Lecture 11. Buffered Solutions (Buffers) Pt. 2.
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ChemistryThin filmChemical reactionChemical elementSolutionMaßanalyseChemische SyntheseTool steelConcentrateDetection limitRapidBurettePortable Document FormatErlenmeyerkolbenTitrationBeerSetzen <Verfahrenstechnik>Grading (tumors)Lecture/Conference
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AcidHydroxideTitrationBase (chemistry)WeaknessAgeingLecture/Conference
Transcript: English(auto-generated)
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Okay. Can I have everyone's attention please? So let's go ahead and start I wanted to remind you that your midterm scores are already posted on
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the class website as we speak, your exams are being scanned and within a few days you will receive a PDF file of your graded exam. All right? So if you have any questions about the grading, you should wait until you receive a PDF file of your scanned exam
00:43
and then take a look at it but in the meantime, it is important that you go to discussion this week because during discussion this week, we will actually go through the answers from the exam. And I I want to remind you guys that this is important because this is the first midterm
01:01
and I want to make sure that you get feedback on your performance on the exam. So the TAs are going to point out to you mistakes that students made we graded fairly strictly so most of the questions were either right or wrong, so you have to get the entire question correctly. All right?
01:23
I must confess that the class did really well I am really pleased all right? The scores were good the exam was not an easy test, and so overall the class did very well and I think kudos for you guys. But
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remember the battle is not over. This is just the first hump so now we need to get through the whole quarter so I want you to keep that momentum. All right? And so please go to discussion this week the TAs will go through the answer key with you, and if you have any questions, they'll answer those questions they're the ones who graded the exam, and they'll tell you how the exam was
02:03
graded as well and this is important because I want you to have that information as you prepare for the second midterm because that's how your exams will be graded on the second midterm as well. Okay? Now before I proceed, does anybody have any questions?
02:23
Great. So if you guys remember, we're just going to pick up where we stopped and last time we talked about acid-base titrations and the timing is pretty good because I understand you're doing that in the lab right now. Okay? So if you take titrations in general
02:41
titrations, we said, are an analytical tool it's a tool used to analyze or determine the concentration of an unknown substance or element in a solution. All right? So if we want to determine the concentration or amount of a substance in a solution
03:01
we have to take advantage of a reaction. All right? And titrations take advantage of a reaction that has to be very clean no side reactions. That's the only reaction taking place. So it has to be a reaction that's clean it has to be quantitative, which means that it has to react completely
03:21
and thirdly, it has to be rapid. You can't sit there for days waiting for the reaction to go to completion so we take advantage of reactions that are clean quantitative and rapid. All right? and so it turns out acid-base reactions are ideal for this because acid-base reactions react
03:42
rapidly, cleanly, and quantitatively. Okay? So when you are looking at titrations we look at a reaction where one of the reactants, you know what the concentration is. All right? and the solution with the known concentration, the reactant with the
04:00
known concentration is always placed in the burette and that is called the titrant. We place the solution of the unknown concentration in the erlenmeyer flask and we call that the analyte. And then what you do is you carefully measure amounts of the titrant
04:21
into the analyte. So carefully, that's why we use the burette, to carefully measure volumes of the titrant into the analyte and you mix it up really well so that the reaction goes to completion. All right? At some point, as you add titrant incrementally, there's going to come a point where the reaction goes to completion.
04:43
and when the reaction goes to completion it's signaled by some change in physical property. So it turns out you can use many different physical properties to signal where the titration goes to completion now the most common way to do that is to add
05:01
another reagent, which we call an indicator and in the laboratory you would have carried out an acid-base titration where you added phenolphthalein as the indicator and so if your analyte is an acid when you add the bromo, the phenolphthalein indicator, it's colorless
05:21
and then you add the base. As you keep adding the base, there comes a point in which the acid and the base would have reacted completely so that now at some point you're going to have a slight excess of base. So if you're adding the base in increments, there's going to come a point where you're going to have a slight excess of base
05:41
over the acid. All right? At that point your indicator turns pink. All right? Because phenolphthalein is colorless when the solution is acidic, but it turns pink when the solution is basic. So when all the acid has been used up in the reaction and now all you have is just a little bit of excess base in there
06:01
then the solution turns pink and that indicates that the reaction is completed. Okay? So that's if you use an indicator. Another way or another physical property that you can use to signal the completion of the reaction is to look at the pH.
