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General Chemistry

Learn the toughest concepts covered in Chemistry with step-by-step video tutorials and practice problems by world-class tutors

18. Aqueous Equilibrium

Acid and Base Titration Curves

Titration Curves

Titration curves help us to understand the neutralization occurring between an acid and base in order to identify the equivalence point. 

Equivalence Point

The equivalence point is when the moles of acid and base titrating are equal in amount. 

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concept

Understanding an Acid–Base Titration Curve

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the shape of a PhD creation curve makes it possible to identify the equivalence point. Now this is just the point at which equal moles of acid and base are mixed together here we have an image of a ph titrate incurred. We're gonna say that on our Y axis we have our ph values and our X axis. We have our mls with trump being added. Now your tight print is what you're adding to your beaker filled with either acid or base. Now we look to see whether the largest rise in ph occurs and we can see that happening at This volume of 35 amounts. This is our equivalence point, volume. This the amount of time and I've added in order to get to my equivalence point. So if we look, we can see that the sharp rise happens between here and here. And if we look exactly in the middle of the sharp rise, that equals my equivalence point. And we can see the equivalence point occurs at this point right here. And if we trace to it, we can see that the equivalence point here has a ph equal to 7.0 Because the ph is 7.0. That means that I have a strong acid and strong based mixing within this reaction. When they're both strong, they're going to completely neutralize each other and at the equivalence point, the ph is equal to seven. Now, if what happened to be strong and what happened to be weak, then our ph would not be equal to seven. Exactly later on. We'll see what happens in those situations. But for now, since the ph is equal to seven at the equivalence point, we know for sure that we have a strong acid and strong base mixing together. Now, the question now, the question we have now is what is being added to? What if we take a look here, We can see that our dots begin at a ph of equal to one. So this tells me a couple of things first, it tells me that the ph is very low. 1.0 p is pretty as sick. So that tells me that I'm starting out with a strong acid. So, you can imagine that you have a beaker and in this beaker you have some strong acid. Now the ph is increasing over time because I'm adding to the strong acid some strong base. So my tie Trent here is just some strong base. As I add strong base to it, it's gonna cause a ph to increase. So that's what's happening here. We're going to say here at the equivalence point, we have equal moles of my strong acid and strong base. So moles of strong acid equals moles of strong base. Before I reached the equivalence point, I still have um more strong acid and strong base. After the equivalence point we've added so much strong base that it's completely neutralized my strong acid. It's no longer there And that's why the ph continues to rise above seven after the equivalence point because in that, in that instance we have excess strong base. So we know that the equivalence volume is 35 MS. We can also say another thing. We're gonna say that your equivalent volume is 35 amounts. Half of that would be our would get us to our half equivalence point. So half of 35 would be 17.5 mls, which is around here later on, when we talk about some certain things such as the ph of buffers and we talk about the Henderson Hasselbach equation and we talk about the half equivalence point, realize that the half equivalence point, that's what we have equal amounts of weak acid and conjugate base. Now the amounts of weak acid and conjugate base don't necessarily have to be equal moles, that could also be equal concentrations. Okay, so here we can say that this PhD attrition curve tells me that I have a strong acid being tight created with a strong base. They reached the equivalent of 35 mls at that equivalence point, the ph is equal to seven, Let's say that we start out with strong base instead. What would that look like? Well, if we started with strong base we have a ph that's pretty high up close to 14. So since this is down to one, let's say the strong base started around 13 here and it would be decreasing over time and then we'll kind of hit the same point where the equals point is still at seven. So we look like that. So this green line will represent if I start out with a strong base and I'm adding strong acid to it. Its ph would decrease over time. The equivalence ph equivalence point ph would still be equal to seven because in this instance I still have a strong acid and strong base mixing together. Okay, so this is just some basic views of a pediatrician curve from it. We can learn some information. What type of strong acid strong base is. We have what kind of weak acid strong basis. We have stuff like that. We can tell who's the tight. We can start. We can figure out what we started with in terms of the reaction. So let's continue on to the next video. And in that video we'll talk about different scenarios where your equivalence point ph may not equal seven.

In a typical titration we begin with an acid or base and slowly add either a Strong Acid or Strong Base. 

