WEBVTT 00:00:00.030 --> 00:00:02.400 The following content is provided under a Creative 00:00:02.400 --> 00:00:03.780 Commons license. 00:00:03.780 --> 00:00:06.020 Your support will help MIT OpenCourseWare 00:00:06.020 --> 00:00:10.080 continue to offer high-quality, educational resources for free. 00:00:10.080 --> 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 --> 00:00:17.744 at ocw.mit.edu. 00:00:59.380 --> 00:01:01.570 OK. 00:01:01.570 --> 00:01:09.600 So we have-- you can show the answer-- 57%, 1 and 3. 00:01:09.600 --> 00:01:13.060 So this is where we were at the end of last lecture, 00:01:13.060 --> 00:01:18.370 so if you didn't get this written down in your notes, 00:01:18.370 --> 00:01:21.424 you want to look at these definitions. 00:01:24.990 --> 00:01:32.470 So here in this, we have NH3 with its lone pair, 00:01:32.470 --> 00:01:36.280 and it is acting as the Lewis base, 00:01:36.280 --> 00:01:40.150 and BF3 is acting as the Lewis acid. 00:01:40.150 --> 00:01:43.830 So a Lewis base donates its lone pair electrons, 00:01:43.830 --> 00:01:46.030 and the acid accepts them. 00:01:46.030 --> 00:01:48.440 So what was the other definition? 00:01:48.440 --> 00:01:50.350 We had the Bronsted-Lowry. 00:01:50.350 --> 00:01:56.170 Does someone want to tell me what that definition was? 00:01:56.170 --> 00:02:01.440 Can we have a volunteer tell us the Bronsted-Lowry definition? 00:02:06.250 --> 00:02:07.260 Pull out your notes. 00:02:17.250 --> 00:02:17.968 There you go. 00:02:21.530 --> 00:02:23.600 AUDIENCE: So a Bronsted-Lowry-- 00:02:23.600 --> 00:02:26.170 CATHERINE DRENNAN: I'm not sure it's on. 00:02:26.170 --> 00:02:27.490 It is on? 00:02:27.490 --> 00:02:27.990 OK. 00:02:27.990 --> 00:02:30.520 AUDIENCE: Bronsted-Lowry base is something that 00:02:30.520 --> 00:02:33.040 accepts H plus or H3O plus. 00:02:33.040 --> 00:02:34.040 CATHERINE DRENNAN: Yeah. 00:02:34.040 --> 00:02:37.750 So the base accepts the hydrogen ion or the proton, 00:02:37.750 --> 00:02:39.720 and the acid donates. 00:02:39.720 --> 00:02:42.740 So is this definition now incompatible, 00:02:42.740 --> 00:02:44.720 or are they completely opposite, or could they 00:02:44.720 --> 00:02:46.650 be worked together? 00:02:46.650 --> 00:02:48.336 Does anyone have an opinion on that? 00:02:53.630 --> 00:02:55.350 So how many people think that these 00:02:55.350 --> 00:02:58.690 could be consistent definitions in some way? 00:02:58.690 --> 00:02:59.370 OK. 00:02:59.370 --> 00:03:00.380 Oh, quite a few people. 00:03:03.180 --> 00:03:04.870 One could make that argument. 00:03:04.870 --> 00:03:07.220 So if you know now that you can make the argument, 00:03:07.220 --> 00:03:08.765 does someone want to try to make it? 00:03:12.950 --> 00:03:15.880 We have a bag. 00:03:15.880 --> 00:03:17.430 All right. 00:03:17.430 --> 00:03:24.460 Our mic went away, but can we get up over there? 00:03:24.460 --> 00:03:28.790 So where did our mic runner go? 00:03:28.790 --> 00:03:31.290 I should have explained they were needed twice. 00:03:31.290 --> 00:03:31.920 All right. 00:03:39.450 --> 00:03:42.777 All right, who said they might try this? 00:03:51.436 --> 00:03:55.500 AUDIENCE: All Bronsted-Lowry bases are Lewis spaces, 00:03:55.500 --> 00:03:57.970 but not all Lewis bases are Bronsted-Lowry bases 00:03:57.970 --> 00:04:02.410 because you can act as a proxy with no hydrogen ion 00:04:02.410 --> 00:04:03.560 if it connects directly. 00:04:03.560 --> 00:04:08.140 But if a hydrogen ion bonds, an example H3O, 00:04:08.140 --> 00:04:10.960 to the lone pair of oxygen, then it's 00:04:10.960 --> 00:04:12.300 the same thing as a Lewis base. 00:04:19.530 --> 00:04:22.060 CATHERINE DRENNAN: OK. 00:04:22.060 --> 00:04:22.980 so that's right. 00:04:22.980 --> 00:04:26.190 The Lewis acid-Lewis base definition 00:04:26.190 --> 00:04:28.630 works if you don't have a hydrogen 00:04:28.630 --> 00:04:30.720 ion involved or a proton involved, 00:04:30.720 --> 00:04:33.660 but the other still applies. 00:04:33.660 --> 00:04:38.500 So remember that when you're accepting H plus, 00:04:38.500 --> 00:04:40.290 you're taking it without an electron, 00:04:40.290 --> 00:04:44.260 so the base is taking H plus, so it's donating its electrons 00:04:44.260 --> 00:04:45.500 to form the bond. 00:04:45.500 --> 00:04:48.700 And the acid, when it gives up H plus, 00:04:48.700 --> 00:04:50.540 it's keeping all of the electrons. 00:04:50.540 --> 00:04:54.190 It's accepting the electrons, so when the acid gives up H plus, 00:04:54.190 --> 00:04:57.210 it's accepting, and when the base takes H plus, 00:04:57.210 --> 00:04:58.870 it's using its electrons. 00:04:58.870 --> 00:05:06.320 So the Lewis definitions are lone-pair or electron-centric 00:05:06.320 --> 00:05:09.340 definitions, whereas, Bronsted-Lowry 00:05:09.340 --> 00:05:13.010 is thinking about the proton, but they both work together. 00:05:13.010 --> 00:05:15.240 So that's a good review of the definitions 00:05:15.240 --> 00:05:17.040 we talked about last time, and now I'll 00:05:17.040 --> 00:05:20.670 try to get my mic back on. 00:05:20.670 --> 00:05:22.190 All right. 00:05:22.190 --> 00:05:26.860 So today we're going to continue talking about acid base, 00:05:26.860 --> 00:05:29.310 and we're going to continue talking about acid base quite 00:05:29.310 --> 00:05:30.000 a bit. 00:05:30.000 --> 00:05:33.390 So we have a number more lectures on acid base. 00:05:33.390 --> 00:05:35.990 So we're going to start today with the relationship 00:05:35.990 --> 00:05:40.810 between pKw, pH, and pOH, we're going 00:05:40.810 --> 00:05:43.540 to talk about the strengths of acids and bases, 00:05:43.540 --> 00:05:46.680 and then we're going to start doing equilibrium 00:05:46.680 --> 00:05:48.450 acid-base problems. 00:05:48.450 --> 00:05:50.170 And we're going to do a bunch of those. 00:05:50.170 --> 00:05:53.010 And students who are doing this and learning it 00:05:53.010 --> 00:05:54.690 for the first time are telling me there 00:05:54.690 --> 00:05:57.290 is an infinite number of different kinds of problems. 00:05:57.290 --> 00:05:58.295 It's really not true. 00:05:58.295 --> 00:06:00.670 There are only five different types, and today hopefully, 00:06:00.670 --> 00:06:02.310 we'll get through two of them. 00:06:02.310 --> 00:06:05.500 So first we need to think about water 00:06:05.500 --> 00:06:07.830 because water is a really important solvent when 00:06:07.830 --> 00:06:11.150 we're talking about acid base equilibrium. 00:06:11.150 --> 00:06:15.280 And we mentioned last time that water 00:06:15.280 --> 00:06:17.490 can act as an acid and a base. 00:06:17.490 --> 00:06:20.070 Does anyone remember what that's called, something that 00:06:20.070 --> 00:06:21.520 can act as an acid and a base? 00:06:21.520 --> 00:06:22.765 AUDIENCE: Amphoteric. 00:06:22.765 --> 00:06:24.570 CATHERINE DRENNAN: Amphoteric. 00:06:24.570 --> 00:06:28.420 So here we can think about two waters 00:06:28.420 --> 00:06:32.684 going to H3O plus and OH. 00:06:32.684 --> 00:06:34.100 We could also write it out instead 00:06:34.100 --> 00:06:36.410 of just saying two waters, one water that's 00:06:36.410 --> 00:06:40.570 acting as the acid and another water is acting as a base. 00:06:40.570 --> 00:06:45.160 So the water that's acting as an acid gives up its hydrogen ion, 00:06:45.160 --> 00:06:46.680 or proton to the base. 00:06:46.680 --> 00:06:49.840 The base accepts it forming a conjugate acid, 00:06:49.840 --> 00:06:54.950 and this water that lost H plus becomes OH minus. 00:06:54.950 --> 00:07:01.170 So water plus water, H2O plus H2O, forms an acid and a base. 00:07:01.170 --> 00:07:04.940 So we can ask the question, then how much water 00:07:04.940 --> 00:07:09.600 is in a glass of water, or how much H2O is actually 00:07:09.600 --> 00:07:14.900 in this water container that I have here? 00:07:14.900 --> 00:07:16.840 So when I'm asking that question, 00:07:16.840 --> 00:07:21.070 how much H2O in a container of water 00:07:21.070 --> 00:07:24.920 and if I know the delta G0 of that process, 00:07:24.920 --> 00:07:28.530 I'm asking about what is the relationship 00:07:28.530 --> 00:07:32.180 between our products here, our ionized acid 00:07:32.180 --> 00:07:35.690 and our base over here, the ionized products of water, 00:07:35.690 --> 00:07:38.870 compared to water at equilibrium. 00:07:38.870 --> 00:07:42.140 Because this container, the water, is in equilibrium. 00:07:42.140 --> 00:07:44.770 So if I'm asking about the ratio of products 00:07:44.770 --> 00:07:50.130 to react as an equilibrium, what am I asking about? 00:07:50.130 --> 00:07:51.224 Just yell it out. 00:07:51.224 --> 00:07:52.140 AUDIENCE: Equilibrium. 00:07:52.140 --> 00:07:54.681 CATHERINE DRENNAN: I'm asking about the equilibrium constant. 00:07:54.681 --> 00:07:55.340 Exactly. 