06:21
Remember, if you have an acid, we're looking at acid-base titrations, and if you place the acid in the flask and you put a pH meter in there. You guys have used pH meters, isn't it? It has electrode, you put the electrode in the solution and then the meter reads out what the pH of that solution is. And if you have an acid
06:40
in there what should the pH read? less than seven? Seven greater than seven. Less than seven. So to begin with, you have only acid there and you're going to read a really low pH. Now as you add the base, what's going to happen is that the base will react with the acid
07:01
and so the acid is consumed. So the pH will go up. All right? And so what we look at is the change in pH. So incrementally you add the base to the acid and in the pH meter you read the pH and then you can plot out what we call a titration curve. All right?
07:20
And we said a titration curve is a plot so if you look at a titration curve a titration curve is a plot of the pH of
07:41
the analyte all right? So this is what is in the flask as a function of the volume of titrant which is in the burette
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added. All right? So if you make a plot of the pH as a function of volume of titrant added usually this is in milliliters All right? If you make a plot of this, we call this plot
08:22
a titration curve. All right? So instead of what you did in the laboratory, I think you're doing both in the laboratory where you're going to look at phenolphthalein using an indicator, that's one way of carrying out a titration where the physical property that you're looking at is adding a third reagent, which we call an indicator
08:43
or the other way is to measure, put a pH meter in there and measure the change in pH as you add the titrant. Is that clear to everybody? So it turns out that acid-base titrations can be of three types so we're going to look at acid-base titrations in detail
09:02
and the reason we're looking at acid-base titrations is because we're going to apply everything that we've learned up to this point. Remember we looked at the fact that you now know how to calculate the pH of a weak acid, you know how to calculate the pH of a strong acid you know how to calculate the pH of a weak base, you know how to calculate the pH of a
09:21
strong base you know how to calculate the pH of a buffer. All right? So this is one place we're going to apply everything that we've learned, and we're going to mix them together, we're going to look at how things change as you progress all right? and so this is a very useful application of all the concepts that we've learned
09:41
so it turns out that acid-base titrations can be of three types and the first is strong acid
10:00
versus strong base the second is weak acid versus strong base the third is weak base versus
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strong acid so it turns out they can be of three types depending on what is the titrant and what is the analyte you can have both being strong. So you can have titrations with strong acid, strong base. All right? one of them will be the analyte the other would be the titrant. Okay?
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or you can have weak acid versus strong base in this case, the weak acid is the analyte and the strong base is the titrant or the reverse where the weak base is the analyte and the strong acid is the titrant. Okay?
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now we never look at titrations between weak acids and weak bases because you can't get any meaningful information out of it. So you can't do titrations with weak acids, both being weak. All right? So either they have to both be strong, or one is weak and the other is strong. Okay? So we're going to take a look at each one of these, and we're going to start by looking at the
11:20
first of these which is a strong acid versus strong base and instead of using the phenolphthalein as the indicator, we're going to look at pH titration curves. All right? So we want to look at titration curves
11:42
and we want to look at the dependence of pH, because that's what we've been calculating all along as the volume of titrant has been added. Okay? So you can see that if I wanted a strong base, the classic strong acid strong base would be HCl
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aqueous versus NaOH. All right? And let's say, to begin with, we will start with an example where a titrant is going to be the base. Okay? So we're going to start with .1
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molar NaOH. So remember that is the known concentration. Okay? In the flask, we're going to put HCl aqueous. So what we have here is a strong base as the titrant
12:42
and a strong acid as the analyte. Okay? So as all of you know, we have a strong acid and strong base and if we combine them, all of you recognize, remember strong acids produces hydronium ion. strong bases, like sodium hydroxide, produces hydroxide and we know that large amounts of hydronium ion
13:03
and hydroxide ion can't coexist. What do they do? They're going to neutralize each other, and what do they form? Water. Okay? They can coexist in small amounts. Like in water, it's about 10-7 molar so hydronium ion and hydroxide can coexist only in very very small amounts, all right?
