Weak Acid-Strong Base Titrations

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## Weak Acid-Strong Base Titrations

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So now we're gonna take a look at weak acid, strong base hit rations. Now we're going to say here that are weak species which is our acid will behave as the an elite And our strong base which will slowly add to it represents our tight trend. Now we're gonna say whenever you're you titrate a weak species in this case the acid weak acid and the strong with a strong species in this case the strong base. The fact that we have an acid and a base mixing together means that we're gonna have to use the I. C. F. Chart. Now when we say I C. F. I C. F stands for initial change final. Now we're gonna use the following road map to determine the ph at different points in our tie Trish in between a weak acid and a strong base. Now, before we even begin all of this, we first look at the equivalent volume. Now remember we counted the equivalent volume V in order to determine the volume of tightrope required to reach the equivalence point in this case the tightrope again is our strong base. Remember the equivalence point is where your moles of acid equals moles of bits. And remember that molds itself equals leaders, times more clarity. So if we take a look here, it says the titrate, 10 of 300 mls of 3000.100 moller nitrous acid with 0.30 moller potassium hydroxide. So nitrous acid represents our weak acid, potassium hydroxide represents our strong base. We're going to say here that m acid times V acid equals and base times six. So the polarity of my acid is 0.100 moller, Its volume is 300. The polarity of my strong bases 0.30 moller. And we're looking for the volume of our base. Our equivalent volume in this case, Divide both sides by 0.30 moller here, you'll hear, you'll see that polarities cancel out and we'll be left with middle leaders as our volume. When we work that out, we'll get 100 MLS of K O H. Is required in order to reach the equivalence point. Now, if we take a look at the next step, this is before any strong base has been added before any strong bass has been added. We just have a weak acid initially. So here we have the titillation of 300 ml of 3000.100 moller nitrous acid with zero mls of 00.300 Mohler K O H. So here there's no strong base being added. So again, we just have weak acid by itself. Remember when we have a weak acid or a weak base by itself? We need to utilize an ice chart in order to determine our ph Now at an I C. F chart represents initial change final but an ice chart represents uh initial change equilibrium. Remember in these types of ice charts are units will be in polarity because no strong bases being added. We don't need this volume initially. All you require is the initial polarity of my weak species. So we plug that in. Remember, weak acids and weak bases react with water within an ice chart. So this nice church acid would react with the water. Remember an acid is a proton donor? Oh, so HN O to donate an H plus to give us N. +02 minus at the end which is R nitrite ion. And then H +20 accepts an H plus to become a +30. Plus. Our change here, we lose reactant in order to create products. So our reactant here will be -1. Our products here, they're being formed there plus X. Initially no information is given on them. So initially there's zero. We bring down everything for our equilibrium line. So 0.100 minus X. And then plus sex. And plus X comes down now at this point we would say that since we're dealing with a weak acid, we have to use our acid dissociation constant. Remember weak acid use K A week basis which we'll see later deal with KB. Now K A. Is the equilibrium constant for a weak acid, it equals products. Overreacting. So we know that will be X times X, which is X squared divided by our initial concentration minus X. If we can isolate our X variable that X variable give us H 30 plus, which is the same thing as H plus. If we know the concentrations of H plus we can take the negative log of that to find ph now there are going to be um situations where we can ignore this minus X. Here in those situations where we can ignore that minus X. We can avoid the quadratic formula In cases where we cannot ignore that -1. We keep it in and we set up all the math that we need to do. And from there we use the quadratic formula. Now in order to determine if we can keep that minus X or not, we do what I call a 5% approximation. So basically we have our initial concentration concentration of our weak acid divided by its K. A value. If this ratio gives us a value greater than 500 then we can ignore the minus x. Now in this case the initial concentration of our weak acid is 0.100 And the K. A. of our nitrous acid from your book is approximately 7.1 times 10 to the -4. When you plug that in, you'll see that. It gives you 140.8 here, it's not greater than 500. So we have to keep this minus x. And use the quadratic formula in order to isolate X. So if we work this out we'd have K. So I'm gonna take this expression here. So Kay is 7.1 times 10 to the negative four equals x squared Divided by 0.100 - X. So you would have, if you work this out you'd have 7.1 times 10 to the minus four times 40.100 minus X equals X squared. Then we're going to say here you're going to distribute, distribute when you work that out, you're gonna get 7.1 times 10 to the negative five minus 7.1 times 10 to the negative four X equals X squared this X has the highest power. So it's the lead term. When you rearrange this it gives you X squared plus 7.1 times 10 to the minus four X minus 7.1 times 10 to the negative five. Then we're going to say here the quadratic formula. Remember is negative B plus or minus square root of B squared minus four A. C over two A. Okay you would plug into that formula So bring it down, it would be negative 7.1 times 10 to the -4 plus or minus 7.1 times 10 to the negative four squared minus four times one times. Don't forget the negative sign for c -7.1 times 10 to the negative five Divided by two times 1. Now because of this plus or minus point here you'd get two X values values one that's positive and one that's negative. But here's the thing at equilibrium you're only allowed to have a positive value so we would disregard the negative X. And go with the positive X answer That would give us x equals .00808 moller. Again, in the situation, acts would be equal to H 30 plus, which is equal to H plus. Taking the negative log of that number will give you my ph which is 2.09. So that would be the long version of this reaction. So again, at this point, we don't have any strong base being added. We just have a weak acid by itself. So we must utilize the nice chart in order to isolate our ph. Now, click on the next video and let's start slowly adding our strong base and see what happens in arbitration.