00:07:55.340 --> 00:08:00.440 I'm asking what is K. What is the equilibrium constant. 00:08:00.440 --> 00:08:04.320 So let's just briefly review the relationship. 00:08:04.320 --> 00:08:06.560 We're given here a delta G0, and we're 00:08:06.560 --> 00:08:10.060 asking about K. What is the relationship, how 00:08:10.060 --> 00:08:14.480 do you calculate K if you know delta G0? 00:08:14.480 --> 00:08:18.090 And we have some equations that will be given to you. 00:08:18.090 --> 00:08:18.590 Sorry. 00:08:18.590 --> 00:08:19.400 Not quite yet. 00:08:19.400 --> 00:08:21.450 There's going to be a clicker question coming. 00:08:21.450 --> 00:08:23.640 We have some equations here. 00:08:23.640 --> 00:08:26.780 So we have delta G0 equals minus RT natural log 00:08:26.780 --> 00:08:31.440 of K, which we can rearrange to solve for K. 00:08:31.440 --> 00:08:34.140 And let's just have a little reminder of what 00:08:34.140 --> 00:08:35.679 these terms are. 00:08:35.679 --> 00:08:37.240 So we'll put this up here. 00:08:37.240 --> 00:08:39.510 T is temperature, and we're going 00:08:39.510 --> 00:08:41.270 to be talking about room temperature. 00:08:41.270 --> 00:08:43.049 This isn't room temperature now. 00:08:43.049 --> 00:08:45.740 And in fact, almost all acid-based problems 00:08:45.740 --> 00:08:47.326 are going to be at room temperature. 00:08:47.326 --> 00:08:48.700 There might be a few differences, 00:08:48.700 --> 00:08:50.800 but we have a lot at room temperature. 00:08:50.800 --> 00:08:56.830 We have a constant, R, and so 8.314 joules 00:08:56.830 --> 00:09:04.470 per Kelvin per mole and delta G. So we were already told 00:09:04.470 --> 00:09:06.470 the value for delta G here. 00:09:06.470 --> 00:09:10.710 Now, thinking about this room temperature, this constant, 00:09:10.710 --> 00:09:12.850 and this value for delta G, do you 00:09:12.850 --> 00:09:16.120 expect a large or small value for K 00:09:16.120 --> 00:09:19.387 if you have this delta G0 value? 00:09:19.387 --> 00:09:20.720 And that's our clicker question. 00:09:51.282 --> 00:09:52.260 All right. 00:09:52.260 --> 00:09:54.290 Let's just do 10 more seconds. 00:10:08.060 --> 00:10:09.170 Yep. 00:10:09.170 --> 00:10:14.320 So K, you would expect to be a small value less than 1. 00:10:14.320 --> 00:10:16.950 And you could think about that mathematically 00:10:16.950 --> 00:10:20.250 from these expressions, or you could think about it 00:10:20.250 --> 00:10:25.960 in terms of the value of for delta G. So if we solve this 00:10:25.960 --> 00:10:28.540 and we put in our value for delta G0, which 00:10:28.540 --> 00:10:31.640 is a positive value-- so the forward direction 00:10:31.640 --> 00:10:35.380 of the reaction is non-spontaneous. 00:10:35.380 --> 00:10:39.820 So we put in our positive delta G0 and our other values here, 00:10:39.820 --> 00:10:44.580 and this is, again, joules per Kelvin per mole. 00:10:44.580 --> 00:10:47.830 And we have to make sure that we convert kilojoules to jewels 00:10:47.830 --> 00:10:49.780 and our units will cancel out. 00:10:49.780 --> 00:10:53.480 And if we do that, we get this value for natural log of K 00:10:53.480 --> 00:10:58.600 and this value for K of 1.0 times 10 to the minus 14th 00:10:58.600 --> 00:11:00.080 at room temperature. 00:11:00.080 --> 00:11:02.310 And you will find that you end up 00:11:02.310 --> 00:11:05.610 memorizing this value if you do enough acid-base problems. 00:11:05.610 --> 00:11:08.650 In fact, you might have it memorized already. 00:11:08.650 --> 00:11:12.120 So this is, in fact, a small value. 00:11:12.120 --> 00:11:15.130 And that indicates that only a small proportion 00:11:15.130 --> 00:11:17.410 of water molecules are ionized. 00:11:17.410 --> 00:11:22.900 About 1 molecule in every 200 million are ionized, 00:11:22.900 --> 00:11:25.910 so it's a very, very small value. 00:11:25.910 --> 00:11:29.720 So there is a lot of H2O in a glass of water. 00:11:29.720 --> 00:11:32.480 So in here it's mostly H2O. 00:11:32.480 --> 00:11:37.000 Very few molecules are ionized in that. 00:11:37.000 --> 00:11:38.720 Now, part of the reason why you're 00:11:38.720 --> 00:11:41.970 likely to have this value of K memorized 00:11:41.970 --> 00:11:44.790 is because it has a special name. 00:11:44.790 --> 00:11:50.550 This K is called Kw for water. 00:11:50.550 --> 00:11:52.640 So that's easy to remember. 00:11:52.640 --> 00:11:57.690 And Kw, the equilibrium constant for water, 00:11:57.690 --> 00:12:01.010 is equal to the hydronium ion concentration 00:12:01.010 --> 00:12:05.010 times the hydroxide ion concentration. 00:12:05.010 --> 00:12:07.650 And since this is an equilibrium constant, 00:12:07.650 --> 00:12:09.610 if you're at constant temperature at room 00:12:09.610 --> 00:12:14.960 temperature, this will always equal 1.0 times 10 00:12:14.960 --> 00:12:16.610 to the minus 14th. 00:12:16.610 --> 00:12:20.930 This product is always going to be this at room temperature. 00:12:20.930 --> 00:12:22.670 And that is why it's going to turn out 00:12:22.670 --> 00:12:24.360 to be important because you're going 00:12:24.360 --> 00:12:27.971 to use that information in solving a lot of problems. 00:12:27.971 --> 00:12:28.470 All right. 00:12:28.470 --> 00:12:31.410 So if this is an equilibrium constant, 00:12:31.410 --> 00:12:35.010 we want to think again about expressions for equilibrium 00:12:35.010 --> 00:12:38.080 and just make a note that we did not 00:12:38.080 --> 00:12:42.610 include water squared on the bottom of this expression. 00:12:42.610 --> 00:12:46.100 So Kw equals hydronium ion concentration 00:12:46.100 --> 00:12:48.530 times hydroxide ion concentration. 00:12:48.530 --> 00:12:50.530 You don't put it over water. 00:12:50.530 --> 00:12:53.060 And the reason for this is because this is a pretty pure 00:12:53.060 --> 00:12:57.060 solvent, and you don't include pure solvents 00:12:57.060 --> 00:12:59.090 in your equilibrium expression. 00:12:59.090 --> 00:13:00.930 You also don't include solids. 00:13:00.930 --> 00:13:04.180 So we talked about that when we were talking about solubility. 00:13:04.180 --> 00:13:07.760 So you have to remember that solvents like water 00:13:07.760 --> 00:13:09.820 is nearly pure, doesn't go in. 00:13:09.820 --> 00:13:12.610 Pure other liquids, pure other solids 00:13:12.610 --> 00:13:16.710 are not included in your equilibrium expression. 00:13:16.710 --> 00:13:17.570 All right. 00:13:17.570 --> 00:13:20.450 So we now know about water. 00:13:20.450 --> 00:13:23.610 We know about Kw. 00:13:23.610 --> 00:13:25.850 Let's do a few more definitions and then 00:13:25.850 --> 00:13:27.300 think about how all of these terms 00:13:27.300 --> 00:13:29.320 are related to each other. 00:13:29.320 --> 00:13:32.230 So a definition that many people already know, 00:13:32.230 --> 00:13:35.290 probably if you've taken any kind of science before, 00:13:35.290 --> 00:13:37.850 you're probably aware that pH equals 00:13:37.850 --> 00:13:43.040 minus log of the hydronium ion concentration of H3O plus. 00:13:43.040 --> 00:13:45.490 If you don't know it, it will be on your equation sheet, 00:13:45.490 --> 00:13:48.920 so it doesn't really matter, but there it is. 00:13:48.920 --> 00:13:50.730 And there's also pOH. 00:13:50.730 --> 00:13:55.180 pOH equals minus log of the hydroxide ion 00:13:55.180 --> 00:13:58.430 concentration, OH minus. 00:13:58.430 --> 00:14:00.900 Now, let's think about the relationships 00:14:00.900 --> 00:14:05.270 of pKw, pH, and pOH. 00:14:05.270 --> 00:14:08.930 So relationships. 00:14:08.930 --> 00:14:10.730 So I just told you and maybe you've 00:14:10.730 --> 00:14:13.400 already memorized that Kw is going 00:14:13.400 --> 00:14:16.280 to be equal to the hydronium ion concentration 00:14:16.280 --> 00:14:19.180 times the hydroxide ion concentration, 00:14:19.180 --> 00:14:22.660 and that's going to be equal to 1.0 times 10 to the minus 14th 00:14:22.660 --> 00:14:24.850 at room temperature. 00:14:24.850 --> 00:14:27.780 So now, if we take this expression 00:14:27.780 --> 00:14:31.240 and we take the log of all of these terms 00:14:31.240 --> 00:14:35.870 and multiply by a negative value, 00:14:35.870 --> 00:14:37.750 then we will get this expression. 00:14:37.750 --> 00:14:43.080 So minus the log of Kw is pKw. 00:14:43.080 --> 00:14:49.080 And minus log of the hydronium ion concentration is what? 00:14:49.080 --> 00:14:53.962 pH minus log of the hydroxide ion concentration is what? 00:14:53.962 --> 00:14:55.378 AUDIENCE: pOH. 00:14:55.378 --> 00:14:56.480 CATHERINE DRENNAN: pOH. 00:14:56.480 --> 00:15:08.210 So pKw equals pH plus pOH, and that is equal to 14.00 at room 00:15:08.210 --> 00:15:09.270 temperature. 00:15:09.270 --> 00:15:12.470 And this is a very useful expression, 00:15:12.470 --> 00:15:16.130 the fact that pH and pOH are equal to 14. 