 --> 00:26:52.880 So initial molarity, change in molarity and your equilibrium 00:26:52.880 --> 00:26:54.070 molarity. 00:26:54.070 --> 00:26:57.770 So it's important this word molarity. 00:26:57.770 --> 00:27:02.030 Don't put mols in here, put molarity in here. 00:27:02.030 --> 00:27:03.880 But I made it really easy for you, 00:27:03.880 --> 00:27:08.360 because we have one mol and one liter so the molarity is 1. 00:27:08.360 --> 00:27:12.260 0.5 mols and one liter, the molarity is 0.5. 00:27:12.260 --> 00:27:14.120 And this is also really important. 00:27:14.120 --> 00:27:17.080 You're so used to only putting things here. 00:27:17.080 --> 00:27:18.990 When it's a buffer problem, you've 00:27:18.990 --> 00:27:21.310 got to put something here, too. 00:27:21.310 --> 00:27:25.730 So you're adding the acid with the conjugate base 00:27:25.730 --> 00:27:27.210 at the same time. 00:27:27.210 --> 00:27:28.750 This is not zero. 00:27:28.750 --> 00:27:30.940 This is 0.5. 00:27:30.940 --> 00:27:34.800 So now as this dynamic equilibrium goes 00:27:34.800 --> 00:27:39.410 you're losing some of this and gaining some of these. 00:27:39.410 --> 00:27:44.020 So at equilibrium we have one molar minus x. 00:27:44.020 --> 00:27:46.680 X is our hydronium ion concentration, 00:27:46.680 --> 00:27:49.740 which is what we want to know to calculate pH. 00:27:49.740 --> 00:27:57.250 And our conjugate base our formic ion is 0.5 plus x. 00:27:57.250 --> 00:28:01.990 We're given a Ka and we've written this expression as acid 00:28:01.990 --> 00:28:04.410 in water so we can use Ka. 00:28:04.410 --> 00:28:08.800 The equilibrium constant is for the expression as written 00:28:08.800 --> 00:28:16.310 so we can put that in and we can fill the rest out. 00:28:16.310 --> 00:28:17.420 We have our products. 00:28:17.420 --> 00:28:20.120 We have the concentration of hydronium ion 00:28:20.120 --> 00:28:24.410 times the concentration of formic ion, the conjugate base, 00:28:24.410 --> 00:28:27.910 over the concentration of our formic acid, 00:28:27.910 --> 00:28:30.430 and again water does not appear in the expression 00:28:30.430 --> 00:28:32.420 because it's the solvent. 00:28:32.420 --> 00:28:35.740 Hydronium ion concentration is x. 00:28:35.740 --> 00:28:37.840 The conjugate base concentration is 00:28:37.840 --> 00:28:42.640 0.5 plus x and the conjugate acid concentration 00:28:42.640 --> 00:28:46.480 is 1 minus x. 00:28:46.480 --> 00:28:51.820 So we can now try that assumption that x is small 00:28:51.820 --> 00:28:54.850 or we can use the quadratic equation, 00:28:54.850 --> 00:28:58.032 but why don't you just try that assumption. 00:28:58.032 --> 00:28:59.490 I'm going to take this expression-- 00:28:59.490 --> 00:29:02.820 if you haven't written it all down yet, put it right up here. 00:29:02.820 --> 00:29:04.450 And now with the clicker why don't you 00:29:04.450 --> 00:29:08.030 tell me, if we use the approximation 00:29:08.030 --> 00:29:11.400 that x is small compared to 1 and 0.5, what 00:29:11.400 --> 00:29:12.980 does this simplify to? 00:29:26.270 --> 00:29:27.420 All right, 10 more seconds. 00:29:43.470 --> 00:29:46.720 So 70 something percent. 00:29:46.720 --> 00:29:51.020 Yep, so let's take a look at that. 00:29:51.020 --> 00:29:52.660 So here we're making the assumption 00:29:52.660 --> 00:29:56.560 that x is small compared to 0.5, compared to 1. 00:29:56.560 --> 00:30:01.370 So that means that we drop the plus x from the 0.5 term 00:30:01.370 --> 00:30:04.620 and drop the minus x from the one term. 00:30:04.620 --> 00:30:07.230 So we're saying that these are going 00:30:07.230 --> 00:30:09.190 to be small enough that it's still going 00:30:09.190 --> 00:30:11.670 to be pretty much 0.5 and 1. 