13:23
of the order of 10-7 otherwise, if you have large amounts of them, they're going to react with each other, neutralize each other, and form water. So let's look at what the reaction would be. All of you recognize that if we want to look at- we start by looking at what we call the net ionic
13:42
equations. So we're going to look at all the major species that we start with at the beginning and then look at the major species after the titration has occurred okay? After you've added the analyte. So we have a strong acid all of you know, what do we know about strong acids? Strong acids do what?
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dissociate completely to give you hydronium ion and chloride ion. So we know that the initial HCl that we started with will give me H3O plus concentration and that should be the initial Cl- concentration as well
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and we know that the initial concentration of sodium hydroxide because it's a strong base, and it dissociates completely, should give me the initial concentration of hydroxide and because we have the same amount of sodium and hydroxide they should all be the same. Okay? So to begin with,
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I have H3O plus aqueous plus Cl- aqueous. This is what's in the flask. It's a strong acid, dissociated completely so these are the species in the flask now if I add sodium hydroxide to that I have sodium hydroxide that is dissociated, so
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before any reaction starts, the instant I combine them I'm going to have all four species in there. Does everybody recognize that? but we know that because of the strong acid, we have lots of this and it's a strong base, we have lots of that and they cannot coexist, so the instant we combine them
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these two are going to react cleanly, rapidly, and quantitatively to give me what? H2O and then I have sodium and chloride. If you see NaCl is a salt and once again, it's a soluble salt and we know salts dissociate completely
15:43
so what I would have is if you want to look at this, this is not the net ionic equation, I'm sorry this is the complete ionic equation so if you look at the complete ionic equation this is what I have. These are the species to begin with at the end of the reaction
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this is what I would have now if you look at these, you can see that really, sodium is there at the beginning it's there at the end chloride is there at the beginning chloride is there at the end. So can everybody see that? sodium and chloride are not doing anything at all they're just hanging around
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all right? They're there at the beginning, they're there at the end, they're not undergoing any change at all and so we call them these are called spectator ions you can see that they're there at the beginning, they're there at the end
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and therefore they're ions that don't do anything at all, so they're just spectators not participating in the actual events that are taking place and so we call them spectator ions. All right? now if I cancel out the spectator ions, because remember, the spectator ions are there at the beginning they're there at the end what I end up with
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is what I call the net ionic equation and so what we have is over here the net ionic equation and in the net ionic equation, we cancel out the spectator ions. Because really, the spectator ions don't participate in the reaction. All right? So if I take
17:21
the net ionic equation, that describes or summarizes exactly what's going on in this reaction and so in acid-base reactions, essentially what happens is the acid and the base react with each other to give you water. All right?