00:15:16.130 --> 00:15:19.020 If you know one of these, then the other one 00:15:19.020 --> 00:15:22.410 by doing a simple subtraction. 00:15:22.410 --> 00:15:25.810 So you will find yourself using this expression quite often 00:15:25.810 --> 00:15:27.870 in the problem sets. 00:15:27.870 --> 00:15:30.380 And so I'll say that one, the problem set that that's 00:15:30.380 --> 00:15:34.040 due on Friday has just a couple of acid-based problems 00:15:34.040 --> 00:15:34.872 at the end. 00:15:34.872 --> 00:15:40.940 The next problem set will be 100% acid-base problems, 00:15:40.940 --> 00:15:46.440 so there's a lot to look forward to. 00:15:46.440 --> 00:15:51.050 So let's talk about the strengths of acids and bases. 00:15:51.050 --> 00:15:55.230 So if you have a pH of pure water, 00:15:55.230 --> 00:16:00.350 it should be equal to minus log times 1.0 times 10 00:16:00.350 --> 00:16:05.600 to the minus 7, or the pH equals 7, which is a neutral pH. 00:16:05.600 --> 00:16:11.650 So if we have a scale here, pH minus 1 to pH 14, 7 00:16:11.650 --> 00:16:14.820 is a neutral value. 00:16:14.820 --> 00:16:18.270 If we're talking about things that are acidic, 00:16:18.270 --> 00:16:22.680 the pH of an acidic solution is less than 7, 00:16:22.680 --> 00:16:26.530 and so this is the acidic part over here. 00:16:26.530 --> 00:16:31.660 And the pH of a basic solution is greater than 7, 00:16:31.660 --> 00:16:35.850 so that is down in this part. 00:16:35.850 --> 00:16:40.800 The EPA defines waste as corrosive 00:16:40.800 --> 00:16:45.750 if the pH is lower than 3, so that 00:16:45.750 --> 00:16:52.230 would be corrosive, or higher than 12.5, also corrosive. 00:16:52.230 --> 00:16:56.420 So living creatures like to be more in the neutral range. 00:16:56.420 --> 00:17:01.510 When you get to things that are very low pH or very high pH, 00:17:01.510 --> 00:17:04.310 that is less good. 00:17:04.310 --> 00:17:08.369 So let's now check out a few pH's, and I'd 00:17:08.369 --> 00:17:13.240 like to have five TAs come down to help me with this. 00:17:13.240 --> 00:17:15.819 And I'll just show you what we're going to do. 00:17:15.819 --> 00:17:18.089 So we'll have some volunteers. 00:17:18.089 --> 00:17:20.069 We have pH paper. 00:17:20.069 --> 00:17:22.490 The pH paper has an indicator on. 00:17:22.490 --> 00:17:24.990 You put the paper in the solution 00:17:24.990 --> 00:17:28.099 and then try to see which thing matches best. 00:17:28.099 --> 00:17:32.270 So this is a very quick and dirty way to estimate pH. 00:17:32.270 --> 00:17:35.780 There's pH meters and indicator dyes that work better, 00:17:35.780 --> 00:17:38.840 but we'll have five people measure five things. 00:17:38.840 --> 00:17:41.280 We have ammonia, a cleaner. 00:17:41.280 --> 00:17:43.030 We talked about the importance of cleaning 00:17:43.030 --> 00:17:45.270 bathrooms last lecture. 00:17:45.270 --> 00:17:47.890 We have soda. 00:17:47.890 --> 00:17:52.840 We have vinegar, which is often used in salad dressings. 00:17:52.840 --> 00:17:55.790 Before I came here I just went to a random sink 00:17:55.790 --> 00:17:59.520 and got some MIT water to measure. 00:17:59.520 --> 00:18:02.660 And then this, this is special. 00:18:02.660 --> 00:18:06.710 This is a prescription medicine. 00:18:06.710 --> 00:18:12.500 So this is a solution of iron 2 sulfate. 00:18:12.500 --> 00:18:16.710 And this is prescribed if have an iron deficiency. 00:18:16.710 --> 00:18:19.600 An iron deficiency is pretty bad, and a lot of kids 00:18:19.600 --> 00:18:20.810 have iron deficiencies. 00:18:20.810 --> 00:18:22.680 It's really common in infants. 00:18:22.680 --> 00:18:25.460 So my daughter had an iron deficiency, 00:18:25.460 --> 00:18:27.170 and this was her medicine. 00:18:27.170 --> 00:18:32.260 In fact, this box is completely full of this medicine. 00:18:32.260 --> 00:18:36.360 So kids cannot swallow pills very easily. 00:18:36.360 --> 00:18:38.940 How many of you actually cannot swallow a pill? 00:18:38.940 --> 00:18:41.340 A lot of adults are pill challenged. 00:18:41.340 --> 00:18:43.400 How many are happy swallowing pills? 00:18:43.400 --> 00:18:44.820 Let's do a more positive thing. 00:18:44.820 --> 00:18:46.820 OK. 00:18:46.820 --> 00:18:51.620 So swallowing pills is not everyone's favorite. 00:18:51.620 --> 00:18:54.970 When you're a kid, it's really impossible 00:18:54.970 --> 00:18:57.930 to tell someone to put something in their throat 00:18:57.930 --> 00:19:00.400 and go back and try to get it down. 00:19:00.400 --> 00:19:02.140 They choke, spit up, it's awful. 00:19:02.140 --> 00:19:05.440 So kids have to take medicine in solution. 00:19:05.440 --> 00:19:10.330 So this medicine is 300 milligrams in 5 milliliters. 00:19:10.330 --> 00:19:12.620 It's very concentrated, so my daughter 00:19:12.620 --> 00:19:15.010 had a pretty severe iron deficiency. 00:19:15.010 --> 00:19:19.030 So when she tried taking it, and I tasted it, 00:19:19.030 --> 00:19:21.276 it was horrific beyond belief. 00:19:21.276 --> 00:19:23.150 And after she had taken it a couple of times, 00:19:23.150 --> 00:19:26.900 she started to have sores on her tongue and in her mouth. 00:19:26.900 --> 00:19:29.950 And I as a chemist said, let's measure the pH. 00:19:29.950 --> 00:19:34.230 So you will measure the pH of this prescription medicine 00:19:34.230 --> 00:19:38.850 for a four-year-old and tell me whether the EPA would prove it 00:19:38.850 --> 00:19:39.380 or not. 00:19:39.380 --> 00:19:42.300 Anyway, so here are the TAs, and they're going to come around. 00:19:42.300 --> 00:19:45.777 Raise your hand if you're willing to measure a pH. 00:19:45.777 --> 00:19:46.860 TAs, just grab a solution. 00:19:46.860 --> 00:19:50.830 I should have had you pour it, but OK, we're doing it. 00:19:50.830 --> 00:19:57.300 And we'll go around, and we'll measure, and tell me 00:19:57.300 --> 00:19:59.288 what you find, and I'll write it on the board. 00:20:07.866 --> 00:20:08.824 Yeah, OK. 00:20:15.600 --> 00:20:16.100 All right. 00:20:16.100 --> 00:20:17.105 So we have pH. 00:20:53.510 --> 00:20:54.010 All right. 00:20:54.010 --> 00:20:54.898 Do we have an answer? 00:21:01.012 --> 00:21:03.532 Did we get one? 00:21:03.532 --> 00:21:04.240 What do you have? 00:21:04.240 --> 00:21:04.989 AUDIENCE: Ammonia. 00:21:04.989 --> 00:21:06.610 CATHERINE DRENNAN: Ammonia is 12. 00:21:15.400 --> 00:21:17.840 So almost corrosive, but not quite. 00:21:17.840 --> 00:21:20.210 You can still have clean, but if you 00:21:20.210 --> 00:21:24.920 want an excuse not to clean, you're like, sorry, too close. 00:21:24.920 --> 00:21:27.210 Too Corrosive Do we have another one? 00:21:27.210 --> 00:21:29.190 AUDIENCE: MIT water is 7. 00:21:29.190 --> 00:21:30.729 CATHERINE DRENNAN: MIT water is 7? 00:21:30.729 --> 00:21:31.770 AUDIENCE: MIT water is 7. 00:21:31.770 --> 00:21:32.920 CATHERINE DRENNAN: Awesome. 00:21:37.160 --> 00:21:40.290 So often, actually, water that you get from a tap 00:21:40.290 --> 00:21:45.370 is not 7 because often there are ions that are dissolved in it. 00:21:45.370 --> 00:21:48.890 But a little bit around 7, a little bit of ions 00:21:48.890 --> 00:21:49.700 never hurt anyone. 00:21:49.700 --> 00:21:51.725 We have lots of ions in our body. 00:21:51.725 --> 00:21:52.225 Soda? 00:21:52.225 --> 00:21:53.680 AUDIENCE: 3 and 1/2. 00:21:53.680 --> 00:21:55.568 CATHERINE DRENNAN: Soda at 3 and 1/2. 00:22:01.020 --> 00:22:04.450 So soda is definitely getting into our corrosive range. 00:22:04.450 --> 00:22:05.955 AUDIENCE: Vinegar at 2. 00:22:05.955 --> 00:22:07.920 CATHERINE DRENNAN: And we have vinegar at 2. 00:22:13.030 --> 00:22:14.630 And that is corrosive. 00:22:14.630 --> 00:22:19.190 People often use pure vinegar to clean out a coffee pot 00:22:19.190 --> 00:22:20.980 because it is pretty corrosive. 00:22:20.980 --> 00:22:23.570 It really does a good job of cleaning it. 00:22:23.570 --> 00:22:25.290 When you're having it in salad dressing, 00:22:25.290 --> 00:22:27.250 you don't want to have it pure vinegar. 00:22:27.250 --> 00:22:29.176 That would not be good to drink. 00:22:29.176 --> 00:22:30.175 And what about medicine? 00:22:30.175 --> 00:22:32.680 AUDIENCE: Medicine has a pH of 2. 00:22:32.680 --> 00:22:33.780 CATHERINE DRENNAN: 2. 00:22:33.780 --> 00:22:38.350 So we also have in the corrosive category 00:22:38.350 --> 00:22:41.480 the medicine that my four-year-old daughter 00:22:41.480 --> 00:22:44.050 was asked to take. 00:22:44.050 --> 00:22:50.760 So when she started getting these sores in her mouth 00:22:50.760 --> 00:22:55.530 from taking her medicine, I brought some pH paper home 00:22:55.530 --> 00:22:57.170 and measured the pH and discovered 00:22:57.170 --> 00:22:59.310 that what she was taking was corrosive. 00:22:59.310 --> 00:23:01.990 So I went to the doctor and said, can you 00:23:01.990 --> 00:23:03.820 prescribe something different. 00:23:03.820 --> 00:23:05.690 This medicine is corrosive. 