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concept

The Equivalence Point

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we've already answered this first part, we're gonna say at the equivalence point, the ph of a strong acid and strong base is equal 27. Now, if we're looking at a strong acid and a weak base, just remember whoever is weak will dictate what kind of solution you have at the end. Since we're dealing with a strong acid, the acid is stronger now than the base. So it's gonna say, since I'm stronger, I'm gonna want my solution at the end to be acidic. So anytime you're tight trading a weak acid, a strong base together at the equivalence point, the ph is going to be less than seven, it's gonna be acidic and it's acidic because the acid is stronger. Whoever is stronger, will tell us what kind of solution we have in the first example, They both were strong. So we wind up with a draw which means neutral. That's why the ph is equal to seven. Now, for the last scenario we have a weak acid and a strong base. Now the base is stronger. So it's going to dictate what kind of solution we have. Because we're dealing with a strong base, it's gonna want to have a basic solution. So the solution has to have a ph greater than seven at the equivalence point. So, just remember these fundamentals and as we start to do more acid and based filtration questions, keep this in mind as we face every type of question we're going to see. So just remember the equivalence point is when we have equal moles of acid and base. And depending on what we're tight trading, whether they both are strong or one is strong or weak, the equivalence point could have a ph equal to seven, less than seven or greater than seven.

Depending on the types of acids and bases mixing, at the equivalence point, the pH can be less than, greater than or equal to 7. 

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example

The following questions refer to the titration curve given below.1) The titration curve shows the titration of    a) a strong acid with a strong base    b) a weak acid with a strong base    c) a strong base with a strong acid    d) a weak base with a strong acid      2) Which point on the titration curve represents a region where a buffer solution has formed

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Hey everyone. So here it says the following questions refer to the hydration curve given by law. So if we take a look at this situation curve we have, let's see on our Y axis. We have our ph volumes from 0 to 14 on our X axis, we have our milliliters of tightrope being added. We have points A, B, C and D. So there's quite a few things we can talk about in terms of this. But let's look at the questions and we'll see um what gets at it or what gets labeled. Alright, so here the titillation curve shows the tight rations of what so different combinations. If we look here, we need to locate what the equivalence point will be. Remember, the equivalence point can be determined by looking at what volume do we have? The sharpest rise within our ph we can see that happens around 30 mls where our sharpest rising peach happens here, midway through there is our equivalence points or equivalence point here is point C. And if we trace over here, we can see that point C has a ph of around nine or so, maybe a little bit higher than nine, but it's about nine. So think about what combination Between acid and base. Give me a page that's greater than seven at the equivalence point. So here, remember that happens when we have a weak acid being titrate, ID by a strong base. So that's the combination, weak acid strong base. That will give me a ph above seven for the equivalence point. So here we want a weak acid with a strong base would be the second option here, which point of the hydration curve represents a region where a buffer solution has formed. Remember a buffer exists between these two Before we get to the equivalence point. But remember for buffer to exist in some way to be generated, some of the titrate has to have been added at point A There is no tie trend that's been added yet, so there is no buffer that's been formed. All we have initially is weak acid. When we get to a point B. This represents our half equivalence point. This represents our ideal buffer. Remember at the half equivalent points where we have equal amounts of weak acid and its conjugate base. This is where we have our most ideal buffer. So, point B represents where a buffer has been formed, which point on the tire traction curve represents the equivalence point. We already discussed this, we said that was point C. And then finally, which of the following would be the best indicator to use in the tight rations. Remember an indicator can approximate what your equivalence point is by using the endpoint. That's the ph in which the indicator changes colors. So here we have our equivalence point around nine maybe slightly higher than nine. So we want to use an indicator that has uh basically a p K. That's close to that value. So, if we look here, we see that our last option here has a PK equal to nine, it's p K is going to be very close to the ph of the equivalence point. So that means it's testing for the endpoint and that endpoints around nine which is right next to the equivalence point, ph So this would be the best indicator to use. So again, the best indicator to use for a PhD attrition curve is the indicator that has a p k a closest to the equivalent point. Ph. So again, in this case, it will be our last option, which has a PK A equal to nine.
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An indicator represents a weak acid or base in low concentration that changes color in an acid base titration. An indicator shows us the location of our endpoint, which is located near our equivalence point. 