00:30:11.670 --> 00:30:14.640 And then we have to test that in a minute. 00:30:14.640 --> 00:30:17.800 So if we use this, we can calculate x 00:30:17.800 --> 00:30:22.280 and it comes out to 3.54 times 10 to the minus 4, 00:30:22.280 --> 00:30:24.660 and then we can check the assumption. 00:30:24.660 --> 00:30:28.300 And before you told me how to check assumptions. 00:30:28.300 --> 00:30:31.140 And that was I take x and I'll divide it 00:30:31.140 --> 00:30:37.150 by 0.5, which is the smaller of these two, and times by 100% 00:30:37.150 --> 00:30:41.790 and we get 0.69%, which is less than 5% 00:30:41.790 --> 00:30:44.590 so the assumption is OK. 00:30:44.590 --> 00:30:47.020 And we don't have to check it against 1, 00:30:47.020 --> 00:30:50.060 because if the assumption x is small compared to the smaller 00:30:50.060 --> 00:30:53.380 number is valid, it will also be valid for the bigger number. 00:30:53.380 --> 00:30:56.280 So you only check it for the smaller number 00:30:56.280 --> 00:30:59.750 and then we can solve. 00:30:59.750 --> 00:31:02.260 So we have to think about-- we solved for x. 00:31:02.260 --> 00:31:03.160 We're happy with x. 00:31:03.160 --> 00:31:04.470 Our assumption was OK. 00:31:04.470 --> 00:31:05.845 But then we have to remember what 00:31:05.845 --> 00:31:11.030 x is and x is the hydronium ion concentration 00:31:11.030 --> 00:31:13.640 and you always want to make sure to think about this, 00:31:13.640 --> 00:31:16.980 because if it's hydroxide ion that's different. 00:31:16.980 --> 00:31:18.620 So we can calculate pH. 00:31:18.620 --> 00:31:24.110 pH is minus log of 3.54 times 10 to the minus 4, 00:31:24.110 --> 00:31:29.120 which is equal to pH of 3.45. 00:31:29.120 --> 00:31:31.710 And here we have two significant figures 00:31:31.710 --> 00:31:34.010 after the decimal point, because the volume 00:31:34.010 --> 00:31:36.320 we had before only had two significant figures. 00:31:36.320 --> 00:31:39.420 Everything else had three, but the volume was just 1.0. 00:31:39.420 --> 00:31:42.340 So that is our answer there. 00:31:42.340 --> 00:31:48.380 All right, so I'm going to just briefly start 00:31:48.380 --> 00:31:52.120 what happens when you-- actually we'll do-- this 00:31:52.120 --> 00:31:54.450 is how you would design the buffer for this. 00:31:54.450 --> 00:31:56.850 Next time we'll see what happens if we stress 00:31:56.850 --> 00:32:00.760 the buffer we design by adding acid to it 00:32:00.760 --> 00:32:04.390 and see what the new result is. 00:32:04.390 --> 00:32:07.450 All right, so today we're going to finish lecture 22. 00:32:07.450 --> 00:32:10.691 So take out those lecture notes on acids and bases. 00:32:10.691 --> 00:32:12.190 And when we're done with that, we'll 00:32:12.190 --> 00:32:14.240 just continue with acids and bases. 00:32:14.240 --> 00:32:16.360 And we're going to continue with some acids 00:32:16.360 --> 00:32:18.190 and bases on Wednesday. 00:32:18.190 --> 00:32:20.610 We should finish on Wednesday and move on 00:32:20.610 --> 00:32:26.710 to oxidation reduction and that will end exam three material. 00:32:26.710 --> 00:32:30.080 So exam three is sneaking up on us 00:32:30.080 --> 00:32:32.780 and it'll have thermodynamics, chemical equilibrium, 00:32:32.780 --> 00:32:34.518 solubility, and acid base. 00:32:37.680 --> 00:32:40.230 So you should have already filled 00:32:40.230 --> 00:32:42.950 in your handout with all the information. 00:32:42.950 --> 00:32:47.590 The parts that you were filling in are in bold here, 00:32:47.590 --> 00:32:51.080 but I just want to remind you of what we were talking about. 00:32:51.080 --> 00:32:53.580 So we had a sample buffer problem. 