00:23:05.690 --> 00:23:08.780 And the doctor looked at me and it's like the pH, 00:23:08.780 --> 00:23:12.470 the pH is like 2 or lower. 00:23:12.470 --> 00:23:15.775 And she looked at me, and she's like, what do you mean pH? 00:23:21.200 --> 00:23:24.390 This is why I spend many lectures 00:23:24.390 --> 00:23:27.510 on pH in this class and acids and bases. 00:23:27.510 --> 00:23:31.200 Some of you will be doctors, and some of you 00:23:31.200 --> 00:23:35.360 will not encourage parents to buy this much corrosive thing 00:23:35.360 --> 00:23:38.980 to feed their child when they're iron deficient. 00:23:38.980 --> 00:23:40.540 So this is what I'm talking about. 00:23:40.540 --> 00:23:43.040 And for those of you who are not going to be doctors, 00:23:43.040 --> 00:23:44.730 many of you will probably have children 00:23:44.730 --> 00:23:45.870 with an iron deficiency. 00:23:45.870 --> 00:23:47.200 It's super common. 00:23:47.200 --> 00:23:50.520 So you will know that you need to measure 00:23:50.520 --> 00:23:53.810 the pH of the solution before giving it to your child. 00:23:53.810 --> 00:23:55.220 So what did I do? 00:23:55.220 --> 00:24:00.010 So what I did was I bought adult pills, same stuff, 00:24:00.010 --> 00:24:04.040 iron sulfate, and I made sure that this 00:24:04.040 --> 00:24:06.380 told me the number of milligrams that were in there. 00:24:06.380 --> 00:24:08.160 I looked at what was prescribed. 00:24:08.160 --> 00:24:11.330 So I got the pills with the correct number of milligrams, 00:24:11.330 --> 00:24:14.840 and then I crushed them, and that stuff also 00:24:14.840 --> 00:24:18.510 tastes really nasty, but a little tip for the future, 00:24:18.510 --> 00:24:21.680 there is one and only one that I discovered, 00:24:21.680 --> 00:24:26.370 taste that can cover the taste of iron 2 sulfate, 00:24:26.370 --> 00:24:28.056 and that is Nutella. 00:24:31.660 --> 00:24:35.290 So don't give your child corrosive medicine. 00:24:35.290 --> 00:24:39.990 Give them crushed pills in Nutella. 00:24:39.990 --> 00:24:42.080 pH is important. 00:24:42.080 --> 00:24:46.010 pH is important. 00:24:46.010 --> 00:24:49.190 So let's talk about the strengths of acids. 00:24:53.770 --> 00:24:57.520 And you might want to reconsider huge soda consumption too. 00:24:57.520 --> 00:25:00.360 I don't really know, but that's something 00:25:00.360 --> 00:25:02.090 you might want to think about. 00:25:02.090 --> 00:25:03.082 Strength of acids. 00:25:06.270 --> 00:25:13.050 So here we have some acetic acid, CH3COOH aqueous, 00:25:13.050 --> 00:25:17.260 dissolved in our solvent, which is liquid water. 00:25:17.260 --> 00:25:20.140 And this is an acid, so it will give up 00:25:20.140 --> 00:25:24.400 a hydrogen ion or a proton to the water, which acts as a base 00:25:24.400 --> 00:25:30.630 and forms our hydronium ions, H3O plus, and also 00:25:30.630 --> 00:25:32.710 the conjugate base of the acid. 00:25:32.710 --> 00:25:40.520 So it's the acid missing H plus, CH3C00 minus. 00:25:40.520 --> 00:25:44.580 So if we're talking about the strength of the acid, what 00:25:44.580 --> 00:25:48.050 we really want to know is how much of that acid 00:25:48.050 --> 00:25:51.230 forms ions, how much of it ionizes. 00:25:51.230 --> 00:25:53.310 That is going to determine how strong it 00:25:53.310 --> 00:25:54.980 is because the amount that ionizes 00:25:54.980 --> 00:25:59.630 is equal to the amount of the hydronium ions you get, 00:25:59.630 --> 00:26:01.850 and pH equals minus the concentration 00:26:01.850 --> 00:26:03.040 of hydronium ions. 00:26:03.040 --> 00:26:07.890 So the pH depends on the extent to which it ionizes. 00:26:07.890 --> 00:26:10.960 And again, we're talking about at equilibrium, 00:26:10.960 --> 00:26:14.870 so we're talking about a equilibrium constant, 00:26:14.870 --> 00:26:17.220 and this one also gets a fancy name. 00:26:17.220 --> 00:26:19.830 In acids and bases, all the equilibrium 00:26:19.830 --> 00:26:21.750 constants get their own little names, 00:26:21.750 --> 00:26:25.480 and this is the acid ionization constant, Ka. 00:26:25.480 --> 00:26:29.440 So it's the equilibrium constant for an acid, Ka. 00:26:29.440 --> 00:26:32.190 So that's at least very easy to remember. 00:26:32.190 --> 00:26:35.620 So now based on what you know about equilibrium constants, 00:26:35.620 --> 00:26:39.545 why don't you tell me the answer to this? 00:27:19.583 --> 00:27:20.666 All right 10 more seconds. 00:27:35.850 --> 00:27:37.920 All right. 00:27:37.920 --> 00:27:40.140 So this one is wrong. 00:27:40.140 --> 00:27:42.920 It's always products over reactants for an equilibrium 00:27:42.920 --> 00:27:43.850 expression. 00:27:43.850 --> 00:27:46.400 Water is a solvent and is nearly pure, 00:27:46.400 --> 00:27:48.220 so it should not be there. 00:27:48.220 --> 00:27:51.480 This should be in the expression because it's aqueous. 00:27:51.480 --> 00:27:54.970 If it were solid, it wouldn't be included, but it's aqueous, 00:27:54.970 --> 00:27:57.440 so its concentration is going to change, 00:27:57.440 --> 00:27:59.800 so it is in our expression. 00:27:59.800 --> 00:28:02.320 See answer to 3 for that one. 00:28:02.320 --> 00:28:05.610 Enough information, and it's not correct. 00:28:05.610 --> 00:28:09.070 So we can write the expression for Ka. 00:28:09.070 --> 00:28:12.520 So that's equal to the products, our hydronium ion 00:28:12.520 --> 00:28:18.190 concentration, our conjugate base over are conjugate acid. 00:28:18.190 --> 00:28:22.360 And so we can look at what the value is for this expression, 00:28:22.360 --> 00:28:24.190 and we can look it up. 00:28:24.190 --> 00:28:27.540 There's lots and lots of tables of these in your book. 00:28:27.540 --> 00:28:33.430 And it is 1.76 times 10 to the minus 5 or minus 3. 00:28:33.430 --> 00:28:36.620 I don't have my glasses, whatever it says there. 00:28:36.620 --> 00:28:41.690 I think it's 5 at room temperature, which is small. 00:28:41.690 --> 00:28:45.690 So when Ka is small, it means that very little of it 00:28:45.690 --> 00:28:48.100 is ionizing. 00:28:48.100 --> 00:28:53.890 And so only a small number of our acetic acid molecules 00:28:53.890 --> 00:28:56.820 are donating their proton when they're dissolved in water. 00:28:56.820 --> 00:28:59.080 So that's the definition of a weak acid. 00:28:59.080 --> 00:29:04.360 When it has a very small Ka, it's not ionizing very much. 00:29:04.360 --> 00:29:06.860 Now, in doing these units, a lot of people 00:29:06.860 --> 00:29:11.840 get hung up on the names of the different acids 00:29:11.840 --> 00:29:13.980 and one of the first steps in solving 00:29:13.980 --> 00:29:17.560 a problem is to write the equilibrium expression out, 00:29:17.560 --> 00:29:19.290 but people get hung up with that. 00:29:19.290 --> 00:29:21.240 So don't get hung up with that. 00:29:21.240 --> 00:29:24.940 You can use generic expressions for acids and water. 00:29:24.940 --> 00:29:27.660 If you don't want to write out the whole name of the acid, 00:29:27.660 --> 00:29:31.330 you can always just say HA, aqueous, plus the solvent, 00:29:31.330 --> 00:29:36.880 water, goes to hydronium ions plus A minus, 00:29:36.880 --> 00:29:39.130 the conjugate of the weak acid. 00:29:39.130 --> 00:29:43.940 So this is an acid in water, and the acid is HA here. 00:29:43.940 --> 00:29:47.740 And an acid expression should be forming hydronium ions. 00:29:47.740 --> 00:29:49.920 If it's acidic, you should have acidic pH, 00:29:49.920 --> 00:29:53.770 and so you need to have some H3O plus around. 00:29:53.770 --> 00:29:55.970 You can also write this expression 00:29:55.970 --> 00:29:59.110 as BH plus plus water. 00:29:59.110 --> 00:30:06.000 BH plus can give up the H plus and become B and also generate 00:30:06.000 --> 00:30:07.610 hydronium ions. 00:30:07.610 --> 00:30:11.175 So here are the acid is BHA. 00:30:11.175 --> 00:30:14.620 And often when you're looking at these kinds of problems, 00:30:14.620 --> 00:30:16.840 a weak acid will be HA, but sometimes you 00:30:16.840 --> 00:30:20.770 have a problem involving the conjugate acid of a weak base, 00:30:20.770 --> 00:30:24.110 and that's often expressed as BH plus. 00:30:24.110 --> 00:30:30.050 So both of these expressions are valid for an acid in water. 00:30:30.050 --> 00:30:34.790 So now let's think about strong acids versus weaker acids, 00:30:34.790 --> 00:30:36.970 and here's our definition in this class. 00:30:36.970 --> 00:30:41.920 A strong acid has a Ka greater than 1, a lot of strong acids 00:30:41.920 --> 00:30:45.480 have a Ka really, really, really greater than 1, 00:30:45.480 --> 00:30:48.280 and the acid ionizes almost completely. 00:30:48.280 --> 00:30:51.100 So if you say it's a strong acid in water, 00:30:51.100 --> 00:30:53.890 whatever concentration of that acid you put in 00:30:53.890 --> 00:30:56.170 is going to be equal to the concentration of hydronium 00:30:56.170 --> 00:30:57.060 ions. 00:30:57.060 --> 00:30:58.890 It basically goes straight. 