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example

 The acid form of an indicator is red and its anion is blue

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Hey, guys, In this new video, we're gonna continue with our discussion of Ph tight Trish in curves when looking at indicators. So in this first example, it says the acid form of an indicator And what we should realize here is that an indicator is really just a weak acid. So an indicator has an acidic h on it. So the acid form is gonna be h A. And it's an ion form Means it's removed. It's h so not a minus. So the acid form of an indicator is red and it's an ion form. Its conjugate base form is blue. The value for this indicator is 10 to the negative nine. What will be the approximate ph range over which this indicator changes color. Now, what you should realize here is that in order to figure out the pH range oven indicator, all you have to remember is this The pH range of an indicator equals PK plus or minus one. So we have the K. So how do we find a peek? A. If we have k, just take the negative log of it. So we're gonna say p k equals negative log of K a so equals negative. Log off 10 to the negative nine. So the P K equals nine. And we just said that the PH range for an indicator is PK a plus or minus one. So the ph range is nine plus or minus one, which means nine minus one is eight to nine, plus one is 10. So the range would be between eight and 10. And that's what we have to remember Now. I'm gonna give you guys a hint on the next question, so just understand it like this. We're going to say we have a peek A that is equal to nine. Well, we should realize here, if your P H is equal to nine, we have pH and PK equally each other. And what did we say about that? We said that when pH equals P k, you're at the half equivalents points, so you have equal amounts off your acid form and your base form. So at this moment, h A equals a minus. And we're gonna say here at P K nine, that means that the Ph has to be at least nine for us to start to remove the acidic H off of our indicator. So what color would our indicator be below Ph of nine? What color would our indicator be above ah ph of nine. This will help us understand the next practice question. So remember this pattern attempt to answer this question on your own and then don't worry, Come back. Look at the next following video. You'll see an example of me explaining how to approach this problem and what the correct answer is. Good luck, guys.

An indicator, like a buffer, has an optimal range in which it works most effectively:

pka +/- 1. 

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Problem

What will be the color of the indicator in the above question in a solution that has a pH of 6?

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example

Consider the titration of 100.0 mL of 0.016 M H2SO4 with 0.400 M NaOH at the equivalence point

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Hey, guys, In this new video, we're gonna continue with our discussions on acid and based hi, Trish in curves while looking at the equivalent volume and the equivalent small aren t so when this question it says considered the Thai tray shin of 100 m. Els off 0.16 Mohler h two s 04 with 0.400 Mueller and ohh at the equivalence point. How many milliliters off 0.400 Mueller and a wage are required to reach the equivalence point. All right, so what do we say? What have we been saying this whole time? We say that at the equivalence point, your moles of acid equals your moles of base. So this is true at our equivalents Point. What else can we say? Well, the word off here means multiply. I don't remember if we multiply leaders times molar ity that's gonna give me moles so we can say this Weaken say m acid times V acid equals M base times V base. And remember, this is similar to something we're used to seeing the dilution equation M one V one equals m two v two. We can Onley use this at the equivalence point because at the equivalence point, we have equal moles of acid and base. And remember, moles also equal more clarity Times leaders. So we formed that connection between these two types of ideas. Now, the next thing we need to realize here is what kind of acid are we dealing with here? This is sulfuric acid, H two s 04 Remember, sulfuric acid is what type of acid it has to wages. What do we call assets that have too acidic ages? We call them die Pro Dick assets, remember, died product assets have too acidic. H is so because it has too acidic. H is. That means it has to or equivalents points because at each equivalents point, we have enough off base to rip off in H. And since we have two acidic ages here, we need two equivalents points. So what we're gonna realize here is what we should do here is find out what the first equivalents point is, and then doubling that amount will tell you the amount of volume you need to get to the second equivalents point. So here we're gonna say we have divide this by 1000 To get leaders, we have a point. 100 leaders of our acid times 0.16 Mohler off our strong acid here doesn't matter for its weak or strong, we still do the same thing. Our base is 0.400 Moeller and we don't know what the volume of our bases. So we're gonna divide both sides now by point 400. Okay? And when we do that, what is it gonna give us? Is going to give us a volume for our base and here is going to give us 0. four leaders for a base. Now I realize this is the volume that we need to get to the first equivalence point. Now, depending on how your professor phrases the question, we're going to say this is the volume at the first equivalence point. What if they ask us how much base we need to get to the second equivalence point? Well, you're just gonna need twice as much acid. I'm in twice as much to get twice as much base to get to the second equivalents point. So this is the answer for the first equivalents point. That's how much we need to get to the first one. To get to the second one, we would need to go twice as much. So it be this number times too. So if they were looking for how much volume of based you need to get to the second equivalence point, you would say 0.0.8 leaders if they had asked you What's the vine? You need to get to the first that we go with the first answer 0.4 leaders. So always be aware how maney acidic H is do you have because that will determine how Maney equivalents points you're dealing with. One more thing if we're dealing with the base, remember, we've been saying this repeatedly. Also, if you're dealing with a strong base to get the correct concentration, you always need to look at the number off. Oh H minus H minus, NH two minus and 02 minus To get the correct concentration here. We only had one. Ohh. So we didn't have to worry about the concentration, but I could have easily given you 0.400 Moeller B. A. O. H. Two. That's a strong bases Well, and it has 20 H is because it has 20 H. Is the correct concentration of our strong base. Would have been 0.800 Moeller. Okay, so that idea never goes away. If you have a strong base, you're supposed to always check to see how many of these ions you may have that will give you the correct concentration of your strong base. In questions like this, we now also have to pay attention to our acid. How maney acidic h is Does it have that will determine how Maney equivalents points we're dealing with? And from there we can know What's the volume to get to the first equivalents point, The second equivalents point, even the third equivalents point. So always keep that in mind when approaching problems like this. If you could remember that, then you won't fall for the trap that professors like to set up on exams.