17:40
now if you want to write the general form of the equation the general form of the equation is sometimes very misleading so general reaction would be we started with HCl plus NaOH giving you H2O plus
18:02
NaCl so often you would see the general form of the reaction where you write down the two reactants and the products that are formed and you can see in the general form of the reaction, it doesn't really convey what's going on because you know that HCl is a strong acid, it dissociates completely, NaOH is a strong
18:21
base, it dissociates completely they're going to give you water and then we know that the salt that's produced, which is NaCl is dissociated as well. Okay? So it just gives you the general form but it does not give you the details of what's going on but it's worthy to remember that when you combine an acid and a base, you
18:41
always end up with water and salt. All right? and that's what that reaction kind of summarizes, that when you take this acid and this base and combine them you're going to get water and then salt being formed. Okay? so now what we're going to do is we're going to apply what we learned. So we know that
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the bottom line is that the reaction that really takes place is really the hydronium ion from the strong acid and the hydroxide from the strong base combining to give you water okay? So that's what we're going to look at. So now we're going to go back and we're going to look at an example and the example that we're going to look at is
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we're going to start with .1 molar NaOH, all right? and over here we're going to have HCl but usually, in a titration, remember the analyte concentration is
19:41
unknown. All right? but because as a practice and as a mental exercise, what we're going to do is usually in an experiment your analyte is unknown and what you measure is pH what we're going to do is we're going to calculate what the pH would be all right? And if we're going to calculate the pH of that solution
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then we need to know the concentration of the analyte as well. So what we have here is 100 milliliters of .1 molar HCl. So usually in an acid-base titration you do not know what the concentration of the analyte is. That's what you're trying to figure out but here what we're going to do is
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we're going to try to figure out what the pH of that solution is but before we do that I want to kind of show you the process and so let's briefly just look at what you have done in the laboratory. All right? So
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we have a solution this indicator guide is clear in acidic solution and pink in basic solution
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the burette is filled with a sodium hydroxide solution of known strength and an initial reading is taken the base is added to the acidic solution until the solution stays a slightly pink color at this end point a final reading is taken the moles of base added equal the moles of acid present
21:23
this same reaction could be followed using a pH meter instead of an indicator guide. Initially, the pH changes very little as base is added. Suddenly, the pH changes rapidly as the end point passes. The solution quickly becomes very basic, and again, the pH changes very little. The end point occurs at this little point on the curve.
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So the end result is that I wanted to show you that curve. So so in the laboratory when you carry out that experiment, what you had was an unknown solution
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of the acid you had the pH electrode placed inside the solution and you measured the pH and so what you did was you made a plot of the pH that you measured as you added, let's say, 5 milliliter increments of the base to the acid and then you plotted pH versus
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the volume of titrant added. And the end result is that you would end up with a titration curve and the titration curve looks something like this so here is the titration curve
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for when you have an acid in the flask and your titrant is a base. Okay? So let's look at this point here this point here is before you added any base so you would expect all you have in the flask is just a strong acid and therefore you would expect a very low pH. All right?
23:04
and you can see that that pH is somewhere around one. Okay? Now as you incrementally add base and if your titration is a strong acid versus a strong base then the shape of this curve comes out to be this S-shaped curve. We call that a sigmoidal curve. All right?
23:25
and you will see that initially your flask is going to have acid, so your pH is going to be very very low because the solution is acidic but as you approach the end of the titration where the two reactants
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are reacting in stoichiometric amounts or in similar amounts then what happens is suddenly the pH changes dramatically. And suddenly you see this steep rise in pH. All right? and then once you've passed the equivalence point now it slopes out. So
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when the two reagents, the strong acid and the strong base have reacted completely with each other we call that the equivalence point or the stoichiometric point. All right? The equivalence point is when they have both reacted in equivalent amounts. We call that the equivalence point.
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Now sometimes in the laboratory, you've used the word endpoint. All right? Now it's important to know that the endpoint and the equivalence point actually convey different information. The endpoint refers to when your indicator, if you're using an indicator
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the endpoint refers to when the indicator changes color. All right? and an equivalence point refers to when they have reacted in equivalent points. In some experiments, the equivalence point and the endpoint will be the same. In others, they will be different. All right? Now let's take
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the phenolphthalein example. Remember, phenolphthalein changes color not when they have reacted completely with each other. Phenolphthalein changes color when you have a slight excess of the base, because remember, when you add the base, phenolphthalein is colorless if it's acidic it's colorless if it's neutral but it only changes color if it's basic. Do you see that?