00:30:58.890 --> 00:31:02.980 You form lots and lots and lots of products at equilibrium. 00:31:02.980 --> 00:31:06.650 A weak acid has a Ka of less than 1, 00:31:06.650 --> 00:31:10.030 and a weak acid does not for many ionized species 00:31:10.030 --> 00:31:11.130 in solution. 00:31:11.130 --> 00:31:14.765 Not very much H3O plus is formed. 00:31:18.450 --> 00:31:23.960 So what about pKa? 00:31:23.960 --> 00:31:28.040 pKa's are really important in organic chemistry, in biology, 00:31:28.040 --> 00:31:29.700 in a lot of areas. 00:31:29.700 --> 00:31:35.470 And every year the organic chemistry faculty in 512 00:31:35.470 --> 00:31:40.114 talk about pKa's in organic, and the students there say, no, 00:31:40.114 --> 00:31:41.280 we never learned about that. 00:31:41.280 --> 00:31:43.990 They're like, you took freshman chem, right? 00:31:43.990 --> 00:31:46.540 It's like a GIR or you pass the test. 00:31:46.540 --> 00:31:49.480 You should know about pKa's, and they're like, no. 00:31:49.480 --> 00:31:53.870 So they contact me, and I'm like they did not take 5.111 if they 00:31:53.870 --> 00:31:55.770 do not know what a pKa is. 00:31:55.770 --> 00:31:59.280 There are other courses that sometimes people decide to take 00:31:59.280 --> 00:32:04.770 that are not 5.111, but in 5.111, you know about pKa's. 00:32:04.770 --> 00:32:08.310 So what I want you to do is later in life 00:32:08.310 --> 00:32:10.670 when you're in a class and pKa's come up 00:32:10.670 --> 00:32:13.210 and everyone else in the class is like, I don't know. 00:32:13.210 --> 00:32:17.080 You're like I took 5.111. 00:32:17.080 --> 00:32:18.350 I can answer that. 00:32:18.350 --> 00:32:20.990 That makes me very happy. 00:32:20.990 --> 00:32:23.000 So pKa's. 00:32:23.000 --> 00:32:27.290 so pKa is minus the log of the Ka. 00:32:27.290 --> 00:32:29.320 That's easy to remember. 00:32:29.320 --> 00:32:32.970 We already talked about the relationship of Ka 00:32:32.970 --> 00:32:35.980 with strong acids or weak acids. 00:32:35.980 --> 00:32:40.060 The lower the value of the Ka the higher 00:32:40.060 --> 00:32:41.600 the value of the pKa. 00:32:41.600 --> 00:32:44.000 That's just out of that expression. 00:32:44.000 --> 00:32:50.990 So the higher the pKa means what about the acid? 00:32:50.990 --> 00:32:54.330 Think about what you know about Ka to answer this question. 00:33:14.230 --> 00:33:14.970 All right. 00:33:14.970 --> 00:33:15.815 10 more seconds. 00:33:30.410 --> 00:33:32.580 All right. 00:33:32.580 --> 00:33:35.300 So that is correct. 00:33:35.300 --> 00:33:37.130 So we have a weaker acid. 00:33:37.130 --> 00:33:43.270 So if we have a low Ka, that means 00:33:43.270 --> 00:33:48.250 that it is a weak acid, and then the higher value of Ka. 00:33:48.250 --> 00:33:51.220 So the higher the Ka, that's going 00:33:51.220 --> 00:33:57.130 to mean the lower the value or the weaker of the acid. 00:33:57.130 --> 00:34:00.870 So just remember the relationship from the equation, 00:34:00.870 --> 00:34:03.090 and think about it, and you can think about the value 00:34:03.090 --> 00:34:05.560 of Ka, products over reactants. 00:34:05.560 --> 00:34:07.190 You might have a lot of products. 00:34:07.190 --> 00:34:10.489 That means a lot of ionization and a stronger acid 00:34:10.489 --> 00:34:15.510 and fewer products, that means it's weaker. 00:34:15.510 --> 00:34:18.320 So let's look at some tables, and I just 00:34:18.320 --> 00:34:21.969 put the values that are with the arrows in your notes. 00:34:21.969 --> 00:34:23.980 I didn't put the entire table. 00:34:23.980 --> 00:34:27.870 The tables are in the book, and this is page one of the table, 00:34:27.870 --> 00:34:29.860 so there's a lot of values here. 00:34:29.860 --> 00:34:31.420 So this has the acid. 00:34:31.420 --> 00:34:34.760 It tells you what the HA term is, what the A minus, 00:34:34.760 --> 00:34:37.679 so what the weak acid is, what the conjugate base is. 00:34:37.679 --> 00:34:40.139 It gives you the Ka and the pKa. 00:34:40.139 --> 00:34:41.739 And so you can see the relationship 00:34:41.739 --> 00:34:44.690 between Ka and pKa. 00:34:44.690 --> 00:34:49.300 So up here, HI is at the top of this table. 00:34:49.300 --> 00:34:52.370 So that probably means it's the strongest or the weakest. 00:34:52.370 --> 00:34:53.270 Which do you think? 00:34:53.270 --> 00:34:55.955 Is this the strongest or the weakest? 00:34:55.955 --> 00:34:56.830 You just yell it out. 00:34:56.830 --> 00:34:57.746 AUDIENCE: Strongest. 00:34:57.746 --> 00:35:00.040 CATHERINE DRENNAN: It is the strongest. 00:35:00.040 --> 00:35:00.730 Right. 00:35:00.730 --> 00:35:04.200 So it has Ka value that is much, much, much, much, much, much, 00:35:04.200 --> 00:35:07.570 much, much, much, much, much greater than 1. 00:35:07.570 --> 00:35:12.510 And it has a very, very, very negative tiny, tiny pKa value. 00:35:12.510 --> 00:35:15.180 So this is a super strong acid. 00:35:15.180 --> 00:35:16.851 In fact, do not use that. 00:35:16.851 --> 00:35:19.350 There's no reason really you would ever want to be using it. 00:35:19.350 --> 00:35:21.540 It is not a good thing to play with. 00:35:21.540 --> 00:35:22.040 All right. 00:35:22.040 --> 00:35:28.000 So HCl is used more often in pH-ing things. 00:35:28.000 --> 00:35:30.740 Is this a strong or weak acid? 00:35:30.740 --> 00:35:32.286 AUDIENCE: Strong. 00:35:32.286 --> 00:35:34.150 CATHERINE DRENNAN: It's also strong. 00:35:34.150 --> 00:35:38.500 It's K or Ka is also greater than 1, 00:35:38.500 --> 00:35:40.390 but not as strong as this. 00:35:40.390 --> 00:35:43.460 We have 10 to the seventh, and that one, gosh, 00:35:43.460 --> 00:35:45.790 I should bring my glasses, 10 to the 11th. 00:35:45.790 --> 00:35:46.860 That's super strong. 00:35:46.860 --> 00:35:48.070 That's still pretty strong. 00:35:48.070 --> 00:35:48.570 All right. 00:35:48.570 --> 00:35:50.880 So let's look down here now. 00:35:50.880 --> 00:35:54.782 Tell me, is this a strong or weak acid? 00:35:54.782 --> 00:35:56.090 AUDIENCE: Weak. 00:35:56.090 --> 00:35:58.920 CATHERINE DRENNAN: That is weak acid. 00:35:58.920 --> 00:36:06.140 The Ka is less than 1 here, and I think that's a minus 2. 00:36:06.140 --> 00:36:09.650 And the pKa value, now we're out of the negative number, 00:36:09.650 --> 00:36:11.630 so it's on the bigger side. 00:36:11.630 --> 00:36:14.710 And down here, is this strong or weak? 00:36:14.710 --> 00:36:16.000 AUDIENCE: [INAUDIBLE]. 00:36:16.000 --> 00:36:17.550 CATHERINE DRENNAN: Also weak. 00:36:17.550 --> 00:36:19.540 And it's even weaker than this one. 00:36:19.540 --> 00:36:25.650 It's like 10 to the minus 4, and pKa value is 3.75. 00:36:25.650 --> 00:36:28.800 So you see you can look at the Ka values 00:36:28.800 --> 00:36:31.440 and think about whether it's a strong or weak acid. 00:36:31.440 --> 00:36:33.940 You can also look at the pKa values. 00:36:33.940 --> 00:36:36.980 This is really, really small negative value. 00:36:36.980 --> 00:36:38.960 This is a bigger value down here. 00:36:38.960 --> 00:36:41.320 And this is not been the weakest acid. 00:36:41.320 --> 00:36:46.470 There's a whole other page of tables for acids, lots and lots 00:36:46.470 --> 00:36:48.220 of acids. 00:36:48.220 --> 00:36:50.510 Less bases. 00:36:50.510 --> 00:36:55.600 There are a few, and you will see this space quite often, 00:36:55.600 --> 00:36:57.640 NH3. 00:36:57.640 --> 00:37:00.010 So we have a base in water. 00:37:00.010 --> 00:37:03.730 The base accepts a hydrogen ion or proton from the water, 00:37:03.730 --> 00:37:06.030 forming NH4 plus. 00:37:06.030 --> 00:37:10.120 And then after water loses its hydrogen ion, 00:37:10.120 --> 00:37:13.120 it forms OH minus. 00:37:13.120 --> 00:37:17.260 So the equilibrium expression or the K 00:37:17.260 --> 00:37:23.560 for this base in water problem is called the base ionization 00:37:23.560 --> 00:37:26.040 constant, or Kb. 00:37:26.040 --> 00:37:29.560 And we can write that expression here. 00:37:29.560 --> 00:37:32.060 We have the ammonium ion concentration 00:37:32.060 --> 00:37:35.040 times the hydroxide ion concentration 00:37:35.040 --> 00:37:37.740 over the concentration of ammonia. 00:37:37.740 --> 00:37:40.220 Again, water is not in the expression. 00:37:40.220 --> 00:37:43.130 It stays pretty much pure throughout this entire thing. 00:37:43.130 --> 00:37:44.500 It's the solvent. 00:37:44.500 --> 00:37:47.480 And so this is our expression for Kb. 00:37:47.480 --> 00:37:50.570 And if you're writing an expression for Kb, 00:37:50.570 --> 00:37:53.040 you should always make sure, check yourself 00:37:53.040 --> 00:37:56.380 that you're putting hydroxide ion concentration in there. 