00:32:53.580 --> 00:32:56.720 We had one mol of the conjugate acid and a half 00:32:56.720 --> 00:33:01.220 a mol of its conjugate base supplied in the form of a salt, 00:33:01.220 --> 00:33:05.240 were put in water and diluted into one liter. 00:33:05.240 --> 00:33:10.510 So we calculated what the hydronium ion concentration 00:33:10.510 --> 00:33:14.230 would be and therefore, the pH, using information 00:33:14.230 --> 00:33:17.230 that was given to us about the Ka, 00:33:17.230 --> 00:33:20.140 the acid ionization constant. 00:33:20.140 --> 00:33:24.470 So we got a pH of 3.45. 00:33:24.470 --> 00:33:27.820 Someone asked me after class, but isn't this conjugate base 00:33:27.820 --> 00:33:33.080 also reacting with water and forming some of this weak acid. 00:33:33.080 --> 00:33:35.550 And the answer is yes. 00:33:35.550 --> 00:33:38.620 That we are writing this as a problem of acid 00:33:38.620 --> 00:33:41.310 in water, because we can use the Ka. 00:33:41.310 --> 00:33:44.854 But we could've also written it the other way. 00:33:44.854 --> 00:33:46.770 And written it, and this is not in your notes, 00:33:46.770 --> 00:33:50.530 but I just want to let you know, that the weak base and water 00:33:50.530 --> 00:33:53.910 could be written that way forming a conjugate acid 00:33:53.910 --> 00:33:56.180 and hydroxide ions. 00:33:56.180 --> 00:34:01.340 And so then it would be 0.5 minus x and 1 plus x and x. 00:34:01.340 --> 00:34:05.240 Use Kb then, because it's a base in water to solve for x 00:34:05.240 --> 00:34:10.840 and calculate pH from POH and if you try it, you get 3.45. 00:34:10.840 --> 00:34:13.690 So you can do these problems either way. 00:34:13.690 --> 00:34:15.909 You can think about them as a weak base 00:34:15.909 --> 00:34:17.889 problem or a weak acid problem. 00:34:17.889 --> 00:34:21.370 You just have to remember that this is not zero 00:34:21.370 --> 00:34:22.580 when you start. 00:34:22.580 --> 00:34:24.960 The conjugate has some amount. 00:34:24.960 --> 00:34:26.650 That's what makes it a good buffer. 00:34:26.650 --> 00:34:29.360 So this can work either way, but you also 00:34:29.360 --> 00:34:32.239 want to remember if you write it as an acid in water, use Ka. 00:34:32.239 --> 00:34:34.650 If you write it as a base in water, use Kb. 00:34:34.650 --> 00:34:36.330 Because those equilibrium constants 00:34:36.330 --> 00:34:40.100 are telling you about those ratios of the conjugate acid 00:34:40.100 --> 00:34:42.400 and the conjugate base at equilibrium. 00:34:42.400 --> 00:34:46.239 So within the Ka and the Kb is information 00:34:46.239 --> 00:34:50.389 that you need about this dynamic chemical equilibrium. 00:34:50.389 --> 00:34:54.520 So both of these ways work and by the end of, sort of halfway 00:34:54.520 --> 00:34:57.240 through today's lecture, you'll see yet another way 00:34:57.240 --> 00:34:59.130 to solve buffer problems. 00:34:59.130 --> 00:35:01.960 And probably will be for most of you, the preferred way 00:35:01.960 --> 00:35:03.060 to do it. 00:35:03.060 --> 00:35:04.880 So there's a number of different ways 00:35:04.880 --> 00:35:07.500 which makes grading the exam lots of fun. 00:35:07.500 --> 00:35:10.470 And we have option 1, option 2, option 3-- 00:35:10.470 --> 00:35:14.400 to make sure that all the options are possibly 00:35:14.400 --> 00:35:16.100 accounted for. 00:35:16.100 --> 00:35:18.780 All right, so the purpose of a buffer 00:35:18.780 --> 00:35:21.500 is to keep the pH pretty much constant. 00:35:21.500 --> 00:35:24.140 So you can add a strong acid to it 00:35:24.140 --> 00:35:26.640 and the acid will be neutralized, 00:35:26.640 --> 00:35:27.840 keeping the pH constant. 00:35:27.840 --> 00:35:29.720 You can add a strong base to it and the base 00:35:29.720 --> 00:35:32.500 will be neutralized, keeping the pH pretty constant. 