# Acid and Base Titrations

## 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.

Concept: Understanding an Acid–Base Titration Curve.

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##### Video Transcript

Hey guys, in this new video, we're going to take a look at acid and base titration curves. Let's take a look at this image. We're going to say here the shape of a titration curve involving an acid and a base makes it possible for us to identify the equivalence point. Now, we're going to say the equivalence point is where we have equal amounts of acid and base together. It's when we have equal moles of both. We'll have equal moles of acid and base. That is called or equivalence point. They basically neutralize each other because they're equal in amount. If we take a look at this curve, we can say here that what looks like we’re beginning around a pH of 1. That pH is very, very low. That would indicate that we're dealing with a strong acid initially. Take a look. Overtime we’re adding more ml of a titrate.
Basically what's happening is we have a jar or a beaker of acid and we're dropping, drop by drop, some base. We’re saying that the strong acid is being titrated by base. The base is our titrate. We're saying over time we can see that the pH is gradually increasing. Then all of a sudden, boom it goes straight up and there’s a huge change in the pH. We're going to say because around this volume where we see the big jump in our pH, this represents the equivalence volume of our base. It looks like once we get to 35 ml, we've reached the equivalence amount of mls of the base we need to get to the equivalence point. It would shoot straight up. This is the steepest climb. The biggest change in pH happens around the equivalence point. We're going to say halfway up this increase, we have this dot right here. That dot right there represents our equivalence point. At that exact moment, we have equal amounts of acid and base together. We're going to say here it looks like the pH is 7 exactly at the equivalence point. This is our equivalence point right here. We're going to say here because the equivalence point is exactly at 7, a pH of 7, this tells us that a strong acid is being titrated by a strong base. Because when they're titrating each other, and when we get to the equivalence point of a strong acid and a strong base together, the pH is always equal to 7 under normal conditions.
What we're going to say here, we see that it keeps climbing, the pH keeps climbing. After the equivalence point, we have what's called an excess of strong base. Remember, above 7 you’re basic. Once we get past this point right here, this equivalence point, all the acid is gone so all we have now is just additional base being added to our beaker of solution. This is exactly how it works. This would represent a pH titration curve of a strong acid and a strong base being mixed together.
We’ll learn later on that we don't only have this type of titration. We could titrate a strong base with a strong acid. We're starting out with strong base. It means we’re going to start off fairly high, maybe around 13 and we're going to add strong base. Overtime, the base will decrease and decrease. We’d say here, this red curve represents the titrating of a strong base with a strong acid. It would also give us a pH of equal to 7, around the equivalence point. So, these are two strong species titrating each other. We’re also going to learn later on that we have a strong species titrating a weak species. As a result, the pH at the equivalence point will be greater than 7 or less than 7.

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

Concept: The Equivalence Point.

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##### Video Transcript

If we take a look down below this graph, we’ve already answered this first part. We’re going to say at the equivalence point, the pH of a strong acid and a strong base is equal to 7. 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. It's going to say since I’m stronger, I’m going to want my solution at the end to be acidic. Anytime you're titrating a weak acid and a strong base together, at the equivalence point the pH is going to be less than 7. It's going to be acidic. 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. We wind up with a draw, which means neutral that's why the pH is equal to 7.
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 going to want to have a basic solution. The solution has to have a pH greater than 7 at the equivalence point. Just remember these fundamentals. As we start to do more acid and base titration questions, keep this in mind as we face every type of question we're going to see. Just remember, the equivalence point is when we have equal moles of acid and base. Depending on what we're titrating, whether they both are strong, or one is strong or weak, the equivalence point could have a pH equal to 7, less than 7 or greater than 7.

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

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?

a) point A      b) point B      c) point C      d) point D

3) Which point on the titration curve represents the equivalence point?

a) point A      b) point B      c) point C      d) point D

4) Which of the following would be the best indicator to use in the titration?

a) erythrosin B, pKa=2.9    b) methyl blue, pKa=5.4    c) bromthymol blue, pKa= 6.8    d) o-cresonphthalein, pKa=9.0

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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.

Example:  The acid form of an indicator is red and its anion is blue. The Ka value for this indicator is 10-9. What will be the approximate pH range over which this indicator changes color?
a) 3-5        b) 4-6        c) 5-7        d) 8-10        e) 9-11

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

pka +/- 1.

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. How many many milliters of 0.400 M NaOH are required to reach the equivalence point?

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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:

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

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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Problem: Consider the titration of 60.0 mL of 0.200 M a 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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## Weak Acid and Base Titrations

Concept: Understanding Weak Acid–Base Titrations.