00:37:56.380 --> 00:38:00.270 If it is a base in water, it should be forming hydroxide ion 00:38:00.270 --> 00:38:01.410 concentration. 00:38:01.410 --> 00:38:04.180 If you start writing a Kb and you have hydronium ion 00:38:04.180 --> 00:38:07.310 concentration in there, you want to stop and rethink 00:38:07.310 --> 00:38:09.320 what you're doing. 00:38:09.320 --> 00:38:12.690 So in this case, we also have a weak base. 00:38:12.690 --> 00:38:18.670 1.8 times 10 to the minus 5 is a small number for Kb. 00:38:18.670 --> 00:38:21.520 It's a small equilibrium number, so that means 00:38:21.520 --> 00:38:23.130 you're not a lot of products. 00:38:23.130 --> 00:38:27.360 Not a lot ionized when you put this weak base in water. 00:38:27.360 --> 00:38:30.730 So only a tiny amount of NH3 ionizes 00:38:30.730 --> 00:38:35.150 to NH4 plus and OH in solution, so this is what 00:38:35.150 --> 00:38:39.440 they call moderately weak base. 00:38:39.440 --> 00:38:45.170 So as we saw before, you can have generic expressions 00:38:45.170 --> 00:38:46.800 for a base in water. 00:38:46.800 --> 00:38:51.440 We can write B aqueous plus water goes to BH plus. 00:38:51.440 --> 00:38:54.810 The base accepts a hydrogen ion or proton, 00:38:54.810 --> 00:38:58.550 and the water loses one forming OH minus. 00:38:58.550 --> 00:39:00.480 We can also write the expression that 00:39:00.480 --> 00:39:05.690 often exists from the conjugate of a weak acid, 00:39:05.690 --> 00:39:07.170 and this is a weak base. 00:39:07.170 --> 00:39:11.620 So A minus plus water goes to HA plus hydroxide ion 00:39:11.620 --> 00:39:13.050 concentration. 00:39:13.050 --> 00:39:15.690 So either of these are generic expressions 00:39:15.690 --> 00:39:20.820 that you can write for a base in water. 00:39:20.820 --> 00:39:24.230 So in terms of the definitions, it's the same. 00:39:24.230 --> 00:39:28.140 You would say a strong base is something that ionizes 00:39:28.140 --> 00:39:31.720 almost completely to give OH. 00:39:31.720 --> 00:39:34.640 There aren't a lot of examples of strong bases. 00:39:34.640 --> 00:39:36.800 Most of the ones you'll see in your class 00:39:36.800 --> 00:39:40.030 are things like sodium hydroxide. 00:39:40.030 --> 00:39:41.480 Yes, that is hydroxide. 00:39:41.480 --> 00:39:44.480 That's a strong base, and if you put it in water, 00:39:44.480 --> 00:39:46.830 you should definitely form a lot of hydroxide. 00:39:46.830 --> 00:39:50.100 So they're not a whole lot of examples there. 00:39:50.100 --> 00:39:53.250 So they're not all those tables. 00:39:53.250 --> 00:39:55.240 It's not like the acids. 00:39:55.240 --> 00:39:58.100 But there are some terms that you still need to know. 00:39:58.100 --> 00:40:04.600 So pKb equals minus log of the Kb. 00:40:04.600 --> 00:40:09.730 And again, the larger the value for Kb, the stronger the base. 00:40:09.730 --> 00:40:14.100 Again, it tells you you have a lot that have ionized. 00:40:14.100 --> 00:40:18.090 And because of this relationship of this equation, the larger 00:40:18.090 --> 00:40:22.677 the pKb the weaker the base. 00:40:22.677 --> 00:40:24.260 Because if you have a big number here, 00:40:24.260 --> 00:40:27.750 you're going to have a small number there. 00:40:27.750 --> 00:40:33.050 So now, let's talk about conjugate acids 00:40:33.050 --> 00:40:34.690 and their bases. 00:40:34.690 --> 00:40:37.370 This is super important for buffers 00:40:37.370 --> 00:40:42.060 that, hopefully, we'll get to in class on Friday. 00:40:42.060 --> 00:40:47.110 So the stronger the acid, the weaker its conjugate base. 00:40:47.110 --> 00:40:51.600 The stronger the base, the weaker its conjugate acid. 00:40:51.600 --> 00:40:54.150 And here we have HCl, which we determined 00:40:54.150 --> 00:40:58.910 was a strong acid a little while ago, giving up its hydrogen 00:40:58.910 --> 00:41:06.450 ion to water, forming hydronium ion concentration and Cl minus. 00:41:06.450 --> 00:41:09.320 Cl minus is not a very good conjugate base. 00:41:09.320 --> 00:41:10.890 It's not a good base. 00:41:10.890 --> 00:41:14.460 So if we look at this table when we have a strong acid, 00:41:14.460 --> 00:41:18.080 its conjugate it is going to be ineffective as a base. 00:41:18.080 --> 00:41:20.930 You're basically not pushing that equilibrium back 00:41:20.930 --> 00:41:22.710 at all, the other direction. 00:41:22.710 --> 00:41:26.470 It's completely ionized, and it stays that way. 00:41:26.470 --> 00:41:29.840 But if you have a moderately weak acid, 00:41:29.840 --> 00:41:33.700 you're going to have a very weak base, a very weak acid, 00:41:33.700 --> 00:41:37.770 you'll have a moderately weak conjugate base, a strong base 00:41:37.770 --> 00:41:40.910 and you'll have something that's ineffective as an acid. 00:41:40.910 --> 00:41:44.970 So they are inversely related to each other. 00:41:44.970 --> 00:41:48.610 So let's think about why this would be true. 00:41:48.610 --> 00:41:57.070 And this relationship holds Ka times Kb equals Kw. 00:41:57.070 --> 00:42:01.930 And we know that Kw is 1.0 times 10 to the minus 00:42:01.930 --> 00:42:04.590 14th at room temperature. 00:42:04.590 --> 00:42:09.920 And if we put logs and then minus logs by everything, 00:42:09.920 --> 00:42:15.330 we can derive this expression, which is the pKa plus the pKb 00:42:15.330 --> 00:42:20.540 equals the pKw equals 14.00. 00:42:20.540 --> 00:42:25.200 So you can't have an acid and its conjugate base 00:42:25.200 --> 00:42:26.630 both be strong. 00:42:26.630 --> 00:42:30.950 You can't have a base in its conjugate acid both be strong. 00:42:30.950 --> 00:42:34.480 The pK's need to add up to 14. 00:42:34.480 --> 00:42:37.540 So if you have something that's a good acid, 00:42:37.540 --> 00:42:42.370 then its conjugate base is not going to be particularly good. 00:42:42.370 --> 00:42:46.840 The pKa and the pKb must add up to 14. 00:42:46.840 --> 00:42:48.930 If you have something that's a good base, 00:42:48.930 --> 00:42:51.740 its conjugate acid is not going to be that good. 00:42:51.740 --> 00:42:57.520 So these are connected to each other. 00:42:57.520 --> 00:43:00.770 So we can think about, then, the strong acids 00:43:00.770 --> 00:43:03.880 and the strong bases again. 00:43:03.880 --> 00:43:06.680 So we talk about equilibrium, but really this 00:43:06.680 --> 00:43:09.650 is pushing the equilibrium pretty much to completion. 00:43:09.650 --> 00:43:13.530 If it's a strong acid in water, however much strong acid 00:43:13.530 --> 00:43:17.650 you put in is how much hydronium ion concentration you get out. 00:43:17.650 --> 00:43:19.990 A strong base is going to give you 00:43:19.990 --> 00:43:23.360 that amount of hydroxide ion concentration. 00:43:23.360 --> 00:43:27.150 Strong acids and bases push the equilibrium pretty much 00:43:27.150 --> 00:43:29.270 completely toward ionization. 00:43:29.270 --> 00:43:32.350 We have these numbers of 10 to the 11th, 10 to the seventh. 00:43:32.350 --> 00:43:34.950 These are hugely over here. 00:43:34.950 --> 00:43:39.060 We're forming almost ionizing completely. 00:43:39.060 --> 00:43:43.620 Now, for weak acids and bases, it's very different. 00:43:43.620 --> 00:43:47.820 Here the equilibrium you are going back and forth. 00:43:47.820 --> 00:43:50.150 You have this dynamic equilibrium. 00:43:50.150 --> 00:43:55.810 The acid in water is forming hydronium ions and an A minus, 00:43:55.810 --> 00:44:00.160 but a minus is also a somewhat good, weak base 00:44:00.160 --> 00:44:03.360 pushing the equilibrium back the other way. 00:44:03.360 --> 00:44:08.330 So in this case, we have a back and forth between the forward 00:44:08.330 --> 00:44:10.300 and the reverse. 00:44:10.300 --> 00:44:12.385 So if you have very weak, you have moderate, 00:44:12.385 --> 00:44:14.720 you have moderate, you have very weak, 00:44:14.720 --> 00:44:17.920 and this is what's important for forming buffers, 00:44:17.920 --> 00:44:21.650 and buffers are really important. 00:44:21.650 --> 00:44:26.570 Let's see if we can get to one of these types of problems 00:44:26.570 --> 00:44:31.250 because they're five we need to get to in this unit. 00:44:31.250 --> 00:44:33.630 And there are only five. 00:44:33.630 --> 00:44:35.850 And people will say salt and water is another, 00:44:35.850 --> 00:44:37.490 but salt and water just breaks down 00:44:37.490 --> 00:44:39.490 into weak acid and weak bases. 00:44:39.490 --> 00:44:42.580 So everyone can learn how to do five types of problems, 00:44:42.580 --> 00:44:45.270 so this is very doable. 00:44:45.270 --> 00:44:45.770 All right. 