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## Weak Acid-Strong Base Titrations

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So remember it's going to require on our part, 100 mls of potassium hydroxide in order to reach the equivalence point in this question here, we have only 50 mls of K O. H. So that means we're dealing with calculations before the equivalence point. Now, remember once our acid and base begin to mix, we transition away from the ice chart and we move to the I. C. F. Chart to determine the ph and remember in an I. C. F chart, the units have to be in moles, moles itself equals leaders, times more clarity. We divide these mls here by 1000 to change them into leaders and then multiply them by their polarities. That would give me the moles of each of these species. So here are moles of nitrous acid would give me 0.30 moles. And then here this would give me the moles of K O H 00.15 moles. We don't have any of our nitrate ion nitrite ion. So we started initially zero, like in ice chart. I cf charts ignore water because it's a liquid. It's not really affecting our ph value. So we can ignore it. Now we look at the react inside, we know on the react inside the smaller moles, which is our limiting amount will deduct from the larger moles. So our smaller moles are these .015 moles. They subtract subtract from themselves because they're being used to neutralize the acid. We subtract them from the acid as well. At the end, we'll have left zero of my strong base and I'll have some of this weak acid remaining based on the law of conservation of mass or matter. Um We know that matter can't be created or destroyed. It just changes forms. So whatever I'm losing on the reacting side, I'm actually gaining as this conjugate base on the product side. So at the end of this what we have is we have weak acid and we have conjugate based remaining. Remember weak acid conjugate base means we have a buffer. And if we have a buffer then we utilize the Henderson Hasselbach equation in order to calculate our ph so if we look here remember our Henderson household back equation as P. H equals P. K. A. Plus log of the conjugate base amount divided by the weak acid amount. We said earlier that the so negative log on P. K. Equals negative log of K. A. And we said earlier that the K. Of nitrous acid is 7.1 times 10 to the negative four according to your book. And then it's log of the conjugate base amount divided by their weak acid amount. When you plug that in. That gives you 3.15 as your ph. So you're seeing as we're slowly adding strong base we see that our ph is increasing. And remember before we reached the equivalent volume of the strong based hatred. That means we will still have a buffer and we can utilize the Henderson Hasselbach equation to calculate our ph this particular example, we see that the end we have equal amounts of my weak acid and conjugate base. This happens we're more at the half equivalence point. And it's important to remember that at the half equivalence point p H equals P K. That's because log of 0.15 divided by 0.15 is really long. Of. One, log of one Is equal to zero. So at the half equivalence point that the half of the volume we needed to get to the equivalence point P H equals P K. A. Now that we've seen these types of calculations, let's move on to what happens when we're at the equivalence point between a weak acid and a strong base.

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## Weak Acid-Strong Base Titrations