00:35:32.500 --> 00:35:36.590 So what you want in a buffer is to have a weak acid conjugate 00:35:36.590 --> 00:35:40.570 base pairing that allows it to be a source 00:35:40.570 --> 00:35:43.790 or sink for a strong acid or a strong base 00:35:43.790 --> 00:35:45.710 to keep the pH constant. 00:35:45.710 --> 00:35:47.370 So now in this problem we're asked 00:35:47.370 --> 00:35:49.940 to calculate what would happen to the pH 00:35:49.940 --> 00:35:53.360 if 0.1 mols of the strong acid had been included 00:35:53.360 --> 00:35:57.380 in our 1 liter solution. 00:35:57.380 --> 00:36:01.350 And because 0.1 mols of our strong acid 00:36:01.350 --> 00:36:04.480 would react with equal number of mols, 00:36:04.480 --> 00:36:06.140 all of that conjugate base, that's 00:36:06.140 --> 00:36:08.310 what the conjugate base does in a buffer, 00:36:08.310 --> 00:36:11.970 it reacts with the strong acid that is supplied. 00:36:11.970 --> 00:36:17.150 And it will form equal mols then of the conjugate, 00:36:17.150 --> 00:36:19.050 its conjugate acid. 00:36:19.050 --> 00:36:22.070 So we have to do some subtraction. 00:36:22.070 --> 00:36:25.930 So for the conjugate acid, we had 0.5 mols. 00:36:29.080 --> 00:36:33.080 For the conjugate base, we had 0.5 mols. 00:36:33.080 --> 00:36:36.430 We used up one of that, 0.1 of that, 00:36:36.430 --> 00:36:40.800 reacting with the strong acid and we have 0.4 left. 00:36:40.800 --> 00:36:46.150 So we have a new concentration for our conjugate base, 0.4 00:36:46.150 --> 00:36:51.300 divided by 1, keep the math simple, 0.4 molar. 00:36:51.300 --> 00:36:55.320 So for our conjugate acid, we had one mol to begin with, 00:36:55.320 --> 00:37:00.260 but we formed 0.1 more when that strong acid was added. 00:37:00.260 --> 00:37:06.400 So now we have 1.1 mols and a new molarity. 00:37:06.400 --> 00:37:11.680 So now we have to go back and we can use this expression again 00:37:11.680 --> 00:37:16.290 and determine what x is now, what the hydronium 00:37:16.290 --> 00:37:18.490 concentration is now using Ka. 00:37:18.490 --> 00:37:22.290 So why don't you tell me how I would solve this. 00:37:22.290 --> 00:37:25.610 What is the correct expression for Ka? 00:37:25.610 --> 00:37:27.800 You can fill in your little table as you do it. 00:37:39.518 --> 00:37:41.226 All right, let's just do 10 more seconds. 00:37:55.570 --> 00:38:00.240 All right, so let's just fill in that table 00:38:00.240 --> 00:38:01.970 if you haven't already. 00:38:01.970 --> 00:38:06.690 So here now, we can write this as an acid and water problem. 00:38:06.690 --> 00:38:09.090 Again, again, you could have done the base in water 00:38:09.090 --> 00:38:13.010 and used Kb, but we'll just do it the same way we did before. 00:38:13.010 --> 00:38:16.630 So we have our acid 1.1 molar. 00:38:16.630 --> 00:38:18.437 Now remember, this is molarity. 00:38:18.437 --> 00:38:20.020 So you don't want to put mols in here, 00:38:20.020 --> 00:38:22.770 you want to put a concentration and some of that 00:38:22.770 --> 00:38:24.220 will be minus x. 00:38:24.220 --> 00:38:27.680 Then we have our 0.4, 0.4 plus x. 00:38:27.680 --> 00:38:29.370 We can fill out the Ka. 00:38:29.370 --> 00:38:32.220 The Ka again, weak acid and water problem. 00:38:32.220 --> 00:38:37.910 We have products-- hydronium ion times our conjugate base over 00:38:37.910 --> 00:38:44.620 our conjugate acid equals 0.400 plus x times x, these 2, 00:38:44.620 --> 00:38:49.490 and 1.1 minus x on the bottom. 00:38:49.490 --> 00:38:53.020 So you can always solve then for x, which will tell you 00:38:53.020 --> 00:38:57.040 about the pH by using the Ka. 00:38:57.040 --> 00:38:59.670 And you just have to remember molarity and remember 00:38:59.670 --> 00:39:04.060 these are the new molarity after the reaction has occurred. 