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##### Video Transcript

Hi guys, in this new video, we're going to get to see how exactly do we approach a weak acid base titration. Now, we already know this, we said in the past, we reacted weak acids and weak bases with water and use an ICE Chart. Remember, when we're dealing with acids and bases in our ICE Charts, the units in the ICE Chart had to be in molarities, so we needed moles over liters. Remember, ICE stood for initial, change, equilibrium.
Now, we're going to react these weak acids and weak bases not with water but with strong acids and bases. We're going to say, when you react a weak species with a strong species, so weak acids with a strong base or a weak base with a strong acid, we no longer going to use an ICE Chart, instead we're going to use a new chart, we're going to use an ICF Chart.
In here, we're going to say ICF stands for initial, change, final. It becomes imperative that you guys remember how to identify compounds, as either being an acid or a base, weak or strong? If you guys can't remember how to do that, then learning to use an ICF Chart becomes that much more difficult. Here we're going to say an Ice Chart is in a molarity and an ICF Chart is in moles.
Just remember this if we have a weak acid or weak base by itself, not being titrated with any other types of compound, it reacts with water in an ICE Chart. If we have a weak acid or base now, being mixed in a strong acid or base and then we now have to go and do an ICF Chart, so remember that difference.

Whenever we react a WEAK ACID with a STRONG BASE or a STRONG ACID with a WEAK BASE we use an ICF CHART.

In an ICF Chart the units will be in moles instead of Molarity.

Example: Consider the titration of 75.0 mL of 0.0300 M H3C3O3 (Ka = 4.1 X 10-3) with 12.0 mL of 0.0450 M KOH. Calculate the pH.