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So when we reach the equivalence point between a weak species and a strong species, we're actually gonna have to utilize two charts. We start off with an I. C. F. Chart because again we have an acid and a base high trading. But at the end we'll have a product which is weakened itself and would need an ice chart in order to determine ph and P or P. O. H. So if we take a look here at the equivalence point, we're gonna say at the equivalence point of a weak acid, strong based filtration. Whatever is stronger, will dictate what kind of P. H. I have since the bases. What's strong, It's gonna create a solution that is basic. And if the solution is basic that means it'll be greater than seven When we have our standard temperature of 25°C. So here we divide our mls by 1000 to get leaders of each and when you multiply them together, you'd see that we have actually the same moles for both. Which makes sense because at the equivalence point we have equal moles of our acid in our base. They would subtract from one another. So at the end we'll have both of them being zero through the law of conservation of mass. We'd be gaining this amount on the product side. So at the end, what we have is conjugate base. This conjugate base um it comes from a weak acid. So it's a little bit stronger. But in actuality it's still a weak base. Okay, so it's still a weak base. And remember with weak acids and weak bases, we need to use an ice chart in order to find our ph so what we do here is we have to now set up an ice chart with this N. 02 minus. Remember in an ice chart the units have to be in polarity. So we take the molds of what's left of our conjugate base and divided by the total leaders used within the titillation, which would be the 0.300 liters of the weak acid plus the 0.100 liters of a strong base. When we do that, we get a new concentration of 0.75 moller of our nitrite ion. So we plug that here. Now remember in an ice chart our weak acid or weak base reacts with water since it's a base it's going to be a proton except er So water will donate an H. Plus to it, giving us nitrous acid plus O. H minus as products. Now we ignore water because liquids and solids are ignored in ice charts. Initially, both of these products are zero we lose react ints to make products, we bring down everything for the equilibrium line. So that's our filled in ice chart now because we're dealing with a base base is weak bases utilized KB. We know what the K. A. Of nitrous acid is. We're gonna use that to find KB KB equals KW divided by K. A. So remember K W is 1.0 times 10 to negative 14 divided now by The 7.1 times 10 to the -4. That gives me a value of 1.4. 1 times 10 to the -11. That's our KB. Which will plug into here at this point in order to isolate acts. We're going to take A B equals X squared divided by the concentration of our conjugate base which is our weak base. So we're gonna do 1.41 times 10 to the -11 equals x squared divided by .075. Multiply these two together. That gives me X squared equals 1.575 times 10 to the negative 12 to get just acts, we take the square root of both sides. So x equals 1.028. 3 times 10 to the -6. Now remember when we find X. X here will give us either H 30 plus or minus. Based on the equation in the ice chart here, X is giving us O H minus. Which means that if I take the negative log of that, I'll get P O H. So that comes out to 5.99. And if I know P O H N o ph because ph is 14 minus P O H Which is 8.01. So again we're seeing that we have the gradual increasing of our ph as we start adding more and more of our strong based hatred. So at the equivalence point, we found out that our ph is 8.1. Now that we've seen this, click on the next video. Let's see what happens when we go a little bit beyond the equivalent volume, so we're gonna go a little bit above 100 mls of our potassium hydroxide.

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## Weak Acid-Strong Base Titrations

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we've now reached the point where we've gone beyond the equivalent volume of potassium hydroxide. So here after the equivalence point of a weak acid, strong base hydration, we will have excess strong based remaining. So here as usual, we divide these mls by 1000 to get leaders multiply them by their polarity, gives us the moles of each. We see that we have the most for nitrous acid and potassium hydroxide. Remember on the reacting side to use the smaller mold, which is our determining or limiting amount and subtract them from both. That gives us zero left of the weak acid. But we're still gonna have some strong based remaining here we have plus. But here we say that the strong base has a much greater impact on the overall ph so we're just gonna go with that amount since it's a strong base. If I can find its concentration then I can use negative log of that concentration to find P. O. H. So we have 00.9 moles potassium hydroxide. We divided by the total volume of .300 L plus .130 L. That equals 0.0 to one Moeller K. O. H. And when we take the negative log of that, that's gonna give us P. O. H. Which comes out to 1.68. And if we know P. O. H then we know ph because ph is 14 minus P. O. H. That's 12.32. So these represent the different points of our weak acid, strong based filtration. So just remember when we have only weak acid by itself, we utilize an ice chart. But once we start adding strong based high trend, we switch over to an i c. F chart. And depending on where in the tight rations you are um looking, we can take different approaches to find either p. H. Or p o h.

Weak Acid-Strong Base Titrations Calculations

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## Weak Acid-Strong Base Titrations Calculations 1

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So here, let's take a look at this question. It says consider the nutrition of 75 mls of 750.300 moller of H three C 303. It's given at having a K. A. Of 4.1 times 10 to the minus three. Um and it's being tight traded with 30 ml of 300.450 Mohler K. O. H. Here we're told to calculate the ph since it's K. Is less than one, we know that this represents a weak acid and we know that potassium hydroxide is a strong base. We're gonna write them here as our reactant. Remember the acid is going to be a proton donor? It's gonna donate a proton two or H plus two O. H minus two. Give us water. And what we have left over here is our conjugate bases. KH 2 C30203. Since we have an acid and a base tight trading one another. We utilize an I. C. F. Chart in this I C. F. Truck. We're gonna ignore water which is a liquid. Remember in an I. C. F. Chart, we use moles as our units moles equals leaders, times more clarity. So divide these mls by a 1000 Multiplied by their polarities gives us the moles of our weak acid which is .00225 moles. Here, K.O. H. is .00135 moles. And we're not giving any initial information on our conjugate base. So initially it's zero. Now remember looking at the react inside the smaller moles which is our limiting amount will subtract from the larger moles. So subtract 0.135. Subtract 0.135. So when we do that We're gonna have zero left of this for our weak acid. We're gonna have .00090 moles. And remember conservation of mass. This side would increase .00135. Now look and see at the end of this hydration. We have left weak acid, we have left its conjugate base. Remember we casted conjugate base means that we have a buffer and with a buffer that means we have to utilize the Henderson Hasselbach equation. So we're gonna stay here that ph equals P. K. A. Which is the negative log of K. A plus log of the conjugate base amount. So there goes my conjugate base amount oops divided by our weak acid amount. Okay, so that equals 2.56. Now remember because we still have a buffer in terms of this hydration, that means we're dealing with calculations before the equivalence point. And because we still have a buffer we can utilize the Henderson Hasselbach equation to find our ph now that we've seen this one, click onto the next video and take a look at the practice question below