00:39:04.060 --> 00:39:07.660 All right, so we can use the approximation 00:39:07.660 --> 00:39:13.430 that x is small compared to 1.1 and 0.4 to simplify this. 00:39:13.430 --> 00:39:16.310 Or we could use the quadratic equation. 00:39:16.310 --> 00:39:21.060 If we simplify it, we calculate x as 4.87 times 10 00:39:21.060 --> 00:39:22.440 to the minus 4. 00:39:22.440 --> 00:39:25.060 And remember again, that the approximation 00:39:25.060 --> 00:39:30.510 is you get rid of the plus x and the minus x here. 00:39:30.510 --> 00:39:32.909 And then, you have to check it with the 5% rule. 00:39:32.909 --> 00:39:34.700 If you did that, if you used the quadratic, 00:39:34.700 --> 00:39:36.030 then you don't have to check. 00:39:36.030 --> 00:39:38.230 But if you use the 5% rule, then you're 00:39:38.230 --> 00:39:43.690 asking is this number 4.87 times 10 to the minus 4 00:39:43.690 --> 00:39:48.210 within 5% of the smaller value, which is 0.4 and it is here. 00:39:48.210 --> 00:39:49.980 It's 0.12%. 00:39:49.980 --> 00:39:51.430 So the assumption is OK. 00:39:51.430 --> 00:39:52.920 That's less than 5%. 00:39:52.920 --> 00:39:54.790 X is small. 00:39:54.790 --> 00:39:58.540 And then we can solve for the pH. 00:39:58.540 --> 00:40:02.420 So pH is minus log of the hydronium ion concentration, 00:40:02.420 --> 00:40:04.720 which here is 3.31. 00:40:04.720 --> 00:40:07.710 This only has two significant figures after the decimal, 00:40:07.710 --> 00:40:09.780 because if you remember, back on the other page, 00:40:09.780 --> 00:40:11.360 the volume only had two. 00:40:11.360 --> 00:40:13.870 So actually all these numbers here really just 00:40:13.870 --> 00:40:15.970 have two significant figures. 00:40:15.970 --> 00:40:20.300 We carried an extra, but it really just had two. 00:40:20.300 --> 00:40:23.050 All right, so our buffer was pretty good 00:40:23.050 --> 00:40:27.390 so we added 0.1 mols of a very strong acid. 00:40:27.390 --> 00:40:29.260 And we only changed the pH. 00:40:29.260 --> 00:40:34.680 We only lowered it from 3.45 to 3.31. 00:40:34.680 --> 00:40:40.970 So that was a pretty good buffer that we had designed there. 00:40:40.970 --> 00:40:44.831 All right, so that is how you do a buffer problem. 00:40:44.831 --> 00:40:46.830 And there are other kinds of things that you can 00:40:46.830 --> 00:40:49.170 be asked about with buffers. 00:40:49.170 --> 00:40:51.490 In particular, you can also often 00:40:51.490 --> 00:40:54.780 be asked to design a buffer. 00:40:54.780 --> 00:40:56.620 And when you design a buffer, you 00:40:56.620 --> 00:40:59.070 must consider the following things. 00:40:59.070 --> 00:41:03.280 The ratio of your conjugate acid base pair 00:41:03.280 --> 00:41:04.940 and that they should also be weak 00:41:04.940 --> 00:41:10.590 conjugate acid base pairs-- the pKa and the pH. 00:41:10.590 --> 00:41:13.400 OK, so here comes a derivation. 00:41:16.330 --> 00:41:19.090 So here is our expression that should be familiar to you 00:41:19.090 --> 00:41:22.690 at this point, for a weak acid, HA and water, 00:41:22.690 --> 00:41:27.540 going to hydronium ions and our conjugate base, A-. 00:41:27.540 --> 00:41:30.070 It should also be familiar to you 00:41:30.070 --> 00:41:32.710 that you can write the equilibrium 00:41:32.710 --> 00:41:35.190 expression for this acid in water 00:41:35.190 --> 00:41:38.830 as hydronium ions concentration times the concentration, 00:41:38.830 --> 00:41:41.150 the conjugate base, over the concentration 00:41:41.150 --> 00:41:42.440 of the conjugate acid. 00:41:42.440 --> 00:41:44.090 Water, which is our solvent, doesn't 00:41:44.090 --> 00:41:46.380 appear in the expression. 00:41:46.380 --> 00:41:50.320 We can rearrange this expression now and solve for hydronium ion 00:41:50.320 --> 00:41:52.170 concentrations. 