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And so when you add phenolphthalein as the indicator, the endpoint is actually when you have added a very slight excess of the base. That's why when you did the experiment, remember, you add sodium hydroxide, you stir it. So you add it in increments. and as you approach the endpoint
25:43
you actually had half a drop. How do you add a half a drop? Did you guys learn that in the laboratory? You kind of let a drop hang just halfway there then you take the lip of your flask and kind of get that half drop in there and then you stir it. All right? And so when you approach the endpoint
26:01
you actually don't even add drops. Now you add half drops so that there comes a point in which you see the first trace of the slightest pink that means that's the endpoint so the half drop that you added has to be subtracted because remember, it turns pink only when you've added a slight excess
26:23
so that's why you do it in half drops and a half drop is about .05 mL. All right? So you let a pendant drop hang on the tip of the burette, just a half a drop and then you take the flask, the edge of the flask, and just touch it and then you take it off and you tilt it and you mix that half a drop of base that you added
26:43
and so at that point you're going to see the first trace of a pale pink if it gets to be dark pink, you've gone way past the endpoint. All right? No help there. All right? You have to see the first trace of a permanent pink because initially as the drop falls in, the solution will turn pink and then when you stir it
27:01
it will go away. All right? and so the first time you see the faintest of the faintest pink that's when the endpoint is and then if you really want to know what the equivalence point was, you take the endpoint and you subtract the half a drop that you added when it turned
27:22
slight pink and that will be the equivalence point. So that's why it's important that you realize the term endpoint refers to when you're using an indicator and the point at which the indicator changes color. Very often when the indicator changes color is not the same as the equivalence point
27:41
the equivalence point, or the stoichiometric point is when the two reagents have reacted in exact amounts. All right? So let's take a look at this. So at the equivalence point here now we know that this is the reaction that's taking place. We know
28:00
that when you have a strong acid and a strong base reacting, at the equivalence point all of this has reacted completely with that so at the equivalence point, what do I have in solution? Can you tell me? Initially, to begin with, you have lots of acid you're slowly adding base at the equivalence point, now you've added exactly the right amount for all the
28:23
acid and all the base to neutralize each other so at the equivalence point what would you have in solution? water and salt. Sodium and chloride. water is neutral Na plus is a group one metal neutral Cl- is what? The conjugate base of a strong acid. The conjugate base of a strong acid is what?
28:44
neutral basic acid. Neutral. So what should the pH be at the equivalence point? Seven. So you know that if you're titrating a strong acid with a strong base, you know that the equivalence point has to be when the pH is seventh so all you have to do
29:00
is plot this graph and then figure out what pH seven is and figure out what the volume is, and that would be the volume of base that you added when all of the strong acid was completely neutralized by the strong base and that would be the equivalence point all right? Or stoichiometric point.
29:20
So one important take-home message is that you need to know what equivalence point is, or stoichiometric point is and you need to know what endpoint is and they're different. Okay? Okay. So now that we know what the plot should look like we're going to start calculating this. All right? and because now we're not doing an experiment anymore
29:43
now we're doing theory we're going to predetermine what the concentration of the acid is, we're going to predetermine what the concentration of the base is and we're going to calculate the pH. Usually we measure the pH all right? And we don't know what the concentration of the analyte is, that's what the
30:00
experiment is but now in class, what we're going to do is we know the concentration of the analyte, we know the concentration of the titrant we're going to calculate what the pH of that solution should be. Okay? So to begin with, I'm going to have you help me out so we're going to look at several scenarios we're going to look at how do I calculate the pH before I add any base?
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how do I calculate the pH after I've added some base? how do I calculate the pH when we're at the equivalence point? and how do I calculate the pH when I have exceeded the equivalence point and I have lots of excess base? Is that clear to everybody? So let's start with the first which is
30:43
pH before addition of base so let's see if I were to take a 0.1 molar HCl and put a pH electrode in there and I measure the pH I should be able to calculate the pH that my pH meter should read. All right?
31:03
So all we have in here is a strong acid what is the pH of that solution? one minute what is the pH of that HCl solution? Do you know?
31:20
what is the pH of that solution? how many say it's one? It's got to be one. Why? it's 0.1 molar. 10 to the negative 1. Got it? it's a strong acid, strong acids dissociate completely and so by now I need you guys to know this, otherwise I have to send you back to Chem 1B. All right?