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Let's take a look at this example here. In this example, it says: Consider the titration of 75 ml of 0.0300 molar H3C3O3. Here it has a Ka of 4.1 times 10 to the negative 3 with 12 ml of 0.0450 molar KOH. I ask you to calculate the pH.
First of all, we should know what KOH is. KOH is a strong base. That goes without saying that we should know that. Next what we're going to say here is this compound. This compound has H, a nonmetal and it has oxygen. It's an oxyacid. Remember, we do the math. If we subtract oxygens by hydrogens, for it to be a strong oxy acid, we need a minimum of two oxygens left. When we do the math, we have 3 oxygens minus 3 hydrogens. We have nothing left. It's a weak oxyacid. Even if you didn't know that, you should realize it’s weak because its Ka value is less than 1. You always use that as the fallback because sometimes they may not give it to you and they might just ask you what can be done with this type of compound. You have to be able to identify that it's a weak acid.
We have a weak species. We have a strong species. We have to use an ICF chart. Number one thing. Each thing that I say, an ICF chart has much more detail involved. Be careful with everything that I'm giving you guys. Write them down precisely. When we're dealing with an ICF chart, whatever is strong has to always be a reactant. We have a strong base, so that has to be our reactant. We're going to say bases naturally attack what? The mortal enemy, I guess, chemical enemy of a base is an acid. This strong base has to react with the weak acid. Our weak acid is on the same side with a strong base. First, remember whatever is strong has to be a reactant. Whatever it is, it attacks its opposite. Since the strong base is a reactant, what do bases attack? Bases attack acids. The weak acid has to be next to it as a reactant. Since we're dealing with a strong species, we no longer have double arrows. We have a single arrow going forward. Remember that the acid is going to give away an H+. That H+ will go to the OH- within the base to give us water. Then what's left, we're going to have K positive which is going to react with H2C3O3 minus, together they give us that compound.
We're going to say ICF. Just remember in an ICF chart, we only care about three things. We only care about whatever is strong. We only care about the weak acid and we only care about conjugate base. Those are the three things we only focus on in an ICF chart. The fourth thing, we never look at it. We just ignore it. In this particular example, the fourth thing happens to be a liquid, water. Just like in an ICE chart, an ICF chart ignores liquids and solids. But even if it wasn't water, we’d still ignore it because in an ICF chart, we only care about what is strong, the weak acid and the conjugate base.
Next thing we're going to say is what are the units in an ICF. The units have to be in moles. What we're going to do here is remember the word ‘of’ means multiply. Remember, moles can be found if you take your molarity and multiply it times your liters. These mls, divide it by a thousand, multiply them with their molarities. When we do that, we're going to get 0.00225 moles. Remember, how did I get that number? I just divided the 75 mls by a thousand and then multiplied that by 0.0300 molar and it gives me that many moles. The base, divide 12 ml by a thousand. Those liters, you multiply times the molarity and it gives you moles. I don't give you any information on the conjugate base so initially it’s zero.
An ICF chart like I've been saying is much more detailed and it's very different from an ICE chart. What we're going to do now is we're only going to pay attention to the reactant side. Remember that these smaller moles will try to neutralize the larger amounts of moles. The smaller moles which are these moles will try to neutralize the larger moles, these moles. The strong base is going to take all of itself and try to neutralize as much of the weak acid as it can. At the end you have no more strong base and you're still going to have some weak acid left.
Remember, the first law of thermodynamics says: Matter is neither created nor destroyed. So, it's okay. The weak acid is decreasing by this much but that's fine because it's not really getting destroyed. It's just getting reshaped into a new form. If our weak acid decreases by that much, its conjugate will increase by the same amount. The conjugate over here increases by the same amount. Just remember, much more detailed. Look at the reactant side. Whichever moles are smaller, they will neutralize, try to neutralize the larger moles. They will take all of themselves and try to subtract it from the larger moles. Just remember that one principle. Remember, whatever the reactant decreases by, it's okay because its conjugate will increase by the same amount. Bring this down.
What you need to realize here is what do you have at the end? At the end you have conjugate base left and you have weak acid left. Weak acid, conjugate base, what does that give us? That gives us a buffer. Remember, if you have a buffer, just use the Henderson-Hasselbalch equation to find pH. Remember, for Henderson-Hasselbach, pH equals pKa plus log of conjugate base over a weak acid. Negative log of Ka plus log of the conjugate base, what we have left, over the weak acid. Punch that all into your calculator and you should get back 1.89 for your pH.
Again, an ICF chart is very detail-oriented. Make sure you’ve paid attention to all the steps that I've talked about. We know that we should have a buffer at the end because remember, what's one of the ways to create a buffer? Mixing a weak acid and a strong base. Weak acid, strong base. As long as the weak acid is larger in initial amount than the strong base, you will have a buffer at the end. The theory we learned earlier, we're now seeing it applied to using calculations. ICF charts, like I've been saying, are much more detail-oriented. We're going to be doing a lot of them. Pay attention to all of the methods that we’re using.
Now that you guys have seen this one, I want you to attempt to do the next one on your own. Don't worry about it. If you get stuck, come back, click on the explanation video and you'll see a video of me explaining how best to approach this problem. Remember the principles that we talked about. If we have a weak acid or base reacting with something strong, it's got to be an ICF. In this example, we have HBr which is a strong acid mixing with acetic acid which is a weak acid and its conjugate base. It has one less H. Here, Ka of acetic acid is actually this number. I forgot to give it to you but just remember, that's the Ka of acetic acid. Weak acid and conjugate base are both weak. We have two weak things mixing with a strong thing. We know we should do an ICF. Remember, strong thing has to be what? What side does it have to be on? From there, follow along all the things that we talked about earlier to solve this question. Come back, click on the explanation button to see what answer will I get and if it matches up with yours. Good luck guys!

If you use and ICF Chart and at the end you have remaining weak acid and conjugate base then you have a buffer so use the Henderson Hasselbalch equation to find pH.

Problem: Calculate the pH of the solution resulting from the mixing of 75.0 mL of 0.100 M NaC2H3O2 and 75.0 mL of 0.60 M HC2H3O2 with 0.0040 moles of HBr.

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In an ICF chart the strong species (Strong Acid or Strong Base) must always be a reactant.

Example:  A buffer contains 167.2 mL of 0.25 M propanoic acid, CH3CH2COOH, with 138.7 mL of 0.42 M sodium propanoate, CH3CH2COONa. Find the pH after the addition of 150.2 mL of 0.56 M HCl. (The Ka of CH3CH2COOH is 1.3 x 10-5).

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If you use an ICF chart and at the end you have a strong species (Strong Acid or Strong Base) remaining then find its molarity to find either pH (if Strong Acid) or pOH (if Strong Base).

Problem: In order to create a buffer 7.510 g of sodium cyanide is mixed with 100.0 mL of 0.250 M hydrocyanic acid, HCN. What is the pH of the buffer solution after the addition of 175.0 mL of 0.300 M NaNH2?
Ka = 4.9 x 10-10.

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If you use an ICF Chart and at the end you have no reactants and only the product then you are at the equivalence point. In this situation we then must use an ICE chart to find the pH.

Example: Consider the titration of 75.0 mL of 0.60 M HNO2 with 0.100 M NaOH at the
equivalence point. What would be the pH of the solution at the equivalence point? The Ka of HNO2 is 4.6 x 10-4

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