00:44:45.770 --> 00:44:48.560 So let's just look at equilibrium of weak acids 00:44:48.560 --> 00:44:50.790 and we'll save weak bases for last time. 00:44:50.790 --> 00:44:55.480 So a weak acid is vitamin C, and I brought some vitamin C here. 00:44:55.480 --> 00:44:59.420 I tried to do a demo once and discovered that vitamin C, 00:44:59.420 --> 00:45:01.510 it's really coated well, so it does not 00:45:01.510 --> 00:45:03.980 dissolve until it hits the acid of your stomach, 00:45:03.980 --> 00:45:05.820 so I could not dissolve it. 00:45:05.820 --> 00:45:08.490 So I'll just hold this up right here. 00:45:08.490 --> 00:45:12.980 But if we had a 500 milligram tablet, which 00:45:12.980 --> 00:45:17.610 I think is what this is and if I had 100 mils of water 00:45:17.610 --> 00:45:19.360 and if this wasn't coated so there's 00:45:19.360 --> 00:45:23.710 no way you can dissolve it, then I could calculate the pH. 00:45:23.710 --> 00:45:25.070 So how am I going to do this? 00:45:25.070 --> 00:45:29.280 I'm given the Ka, I'm told the number of milligrams, 00:45:29.280 --> 00:45:31.370 and I'm told the volume of water. 00:45:31.370 --> 00:45:35.110 So the first thing you want to do is calculate molarity. 00:45:35.110 --> 00:45:39.970 So you want convert grams to moles or milligrams 00:45:39.970 --> 00:45:41.840 to grams to moles. 00:45:41.840 --> 00:45:45.389 And then you want to use your volume, and you have 100 mils, 00:45:45.389 --> 00:45:46.680 but we're going to do molarity. 00:45:46.680 --> 00:45:49.600 So we want to convert milliliters to liters. 00:45:49.600 --> 00:45:56.680 And we can calculate 0.0284 molar moles per liter. 00:45:56.680 --> 00:45:59.560 Then we can write our expression, and if you want to, 00:45:59.560 --> 00:46:02.290 you can just write HA here and A minus. 00:46:02.290 --> 00:46:04.620 You don't have to write out the whole thing 00:46:04.620 --> 00:46:07.710 if you don't want to. 00:46:07.710 --> 00:46:08.690 All right. 00:46:08.690 --> 00:46:10.990 So here is the expression again. 00:46:10.990 --> 00:46:13.960 Now, just as we saw with chemical equilibrium, 00:46:13.960 --> 00:46:17.970 we can write this table talking about the initial molarity. 00:46:17.970 --> 00:46:22.550 So we have a weak acid we have no hydronium ion concentration. 00:46:22.550 --> 00:46:26.110 We have no weak conjugate base over here, 00:46:26.110 --> 00:46:29.690 so the change then is going to be the constant, the molarity 00:46:29.690 --> 00:46:31.500 that we had, and these are change 00:46:31.500 --> 00:46:34.580 in molarities, so don't put moles or other things here, 00:46:34.580 --> 00:46:39.100 molarity here, minus x, that's what you have in equilibrium, 00:46:39.100 --> 00:46:42.880 plus x plus x. 00:46:42.880 --> 00:46:46.510 So we can write our expression now for Ka. 00:46:46.510 --> 00:46:48.910 We're given the value Ka, and we know 00:46:48.910 --> 00:46:50.730 how to write an expression. 00:46:50.730 --> 00:46:53.000 We have our hydronium ion concentration, 00:46:53.000 --> 00:46:57.180 our conjugate base over here over our conjugate acid. 00:46:57.180 --> 00:47:04.170 This is equal to x squared 0.0284 minus x. 00:47:04.170 --> 00:47:07.220 Now, if you want to with these problems, 00:47:07.220 --> 00:47:09.690 you can make an assumption that x 00:47:09.690 --> 00:47:12.450 is going to be small and then not have 00:47:12.450 --> 00:47:14.710 to use the quadratic equation, but you do 00:47:14.710 --> 00:47:16.460 need to check your assumption. 00:47:16.460 --> 00:47:18.870 But I'll show you how to do it with an assumption, 00:47:18.870 --> 00:47:22.620 so we're going to assume x is small, and this value, the x, 00:47:22.620 --> 00:47:23.990 will drop out. 00:47:23.990 --> 00:47:26.080 So we can rewrite this expression 00:47:26.080 --> 00:47:31.660 as x squared over just the concentration we started with. 00:47:31.660 --> 00:47:35.330 And then we can solve for x. 00:47:35.330 --> 00:47:40.170 And x, in that case, is point 0.00151, but really 00:47:40.170 --> 00:47:41.750 two significant figures. 00:47:41.750 --> 00:47:44.350 Our Ka is just 2. 00:47:44.350 --> 00:47:46.590 Now, we can check the assumption. 00:47:46.590 --> 00:47:48.350 And we're going to check the assumption 00:47:48.350 --> 00:47:50.730 that this is, in fact, small. 00:47:50.730 --> 00:47:56.950 And if it's less than 5%, then we can use that. 00:47:56.950 --> 00:48:00.320 So here this is the x we calculated. 00:48:00.320 --> 00:48:03.470 Here is the amount times 100% gives us 00:48:03.470 --> 00:48:07.260 5.3%, which is more than 5. 00:48:07.260 --> 00:48:09.800 5 is the magic number for the course, 00:48:09.800 --> 00:48:12.499 and so then we have to use the quadratic equation. 00:48:12.499 --> 00:48:14.290 Now, a lot of you probably have calculators 00:48:14.290 --> 00:48:16.700 that can work with quadratic equation, 00:48:16.700 --> 00:48:18.240 so you don't really care, but if you 00:48:18.240 --> 00:48:20.860 want to check the assumption, you can, and sometimes 00:48:20.860 --> 00:48:22.700 we'll need to check it. 00:48:22.700 --> 00:48:25.190 So this value, this percent here, 00:48:25.190 --> 00:48:28.210 is sometimes called percent ionization 00:48:28.210 --> 00:48:31.170 because it's x over the amount you started with. 00:48:31.170 --> 00:48:35.090 It's the percent that ionized or percent deprotonated. 00:48:35.090 --> 00:48:37.240 If this is an acid, it's the amount 00:48:37.240 --> 00:48:39.660 of hydronium, the amount that deprotonated 00:48:39.660 --> 00:48:41.309 over what you started with. 00:48:41.309 --> 00:48:43.600 So sometimes you're asked to do this even if you're not 00:48:43.600 --> 00:48:46.440 checking any assumptions. 00:48:46.440 --> 00:48:46.950 All right. 00:48:46.950 --> 00:48:49.560 So we got to end with if a quicker question. 00:48:49.560 --> 00:48:52.540 We get here this is really two significant figures. 00:48:52.540 --> 00:48:55.430 So why don't you tell me how many significant figures 00:48:55.430 --> 00:48:57.445 are in your answer for pH. 00:49:20.830 --> 00:49:21.330 All right. 00:49:21.330 --> 00:49:22.120 10 more seconds. 00:49:42.890 --> 00:49:47.900 So let's take a look at the answer here. 00:49:47.900 --> 00:49:50.360 So there's the answer. 00:49:50.360 --> 00:49:52.930 So this had two significant figures, 00:49:52.930 --> 00:49:55.190 which means you get two significant figures 00:49:55.190 --> 00:49:56.912 after the decimal point. 00:49:56.912 --> 00:49:58.870 So maybe we'll have one of these in the clicker 00:49:58.870 --> 00:50:05.250 competition on Friday, and we'll do our weak bases next time. 00:50:05.250 --> 00:50:08.716 So again, we've been studying acid base. 00:50:11.670 --> 00:50:17.940 And there are only five types of acid-base problems, weak acid 00:50:17.940 --> 00:50:22.510 in water, which we already did, check, weak basin water, which 00:50:22.510 --> 00:50:24.980 we're going to do right now, and as soon as we're 00:50:24.980 --> 00:50:27.580 done doing week base in water, I'm 00:50:27.580 --> 00:50:30.470 going to explain to you how salt and water are just 00:50:30.470 --> 00:50:33.300 weak acid in water or weak base in water problems. 00:50:33.300 --> 00:50:35.800 So you already know how to do them as soon as they teach you 00:50:35.800 --> 00:50:37.680 about weak bases. 00:50:37.680 --> 00:50:40.820 And then we're going to move on and do buffers. 00:50:40.820 --> 00:50:42.510 And then next week we're going to do 00:50:42.510 --> 00:50:48.090 strong acids and strong bases, and then you'll have all five. 00:50:48.090 --> 00:50:52.820 You already have enough that after today's lecture, 00:50:52.820 --> 00:50:55.040 you can do, I think, all the problems 00:50:55.040 --> 00:50:57.720 set 7 except for the last two questions, 00:50:57.720 --> 00:51:01.030 I believe, or at least a large fraction of problem set 7. 00:51:01.030 --> 00:51:07.350 I will warn you that acid-base problems take a lot of writing 00:51:07.350 --> 00:51:09.290 and a lot of time to work. 00:51:09.290 --> 00:51:14.310 One problem often has five or six parts to it, 00:51:14.310 --> 00:51:16.970 and they're all time-consuming part pretty much. 00:51:16.970 --> 00:51:20.450 So don't leave problem set 7 to the last minute. 00:51:20.450 --> 00:51:23.716 That would be a mistake on this particular problem set. 00:51:27.460 --> 00:51:29.720 Weak bases. 00:51:29.720 --> 00:51:33.910 Acid-base type problem 2. 00:51:33.910 --> 00:51:41.370 So in this example, we have ammonia, NH3, in water, 00:51:41.370 --> 00:51:44.880 and we measured the pH of some solutions 00:51:44.880 --> 00:51:47.100 before and saw they were basic. 00:51:47.100 --> 00:51:49.800 We had a pH of, I think, 12 last time. 00:51:49.800 --> 00:51:53.780 And so this conjugate base goes to a conjugate acid. 00:51:53.780 --> 00:51:57.550 So the base accepts a hydrogen ion or proton from water, 00:51:57.550 --> 00:52:00.470 becomes NH4 plus, and the water that 00:52:00.470 --> 00:52:03.880 lost its hydrogen ion becomes OH minus, 00:52:03.880 --> 00:52:06.220 and that is a base in water problem 00:52:06.220 --> 00:52:09.690 because you're forming hydroxide ions. 00:52:09.690 --> 00:52:13.730 For a base in water, you're talking about the equilibrium 00:52:13.730 --> 00:52:16.720 constant for that base in water, which has a special name 00:52:16.720 --> 00:52:19.170 KB, B for base. 00:52:19.170 --> 00:52:22.520 And it's important to remember the A's and B's 00:52:22.520 --> 00:52:25.310 on the equilibrium constant because it's always 00:52:25.310 --> 00:52:27.220 checking your work. 00:52:27.220 --> 00:52:28.830 Is this a base in water problem. 