31:41
because we've done many problems. You know that it's a strong acid and so what I have is that we have the initial concentration of HCl is 0.1 molar and we know that equals the initial concentration of the hydronium ion because we know a strong acid
32:01
dissociates completely and remember that means that is 1 times 10 to the negative 1 molar. 0.1 is 1 times 10 to the negative 1 therefore pH should be 1. and it goes to three decimals because our concentration is given to three significant figures. All right? So to begin with, we know the pH of the solution in the flask. All right?
32:25
now we're going to calculate the pH of the solution if I added 30 milliliters of NaOH so the second case is pH after 30 milliliters
32:42
of 0.1 molar NaOH remember, this is the titrant is added. Okay? So what we have to keep in mind is, now if I wanted to figure out
33:00
the pH of the analyte, because we're measuring the pH of the HCl after you added 30 milliliters of HCl you want to keep in mind that in titrations because we're adding base all the time to the analyte, can you see that the volume keeps changing? All right? if the volume changes, what does that tell us about concentration? What is the
33:22
definition of concentration? moles divided by volume so if the volume keeps changing, what is that telling you about the concentration? it's going to keep changing all the time. All right? and because the volume is going to be changing all the time, what we're going to keep in mind is that what doesn't change is the moles of acid and the moles of base. Do you understand that?
33:43
So what we're going to have to do is actually instead of looking at in terms of concentration up to this point, every example of the problem that we dealt with when we looked at weak acids and calculated the pH when we looked at weak bases and calculated the pH when we looked at strong acids, strong bases and even when we looked at buffers
34:01
one of the assumptions that we made was the volume never changed so if the volume doesn't change, we know the concentration does not, you know we can keep the concentrations and we can calculate them based on the concentrations because they're not changing altogether. Do you understand that? Here, because we keep adding more and more base in our flask, the volume of the flask is continuously changing
34:23
and if it's continuously changing the concentration is continuously changing as well so what we need to do is actually calculate the moles rather than the concentration. Okay? So what we're going to do is we're going to calculate the moles of acid
34:40
so remember, the way to remember this is what I taught you last quarter remember, concentration on molarity is always moles times volume that's all you need to remember so if I need to calculate moles what does that equal? concentration times volume and remember, concentration is always moles per liter
35:03
what is the unit for volume? liters. So I have to make sure always that my volume is in liters. Okay? So if I want to calculate the initial moles so I want to calculate the initial moles of hydronium ion
35:21
remember, what is the universal symbol for moles? it's a lowercase n. All right? So if I'm calculating hydronium ion concentration, HCl is a strong acid it dissociates completely so whether I calculate the concentration of HCl or whether I calculate the concentration of hydronium ion, they're the same thing. All right?
35:41
So if I want to calculate the moles of hydronium ion this is going to be concentration times volume the concentration we know in the flask is .1 moles per liter and we said we have 100 milliliters of that solution
36:00
all right? So to begin with the volume would be .100 liters. 100 milliliters, all right? and therefore this comes out to be, it's in three significant figures comes out to be 3 times 10 to the negative 2 moles of hydronium ion
36:21
so this is what I started with this is the amount or the number of moles of HCl that's there to begin with. Okay? Now if I want to calculate my initial number of moles of hydroxide how much hydroxide did I add? 30 milliliters. Okay? So I have, once again, it's concentration times volume
36:43
so I know that I have .10 moles per liter, that's the concentration of my titrant I added 30 milliliters 30 milliliters makes .03 liters and you can see liters and liters will cancel out
37:01
and this gives me 3 times 10 to the negative 3 moles of hydroxide Is that clear to everybody? So what we've calculated is, before we added, before any reaction took place, we've calculated the amount of hydronium I had and the amount of hydroxide that I had Now remember, this is an acid-base reaction
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between a strong acid and a strong base, and we know that the net equation is where the hydroxide, hydronium, reacts with hydroxide to give me liquid water. So before reaction
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before any reaction took place, I just calculated that I have 1 times 10 to the negative 2 moles of hydronium and I have 3 times 10 to the negative 3 moles of hydroxide Is that clear to everybody? So this is what I start with. Before any reaction took place,
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I've calculated the moles in the flask and I've calculated the moles of the 30 milliliters of base that I added to the flask. Okay? So now they're going to react with each other so after reaction so can you see this is a stoichiometric problem? All right?