If at the equivalence point, the moles of acid equal the moles of base and moles equal molarity multiplied by liters then at the equivalence point we can use the formula: 

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example

Consider the titration of 40.0 mL of 0.0800 M HCl with 0.0160 M Ca(NH2)2.a) How many milliliters of 0.0160 M Ca(NH2)2 are required to reach the equivalence point

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Hey guys, in this new video, we're going to continue with our discussion off equivalents, molar ity and equivalent volume. So in this example, it says, consider the Thai Trey Shin off 40 miles off 400.0 800 Mueller HCL with 8000.16 Mohler Calcium Hmeid. It says How many milliliters off the 0.160 Moeller calcium. My solution are required to reach the equivalence point. So remember, we sit at the equivalents point. We have equal moles of acid and base. So as a result, M acid times V acid equals M base times V base and we need to make certain checks to see if everything is correct. So we look to see calcium. A mind is a strong base based on the rules that we've learned several videos back. It's a strong base, so we need to look at Hominy. NH two minuses. It has. It has two of them, so it's really concentration would be 0.3 to 0. Moeller always have to check that when it comes to strong basis. So that's the concentration we're gonna plug in here. We're looking for its volume. So the base we don't know. Now for the acid form here, it only has one acidic H that we're dealing with. So only dealing with one equivalents point. Let's say, for example, we had h two s 04 in this. We would have toe figure out further information. Are they talking about the first equivalents point? Are they talking about the second they're talking about the second? We'd have to multiply the concentration times to in order to get the correct answer. So here we're gonna say it's dealing with one acidic age, so we don't have to worry about the concentration, the volume we're gonna put in as 0.40 Leaders, remember, we're looking for V base, So divide both sides by 0.3 to 0. Mueller, MLS cancel out. So our units at the end will be in leaders the only units that don't cancel out. When we do that, we'll get back an answer off point 100 leaders. So the base will be 0.100 leaders or 100 MLS if they ask for it in Emil's

When dealing with the equivalence point make sure you correctly calculate the molarity for both the acid and base. 

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example

Consider the titration of 40.0 mL of 0.0800 M HCl with 0.0160 M Ca(NH2)2.b) What is the pH of this solution

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now part B of this question, it says, What is the Ph of the solution? This part doesn't require any math on our part. We're dealing with the equivalence point between a strong acid and a strong base, and we've already heard this several times already. At the equivalence point between a strong acid and a strong base, Ph equals exactly seven under normal conditions. I remember when I keep saying normal conditions, all I mean is the temperature is 25 degrees Celsius. Because remember, all these things are connected to K W. 1.0 times 10 to the negative 14. And in our earlier videos we saw that if we change the temperature, we change our K W. And the new definition for neutral would change. It would no longer be seven. So remember the equivalence point for a strong acid and strong base is equal to exactly seven under normal conditions. If it were a weak acid with a strong base or a week faced with a strong acid, the equivalents point ph would be greater than or less than some seven in those cases will learn later on how exactly to find the exact Ph under those different circumstances and this one, we didn't need to do any math because when they're both strong, the answer is exactly seven. Now that we've seen this example, I want you guys to attempt to do the practice, one that's left on the bottom.
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Problem

Consider the titration of 60.0 mL of 0.200 M H3PO3 solution with 0.350 M potassium hydroxide, KOH solution. How many milliliters of base would be required to reach each of its equivalence points? 

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