00:41:52.170 --> 00:41:56.320 We can take a log of both sides, and get this, 00:41:56.320 --> 00:42:00.140 log of hydronium ion concentration, log of Ka, 00:42:00.140 --> 00:42:07.900 plus log of HA over A-, multiply by negative to get this. 00:42:07.900 --> 00:42:10.530 And so we have minus, minus, minus, 00:42:10.530 --> 00:42:14.020 and minus the log of the hydronium ion concentration 00:42:14.020 --> 00:42:15.450 is what? 00:42:15.450 --> 00:42:22.300 pH minus log of Ka is pKa and this is the same as that. 00:42:22.300 --> 00:42:29.010 So that gives us this expression that pH equals pKa minus 00:42:29.010 --> 00:42:32.300 the log of HA over A-. 00:42:32.300 --> 00:42:35.390 Now it's important to point out that these are equilibrium 00:42:35.390 --> 00:42:39.870 concentrations of HA and A-, because we derived this 00:42:39.870 --> 00:42:44.630 expression from Ka and that's an equilibrium constant. 00:42:44.630 --> 00:42:47.140 So these are equilibrium expressions. 00:42:47.140 --> 00:42:50.430 And that makes this particular expression slightly less 00:42:50.430 --> 00:42:53.040 useful, because we often don't want 00:42:53.040 --> 00:42:55.400 to have to calculate the equilibrium concentration. 00:42:55.400 --> 00:42:58.200 We know how much we added and so we often want 00:42:58.200 --> 00:43:00.520 to use initial concentrations. 00:43:00.520 --> 00:43:04.370 But we can consider whether the initial concentrations 00:43:04.370 --> 00:43:07.530 are actually pretty similar to the equilibrium concentrations 00:43:07.530 --> 00:43:08.170 i.e. 00:43:08.170 --> 00:43:10.920 the x is small, less than 5%. 00:43:10.920 --> 00:43:13.830 So we know that a weak acid typically 00:43:13.830 --> 00:43:17.010 only loses a fraction of its protons, 00:43:17.010 --> 00:43:19.030 hence the definition of weak acid. 00:43:19.030 --> 00:43:21.880 Weak acid in water doesn't ionize that much. 00:43:21.880 --> 00:43:25.380 And a weak base typically only accepts a fraction 00:43:25.380 --> 00:43:27.070 of the protons that it could. 00:43:27.070 --> 00:43:28.930 It's a weak base. 00:43:28.930 --> 00:43:32.700 So the initial concentration is often 00:43:32.700 --> 00:43:36.354 approximately equal to the equilibrium concentration 00:43:36.354 --> 00:43:37.770 and that's what we've been finding 00:43:37.770 --> 00:43:38.811 in a lot of the problems. 00:43:38.811 --> 00:43:41.760 We've found that the 5% rule works pretty well. 00:43:41.760 --> 00:43:43.710 It's usually less than 5%. 00:43:43.710 --> 00:43:48.670 X is usually less than 5% of the initial concentration we had 00:43:48.670 --> 00:43:51.180 of HA or A-. 00:43:51.180 --> 00:43:55.530 And so therefore, we can say that the pH is in fact, 00:43:55.530 --> 00:44:00.760 approximately equal to the pKa minus the log of the initial 00:44:00.760 --> 00:44:04.950 concentration of your HA over your initial concentration 00:44:04.950 --> 00:44:06.330 of A-. 00:44:06.330 --> 00:44:10.080 And this expression is known as the Henderson-Hasselbalch 00:44:10.080 --> 00:44:11.420 Equation. 00:44:11.420 --> 00:44:18.420 And so this equation is only valid when your hydronium ion 00:44:18.420 --> 00:44:23.700 concentration is small compared to HA and A-, i.e., 00:44:23.700 --> 00:44:25.740 less than 5%. 00:44:25.740 --> 00:44:30.250 So this 5% rule must apply to use the Henderson-Hasselbalch 00:44:30.250 --> 00:44:31.450 Equation. 00:44:31.450 --> 00:44:33.590 The Henderson-Hasselbalch Equation 00:44:33.590 --> 00:44:37.240 is a great equation to use for buffer problems. 00:44:37.240 --> 00:44:39.140 And so, we've showed you a couple 00:44:39.140 --> 00:44:41.170 different ways of doing buffer problems. 