38:20
and that means it's a limiting reagent problem. So which is limiting, which is excess? Can everybody see that hydroxide is limiting? It's in lesser amount. All right? So that means if it's limiting when the reaction is complete, I'm going to end up with zero of that and so if I subtract this from this I will have
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7 times 10 to the negative 3 moles where this is limiting and this is excess we're not really concerned, we're just forming water, and we know water does not affect the pH. All right? and so, and it's in excess amount, it's the solvent
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so we're really not concerned about how much water is being produced we're really just interested in how much acid and base are left over. All the base is consumed because it's limiting and so what we're left over with is the excess acid so when you add 30 milliliters of water to that solution, all the base is consumed
39:20
and all we're left with is hydronium ion. So now I need to figure out what is the hydronium ion concentration, because if I want to calculate pH, remember, ultimate goal is to calculate the pH. So if I want to calculate the hydronium ion concentration, so I'm going to say hydronium ion concentration and this is the excess that's left over
39:41
from this. All right? and what is the definition of concentration? It's always moles divided by volume we just calculated the moles, which is 7 times 10 to the negative 3 moles. Now what is the volume? Remember, the reason that we're calculating all of these in terms of moles is
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because the volume keeps changing I started with 100 milliliters I had a 30 milliliters of base, so at that point, what is my volume now? 130. Can you see that? So what I have is, I'm going to divide by the volume which is 130 milliliters or .130
40:23
liters. All right? So now that works out to .0538 molar. So I want you to keep in mind, in these problems, lots of things are going on there is acid, there is base
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we're having a reaction going on neutralization taking place and then we are left with what's left over and you guys can handle problems of this type now because we've done so many complicated problems now you have to be able to bring all these multiple ideas together and kind of solve this problem and you can do it because you already have all the tools to do it. Okay?
41:04
So now that will be the hydronium ion concentration of that solution how do I calculate pH? take the negative log of that and if you take the negative log of that, the pH of this solution comes out to be 1.269
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so to begin with, the pH was 1 we added the strong base, 30 milliliters, now you can see the pH went up because some of that hydronium ion has been consumed, so you have less hydronium ion in solution, pH goes up. Okay? so it turns out that you can calculate in this plot
41:44
we calculated we figured out what the pH is to begin with, so we figured out this point we added 30 milliliters, you can figure that out at home, can you guys figure out what the pH would be when it's 50? All right? and then you should be able to figure out as you add incrementally
42:02
you can figure out what the pH of that solution is. All right? now we're going to look at what happens at the equivalence point. So the third scenario is at the equivalence point or
42:20
stoichiometric point now this is when they have both neutralized each other. So what you need to know is at the equivalence point, the moles of hydronium ion okay? should equal the moles of hydroxide. All right?
42:42
and so remember, we know that C equals N over V, therefore N equals C times V so the moles of acid that you added would be the concentration of H3O plus times the volume of the acid
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should equal the concentration of hydroxide times the volume of hydroxide that's added so you can see that if this is .10 moles per liter and we started with 100 milliliters, let's say we know that on the other hand, if this is 1
43:21
moles per liter, what should this volume come out to be? Can you see that? So that means you know that if you start with 100 milliliters of .1 mole or HCl what is the volume of any of which that you need to add? You have to add 100 milliliters. All right? So so this is what you calculate
43:42
you have to figure out so usually you know that if you want to calculate the volume of hydroxide that needs to be added that would be the concentration of hydronium ion times the volume of the hydronium ion divided by the concentration
44:00
of hydroxide so for a strong acid-strong base, you're going to have to calculate, if you know the concentration of your analyte you know the volume of the analyte you know the concentration of a titrant, you can calculate how much volume you need to add, and we know that when you add 100 milliliters of the base, it's going to be completely neutralized
44:20
when it's completely neutralized what is the pH? pH should equal because all we have there is just water and salt and therefore when the for strong acid-strong bases, when the pH is 7 we know it's neutralized and that is the stoichiometric point
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or the equivalent point. Now what happens if we add an excess of base? okay? So let's say now we have hit the equivalence point now we're going to add an excess so the fourth scenario is
45:00
pH after two point two hundred and five 200.05 milliliters of base is added. Is that clear to everybody? All right? So now we've gone beyond the equivalence point, and now we have an excess base. All right?