00:52:28.830 --> 00:52:32.380 People sometimes try to apply Ka's when they should be doing 00:52:32.380 --> 00:52:33.020 Kb's. 00:52:33.020 --> 00:52:35.670 So pay attention to basin water. 00:52:35.670 --> 00:52:37.930 We're thinking about Kb. 00:52:37.930 --> 00:52:41.170 So here if we're going to calculate the pH of a solution, 00:52:41.170 --> 00:52:45.310 we have molarity of 0.15, and room temperature, 00:52:45.310 --> 00:52:47.500 pretty much everything is at room temperature. 00:52:47.500 --> 00:52:49.160 So whenever you're asked to calculate 00:52:49.160 --> 00:52:51.460 the pH of a weak base in water, you 00:52:51.460 --> 00:52:54.580 want to think about at equilibrium, what's 00:52:54.580 --> 00:52:57.610 the condition now, what will be the condition, what's 00:52:57.610 --> 00:53:00.790 the change, and what will be the condition at equilibrium. 00:53:00.790 --> 00:53:03.050 And so you can make this table. 00:53:03.050 --> 00:53:04.820 You can write out the expression. 00:53:04.820 --> 00:53:06.500 Again, you can forget about water. 00:53:06.500 --> 00:53:07.730 Water is our solvent. 00:53:07.730 --> 00:53:10.270 It's not going to be showing up. 00:53:10.270 --> 00:53:14.020 And then put in our initial molarity, 0.15. 00:53:14.020 --> 00:53:17.030 And we put zeros in the other categories. 00:53:17.030 --> 00:53:20.313 And why don't you try the rest? 00:53:44.930 --> 00:53:46.728 Is it slowing down? 00:53:46.728 --> 00:53:49.352 SAM: [INAUDIBLE] answers are really quick. 00:53:49.352 --> 00:53:50.560 CATHERINE DRENNAN: All right. 00:53:50.560 --> 00:53:51.835 Let's just do 10 more seconds. 00:54:05.981 --> 00:54:06.480 Yup. 00:54:06.480 --> 00:54:07.970 Excellent. 00:54:07.970 --> 00:54:11.990 Sam told me everyone responded really quickly. 00:54:11.990 --> 00:54:14.230 So that is, in fact, what you're going to do. 00:54:14.230 --> 00:54:16.890 We'll put that up here as well. 00:54:16.890 --> 00:54:21.190 So we lose some of this minus x. 00:54:21.190 --> 00:54:24.540 So at equilibrium, we have point 1.5 minus x. 00:54:24.540 --> 00:54:30.560 And we get plus x here and plus x there. 00:54:30.560 --> 00:54:35.570 Now, we can write our Kb for our base in water, its products, 00:54:35.570 --> 00:54:40.150 the conjugate acid, NH4 plus, times the concentration 00:54:40.150 --> 00:54:43.190 of hydroxide ions over NH3. 00:54:43.190 --> 00:54:44.710 Again, water is the solvent. 00:54:44.710 --> 00:54:46.950 It's not in the equation. 00:54:46.950 --> 00:54:50.380 And then we can write it out-- this is x. 00:54:50.380 --> 00:54:53.240 That's x, so we have x squared. 00:54:53.240 --> 00:54:56.740 And then the change in the amount of the weak base, 00:54:56.740 --> 00:55:00.880 when it's in water, is 0.15 minus x. 00:55:00.880 --> 00:55:05.350 So at this point, you can either use the quadratic equation, 00:55:05.350 --> 00:55:08.830 or you can make an assumption that x is going 00:55:08.830 --> 00:55:11.370 to be small compared to 0.5. 00:55:11.370 --> 00:55:13.650 We don't want to make the assumption up here. 00:55:13.650 --> 00:55:17.060 We want to get to this point before we try the assumption, 00:55:17.060 --> 00:55:19.770 and you always need to check your assumptions 00:55:19.770 --> 00:55:22.900 to make sure they are correct. 00:55:22.900 --> 00:55:27.040 But if we use the assumption here just to simplify the math. 00:55:27.040 --> 00:55:29.690 And so the assumption is that this x is small, 00:55:29.690 --> 00:55:33.530 so we can drop that x minus x out, 00:55:33.530 --> 00:55:41.270 and then we can calculate that x is 0.00164. 00:55:41.270 --> 00:55:44.870 And then we can check the assumption, 00:55:44.870 --> 00:55:46.847 and that is another clicker question. 00:56:35.011 --> 00:56:35.510 All right. 00:56:35.510 --> 00:56:36.450 10 more seconds. 00:56:52.200 --> 00:56:53.950 All right. 00:56:53.950 --> 00:56:56.010 It is number 1. 00:56:56.010 --> 00:56:58.760 So here you're checking the assumption and the way 00:56:58.760 --> 00:57:02.500 that you check the assumption is that you put x that you've 00:57:02.500 --> 00:57:07.410 calculated by simplifying it, divide it by the number 00:57:07.410 --> 00:57:11.650 that you're asking is it smaller than, and then times 100 00:57:11.650 --> 00:57:14.140 because our rule is 5%. 00:57:14.140 --> 00:57:18.460 So if this value is greater than 5% of this value, 00:57:18.460 --> 00:57:20.300 you need to use the quadratic. 00:57:20.300 --> 00:57:23.160 If it's less than 5%, then you can go ahead 00:57:23.160 --> 00:57:24.790 and use your assumption. 00:57:24.790 --> 00:57:26.980 And so this is the assumption we're talking about, 00:57:26.980 --> 00:57:29.840 that this number is under 5%. 00:57:29.840 --> 00:57:37.250 And for weak acids and bases, it very often is less than 5% 00:57:37.250 --> 00:57:40.450 because they're weak, so there's not a lot of ionization. 00:57:40.450 --> 00:57:45.940 And this is often referred to as percentage ionization as well. 00:57:45.940 --> 00:57:46.440 All right. 00:57:46.440 --> 00:57:50.130 So our checking assumption, again, 00:57:50.130 --> 00:57:58.960 that x 0.00164 divided by 0.15 times 100% is 1%, 00:57:58.960 --> 00:58:04.870 1.1, that's less than 5, so the assumption is OK. 00:58:04.870 --> 00:58:09.670 And then we can calculate pOH because this 00:58:09.670 --> 00:58:13.350 is a weak base in water, so the x that we calculated 00:58:13.350 --> 00:58:17.140 is the amount of hydroxide ion in solution. 00:58:17.140 --> 00:58:22.050 So we calculate pOH, and we get 2.79. 00:58:22.050 --> 00:58:24.000 And that's two significant figures, 00:58:24.000 --> 00:58:26.070 everything we had after the decimal 00:58:26.070 --> 00:58:29.610 because everything that we had was two significant figures. 00:58:29.610 --> 00:58:31.780 And so this is two significant figures, 00:58:31.780 --> 00:58:34.660 two significant figures after the decimal point. 00:58:34.660 --> 00:58:36.720 And then you need to calculate pH 00:58:36.720 --> 00:58:38.550 because the problem asked for pH. 00:58:38.550 --> 00:58:40.750 So this is, again, at room temperature. 00:58:40.750 --> 00:58:47.490 So we can use 14 minus 2.79 is 11.21. 00:58:47.490 --> 00:58:49.420 That's our pH. 00:58:49.420 --> 00:58:51.640 And don't make the mistake of stopping here 00:58:51.640 --> 00:58:56.690 forgetting that x is hydroxide instead of hydronium ion 00:58:56.690 --> 00:59:02.630 and tell me that the pH of my weak base in solution is pH 2. 00:59:02.630 --> 00:59:05.977 So one of the things that's really good about this unit 00:59:05.977 --> 00:59:08.060 is that there are some good checks that you've got 00:59:08.060 --> 00:59:09.830 the right answer at the end. 00:59:09.830 --> 00:59:14.110 If you're talking about a base in solution, 00:59:14.110 --> 00:59:16.360 you should have a pH above what value? 00:59:16.360 --> 00:59:17.306 AUDIENCE: 7. 00:59:17.306 --> 00:59:18.690 CATHERINE DRENNAN: About 7. 00:59:18.690 --> 00:59:20.980 So it should be on the basic side of neutral. 00:59:20.980 --> 00:59:23.890 pH 7 is neutral, so it should be above 7. 00:59:23.890 --> 00:59:26.600 And so if this was your answer for pH, 00:59:26.600 --> 00:59:28.570 that wouldn't make a lot of sense. 00:59:28.570 --> 00:59:30.050 So always check at the end. 00:59:30.050 --> 00:59:33.430 And it's fine if you get to an exam and you get to the end 00:59:33.430 --> 00:59:35.460 and you did something wrong and you 00:59:35.460 --> 00:59:38.290 realize that your answer doesn't make any sense, if you write, 00:59:38.290 --> 00:59:40.350 this answer doesn't make any sense, 00:59:40.350 --> 00:59:42.730 but I don't have time to figure out what I gave wrong, 00:59:42.730 --> 00:59:46.970 you will get points for recognizing that that is not 00:59:46.970 --> 00:59:48.380 a valid answer. 00:59:48.380 --> 00:59:50.520 Because it's a weak acid problem and you 00:59:50.520 --> 00:59:52.850 have a basic pH or vice versa. 00:59:52.850 --> 00:59:54.005 So keep that in mind. 00:59:54.005 --> 00:59:55.630 There's lots of partial credit. 00:59:55.630 --> 00:59:58.800 Grading acid-base problems on exams 00:59:58.800 --> 01:00:04.770 is a whole new fun adventure that the TAs have no idea what 01:00:04.770 --> 01:00:06.090 is going to be happening. 01:00:06.090 --> 01:00:09.020 But I'll be right with you there for 10 hours of grading, 01:00:09.020 --> 01:00:10.300 and we'll have a good time. 01:00:10.300 --> 01:00:12.520 Write neatly, please.