00:44:41.170 --> 00:44:44.170 This is the final way I'm going to show you using 00:44:44.170 --> 00:44:46.050 the Henderson-Hasselbalch Equation, 00:44:46.050 --> 00:44:49.620 but you can only use it if x is small. 00:44:49.620 --> 00:44:51.860 But most of the time, x is going to be small, 00:44:51.860 --> 00:44:53.970 because buffers are only buffers when 00:44:53.970 --> 00:44:57.600 you have a weak acid with a conjugate weak base. 00:44:57.600 --> 00:45:01.090 And when you're talking about weak acids and bases, 00:45:01.090 --> 00:45:02.310 x is small. 00:45:02.310 --> 00:45:04.690 They don't ionize that much. 00:45:04.690 --> 00:45:07.440 And importantly, and I'll emphasize this, 00:45:07.440 --> 00:45:11.410 this equation only works for buffers. 00:45:11.410 --> 00:45:15.970 Don't apply it for just regular weak acid in water or weak base 00:45:15.970 --> 00:45:19.770 in water, a strong acid in water, a strong base in water-- 00:45:19.770 --> 00:45:22.805 it only applies for buffers. 00:45:25.400 --> 00:45:28.420 Buffers, buffers. 00:45:28.420 --> 00:45:31.700 Now I know that MIT students love equations 00:45:31.700 --> 00:45:33.990 and they love doing math, and so they 00:45:33.990 --> 00:45:36.910 try to apply this equation to every type 00:45:36.910 --> 00:45:39.080 of acid-base problem. 00:45:39.080 --> 00:45:40.830 Don't do it. 00:45:40.830 --> 00:45:42.715 Buffers, buffers. 00:45:45.530 --> 00:45:49.270 You'll remember that now, right? 00:45:49.270 --> 00:45:51.870 Because I'll make noises again if you don't. 00:45:51.870 --> 00:45:53.215 You remember that now, right? 00:45:55.780 --> 00:45:59.890 All right, so let's use the Henderson-Hasselbalch 00:45:59.890 --> 00:46:01.760 to design a buffer then. 00:46:01.760 --> 00:46:06.450 So say we want to design a buffer of pH 4.6. 00:46:06.450 --> 00:46:10.560 Say you're interviewing for a UROP position and the UROP 00:46:10.560 --> 00:46:14.030 supervisor, the PI says, tell me how you 00:46:14.030 --> 00:46:17.630 would design a buffer pH 4.6. 00:46:17.630 --> 00:46:20.790 And you might go to the shelf and see what was available 00:46:20.790 --> 00:46:25.150 and then look up what the Ka and the pKa are, 00:46:25.150 --> 00:46:28.350 because a buffer solution is most effective in the range 00:46:28.350 --> 00:46:30.860 of the pKa plus or minus 1. 00:46:30.860 --> 00:46:35.500 In fact, the closer the pH you want is to the pKa, 00:46:35.500 --> 00:46:37.460 the better the buffer is going to be. 00:46:37.460 --> 00:46:39.760 So we can look and see what's in the range. 00:46:39.760 --> 00:46:44.340 There are several that are close to 4.6 that we can choose from. 00:46:44.340 --> 00:46:46.370 And probably would end up choosing 00:46:46.370 --> 00:46:49.110 acetic acid, because that would be on the shelf, 00:46:49.110 --> 00:46:51.980 whereas, some of the others of these would not be there. 00:46:51.980 --> 00:46:53.830 All right, so acetate is going to work. 00:46:53.830 --> 00:46:56.480 It's a pretty common buffer. 00:46:56.480 --> 00:47:04.220 So we can use acetic acid with a suitable pKa of 4.75. 00:47:04.220 --> 00:47:07.370 Then we can use the Henderson-Hasselbalch Equation 00:47:07.370 --> 00:47:09.170 because we're designing a buffer. 00:47:09.170 --> 00:47:12.110 So we can use that equation and figure out 00:47:12.110 --> 00:47:18.110 what the ratio of acetic acid to its conjugate base should be. 00:47:18.110 --> 00:47:20.980 So we can rearrange this expression. 00:47:20.980 --> 00:47:26.360 We know the pKa and we know the pH that we want, 00:47:26.360 --> 00:47:29.390 and so we can subtract those. 00:47:29.390 --> 00:47:35.630 And we get that the log of the ratio should be 0.15. 00:47:35.630 --> 00:47:38.280 And then inverse log will tell us 00:47:38.280 --> 00:47:42.100 that the ratio then of the acid to the conjugate base 00:47:42.100 --> 00:47:44.560 should be 1.4. 