45:24
So so what I want to start by asking you is what is the total volume of that solution when we're at the equivalence point? Remember we said that the equivalence point you have to add 100 milliliters of base. So what is the total volume at the equivalence point?
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200. So we know total volume equivalence point I'm writing too fast now. If you can't read what I'm writing, let me know. So total volume at equivalence point
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would be 200 milliliters. All right? So what is the volume of excess hydroxide? Can everybody see? It would be 200.05 milliliters minus
46:21
200 milliliters which is .05 milliliters All right? So that's the volume of the excess hydroxide that we figured out. Okay? So now if I want to figure out what the pH of the solution is, I need to figure out how many moles are in that .50, because
46:41
the earlier amount was consumed and neutralized. So the only extra hydroxide that you have in there is .05 milliliters. So what is the moles of that? So remember moles of excess hydroxide is always, moles is what? Concentration times volume.
47:04
The concentration of this is .10 moles per liter times the volume now would be .05 divided by a thousand liters. All right? So I'm it's .05 milliliters I have to convert that to liters
47:22
and so if you work this out this comes out to be 5 times 10 to the negative 5 moles oh, actually it's 10 to the negative 6. Sorry. All right?
47:44
So I've calculated the moles of excess you can see that I now have, because I'm subtracting these two numbers, I end up with a one sig fig number and I'm carrying it over to one sig fig number. Okay? So this is the amount of excess number of moles.
48:01
So now because the volume changed, I know I added .05 of NaOH, I figured out the moles but now my total volume is what? 200.05. Do you see that? So that means if I want to calculate the concentration I figured out the excess hydroxide the moles and therefore if I want to calculate the amount of concentration of excess hydroxide
48:24
this would be 5 times 10 to the negative 6 moles divided by the new volume which is .20, 200.05 liters Do you guys get that? I've kind of converted the total volume is now 200.05 milliliters, converting that to liters
48:45
and therefore this comes out to be 2.0 10 to the negative 5 molar Now I want to remind you guys that this is a one sig fig number
49:05
and therefore this outcome should be one sig fig, but what I'm doing is I don't want to artificially inflate this number, so I'm just carrying this 5 if you divide 5 by 2 you end up with 2.5. All right? and so I'm just carrying- this number should strictly be a one sig fig number and I should round it
49:24
off to 3 but if I carry that number 3 over, you can see that I'm artificially inflating that number. So I'm putting that subscript 5 to remind me that I'm just going to carry this number over and at the last, I'm just going to round off to one sig fig. All right? Yes.
49:41
Because remember at the equivalence point, you have 100 milliliters of this and we had to have 100 milliliters of the other. All right? And at the equivalence point you're going to have equal moles of acid and base. So that's the calculation that we did here. You see that at the equivalence point we calculate that we have to have 100 milliliters of base. So that means you have 200 milliliters of this.
50:02
So now that I have hydroxide I can calculate hydronium we know that's Kw divided by hydroxide, which is 1 times 10 to the negative 14 divided by 2.5 times 10 to the negative 5 which gives me
50:22
4.0 times 10 to the negative 10 molar So again, I'm just carrying this to two sig figs, my results should be one sig fig now if I take the pH of that that comes out to be 9.4 You guys understand how I calculated the pH? So I calculated the pH corresponding to that
50:43
little excess of hydroxide that I added beyond the equivalence point. So in this way you can calculate the pH of any point in the titration. All right? Next class we're going to look at weak acid strong base titration.