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example

## Weak Acid-Strong Base Titrations Calculations 1

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So here we're dealing with the calculation at the equivalence point here, it says, consider the determination of 50 mls of 500.1 50 moller Hydrofluoric acid with 500.100 moller sodium hydroxide at the equivalence point, what would be the ph of the solution at the equivalence point we're told here that R. K. Value for Hydrofluoric acid is a 3.5 times 10 to negative four. Now we have our weak acid reacting with a strong base. Remember the weak acid is a proton donor. So H plus will combine with O. H minus to give us water. The N A plus will combine with the F minus to give us an A. F. We have here because we're mixing acid and base. We know we're utilizing an I. C. F. Chart. And now I'm writing this pretty small because remember we said that at the equivalence point between a weak acid and a strong base, we first have to do an ice I. C. F. Chart, followed by an ice chart. Alright, so here water is ignored. Now we divide these on these mls here by a 1000 to get the most And to get the leaders which are multiplied by malaria T to get the moles. So it's gonna give me .0075 moles of HF. Since we're at the equivalence point we have equal moles of our weak acid and strong base. So even though I don't have the volume of N A. O. H. Which I'll need eventually though, I don't need it because I know at the equivalence point, both of these have the same moles. We don't have any initial information on any F. So initially it's zero. Now remember on the react inside the smaller mold subtract from the larger moles. Since they're both the same, we're going to get zero at the end for both. They've completely neutralized each other. But remember on this side we have the creation of this many moles of the conjugate base and a F. Now remember this is our conjugate base. A conjugate base here is a weak base. And because it's a weak base in order to find its ph we'd have to use an ice chart. Now, in order to figure out in order to use an ice chart, we need to use the units of polarity. So we need the polarity of this conjugate base. Now we don't really need the N. A. There it's just a spectator ion. So it's just F minus. That's important. We need its concentration. So we need the moles of its that's left which is the same number, but we need the total volume, the volume of both. The H. F. And the N. A. O. H. Now to figure out the volume of the base. Remember at the equivalence point, their moles are equal because they're at the equivalence point where the molds are equal. You can say M acid times V acid equals M base times V base plug in the concentration of the acid times its mls equals polarity of the base And we're looking for its volume again, we need the volume of the base because we need the total volume in order to figure out the final the new concentration of F minus. So polarities cancel out here. So I'll have my Volume of my base which comes out to be 75 mm. So now I'm gonna come over here and say that my total volume is 0.50 liters of the weak acid, 0.75 liters of the strong base Together. That gives me a concentration of .06 Mohler for my fluoride ion. Now we can bring it down and utilize an ice chart. Remember weak acids and weak bases react with water within an ice chart. Remember also that bases are proton except ear's. So water is going to act as the acid and donate an H plus f minus that gives us back H F. And the creation of minus. So we have initial change equilibrium in a nice chart. We don't care about solids and liquids so water is ignored. Bring in the initial concentration of the F minus Our products initially are zero. We lose react ints to make product now because we have a base here weak base. Remember weak bases utilize KB. So there's a lot of conversions that are going on in this problem. We have the K. A. We need KB. Remember KB equals KW divided by K. A. So if you plug that incorrectly in your calculator, make sure you put parenthesis around it, you get 2.9 times 10 to the negative 11. So that is our K. B. Value for f minus. Bring that down. So KB equals products. Overreact ints so 2.9 times 10 to the negative 11 equals X squared divided by 0.6. Remember at the equivalence point we can ignore the minus X here because it's just KB equals X squared over the concentration of our conjugate base which is our weak base. Alright now multiply these two together. So that gives me X squared equals 1.74 times 10 to the negative 12. Take the square root of both sides. So x equals 1.3. 2 times 10 to the -6. Now remember at this point when we find X X will either give me a 30 plus or minus. Go back and look at your ice chart. In the ice chart we see here that X gives us O H minus. So since I know the concentration of O H minus, that means if I take its negative log that gives me P O. H. And if I know P O H. I know ph because ph equals 14 minus P O H. So that comes out to be 8.120. So here are answers reasonable because we know that when it comes to a weak acid and and strong based filtration at the equivalence point, our solution should be basic, so we should expect to get a ph above seven. Alright, so just remember within the different points of our titrate nation between a weak acid a strong base. You have to remember when to utilize an ice chart when utilizing I cf chart or in this case utilizing first in i c f chart, followed by an ice chart.