00:47:44.560 --> 00:47:48.820 So you should use things with that ratio. 00:47:48.820 --> 00:47:53.330 So for example, you could use 1.4 molar of the acid 00:47:53.330 --> 00:47:56.300 to one molar of the conjugate base 00:47:56.300 --> 00:48:03.070 and the total amounts are often less important than the ratio. 00:48:03.070 --> 00:48:07.980 The ratio is very important, but if you go too low 00:48:07.980 --> 00:48:10.640 in concentrations, then that will 00:48:10.640 --> 00:48:13.900 affect what's known as the buffering capacity, which 00:48:13.900 --> 00:48:17.040 is the ability of the buffer to resist changes. 00:48:17.040 --> 00:48:19.640 So if it's too dilute, and a lot of strong acid 00:48:19.640 --> 00:48:21.810 or a lot of strong base is added, 00:48:21.810 --> 00:48:24.280 then it won't be a good buffer anymore. 00:48:24.280 --> 00:48:26.600 So the ratio is very important. 00:48:26.600 --> 00:48:30.750 The amounts are important such that you have some resistance 00:48:30.750 --> 00:48:32.350 to change. 00:48:32.350 --> 00:48:36.520 So the higher concentrations, the more resistant to change. 00:48:40.430 --> 00:48:45.460 And also, if you use too low a concentration, 00:48:45.460 --> 00:48:49.680 the Henderson-Hasselbalch Equation is no longer valid. 00:48:49.680 --> 00:48:51.280 So you could be asked to calculate 00:48:51.280 --> 00:48:53.490 sort of what the minimum concentration is 00:48:53.490 --> 00:48:55.570 that you would need to use. 00:48:55.570 --> 00:49:02.580 And so for a pH 4.60, you can back calculate what 00:49:02.580 --> 00:49:04.910 the hydronium ion concentration is. 00:49:04.910 --> 00:49:08.370 And it's 2.5 times 10 to the minus 5. 00:49:08.370 --> 00:49:12.740 So for our 5% assumption to hold or to be valid, 00:49:12.740 --> 00:49:16.740 that this number, the hydronium ion concentration, 00:49:16.740 --> 00:49:20.390 is less than 5% of either one of these. 00:49:20.390 --> 00:49:22.700 The concentrations here would have 00:49:22.700 --> 00:49:26.510 to be greater than 5 times 10 to the minus 4. 00:49:26.510 --> 00:49:28.360 So if we use one molar or something, 00:49:28.360 --> 00:49:30.980 that's way above this, but that would be the minimum. 00:49:30.980 --> 00:49:34.250 If it's less than that, that 5% doesn't really hold 00:49:34.250 --> 00:49:37.240 and you would not have a very good buffer in that case. 00:49:37.240 --> 00:49:39.570 It wouldn't be very resistant to change. 00:49:39.570 --> 00:49:42.490 X would be big compared to those numbers. 00:49:42.490 --> 00:49:44.916 So that's how you go about designing a buffer. 00:49:44.916 --> 00:49:46.540 And in that, there were two things that 00:49:46.540 --> 00:49:48.190 are really common mistakes. 00:49:48.190 --> 00:49:50.630 When I'm reviewing a paper for publication, 00:49:50.630 --> 00:49:53.340 two of the things that I see the most often 00:49:53.340 --> 00:49:56.720 is that people one, do not use the right buffer 00:49:56.720 --> 00:49:57.730 for their experiment. 00:49:57.730 --> 00:50:00.410 They say, oh, I'm at pH 8. 00:50:00.410 --> 00:50:02.160 And they'll use a buffer that is in fact, 00:50:02.160 --> 00:50:04.150 not a good buffer at pH 8. 00:50:04.150 --> 00:50:07.120 So who knows what their data is telling us. 00:50:07.120 --> 00:50:09.610 And the other thing that people will do 00:50:09.610 --> 00:50:11.810 is that they'll say, oh yes, it was buffered. 00:50:11.810 --> 00:50:15.140 And the pKa might be right, but the concentration of the buffer 00:50:15.140 --> 00:50:18.190 is so low that you don't really imagine 00:50:18.190 --> 00:50:19.680 the buffer's doing anything. 00:50:19.680 --> 00:50:24.050 So now you know how to avoid both of those pitfalls.