Intro to Acid-Base Titration Curves - Online Tutor, Practice Problems & Exam Prep

Acid-base titration is a method used to determine the unknown concentration of an acid or base by neutralizing it with a titrant of known concentration. The process generates a titration curve, which is a graph plotting the pH of the solution against the volume of titrant added. The equivalence point, a crucial part of the curve, is where the moles of acid equal the moles of base, indicating complete neutralization. The titration curve's shape varies depending on whether the reactants are strong or weak acids or bases. For instance, a sigmoidal curve is observed when both the titrant and the titrate are strong. The equation:

$M_A\times V_A=M_B\times V_B$

simplifies stoichiometry calculations, where $M_A$ and $M_B$ are the molarities of the acid and base, and $V_A$ and $V_B$ are their respective volumes. It's essential to account for the number of $H^{+}$ or ${\mathrm{OH}}^{-}$ ions in di- or polyprotic acids and bases, as this affects the concentration calculations.

Acid-Base Titration Curve

Now when it comes to an asset based titration, realize that it is a neutralization reaction used in determining the concentration of an acid and a base. Here we have some terms to remember when it comes to an acid base titration, the first one being a titrate. A titrant is a strong acid or base solution with a known concentration that is added to the titrate.

Now what's a titrate? Well, a titrate is an acidic or basic solution with an unknown concentration being neutralized by the titrant. The titration curve results from their interacting with one another. Here we're going to say the titration curve is a graph of the pH of the titrate during the titration with a titrant. So these are terms that you need to remember.

So if we were to visualize this, we would say that in an acid base titration we have our setup. In our setup we have our flask. Within this flask we have our titrate. Above it we have our burette and drop by drop we're adding our titrant. Here we're saying that our titrate is in the form of potassium hydroxide, a known strong base.

Here we're showing the pH before any of our strong base has been added. So before any strong base has been added, we have here a pH of 1. And what we're seeing here is the gradual addition of various volumes of potassium hydroxide. When we've gotten to 10 mL of potassium hydroxide added, the pH has increased to 4.15. When we got to 50 mL of potassium hydroxide, the pH is around 8.76 and then once we got to 100 mL of potassium hydroxide, we can see that our pH is 12.95.

Here, if we take each one of these basic volumes and pH values, we can put them on a graph and create our titration curve. Here our pH is on the Y axis and then various volumes of our titrant being added are on our X axis. This is how our curve is actually formed. So this curve is the result of adding our potassium hydroxide titrant to our titrate within this flask.

Now, the titrate itself, as we said, is an acidic or basic solution. It doesn't necessarily have to be a strong acid or strong base. All that's important is that it's acidic or basic in nature. OK, so it could be strong or weak. The titrant, on the other hand, has to be a strong species when doing these typical types of acid base titrations. Later on, we'll go into greater detail and talk about the various parts of a titration curve that results from the interaction between a titrate and a titrant.

The Equivalence Point

Now when it comes to acid base titration curves, you'll hear the term equivalence point. Now the equivalence point is just a point of complete neutralization where the moles of acid equal the moles of base. Here we're going to say the equivalence point volume equation represents a simplified approach to solution stoichiometric calculations.

So in the past we've talked about doing stoichiometry and incorporating calculations dealing with molarity. We can bypass that by using this simplified version of the equivalence point volume formula. Here it represents MA⁢VA=MB⁢VB. Here MA equals the molarity of the acid, and VA equals the volume of the acid. So MB would be the molarity of the base, and VB would be the volume of the base.

Now what's important in terms of this equation is it helps to simplify solution stoichiometric calculations, but you still need to pay close attention to the type of acid and base that you have. Here we're going to say for diprotic, which means you have two acidic hydrogens, and for polyprotic acids, when you have more than two, the number of H+ ions will affect the overall concentration.

So for example, let's say we had 0.40 molar sulfuric acid. Sulfuric acid in itself has a total of 2 acidic H+ ions. Yes, I know that the first one is strong, but the second one is very weak. But here we're looking at the totality of the number of H+ ions within sulfuric acid, that being two. That means that the true concentration when it comes to the equivalence point would be H+ equals the concentration of the whole compound times the number of H+ ions, which is 2. So that gives us a true concentration of 0.80 molar.

Now for strong bases, we've done what we've always done. We've looked at the number of OH-, H-, O2-, and H2- ions. This gives us the true concentration of our strong base. So for example, we have 0.10 molar of barium hydroxide. It has two OH- ions within it. So the true concentration of OH- would be 0.10, which is the concentration of the entire compound, times 2, the number of OH- ions. So this would be 0.20 molar, right?

So keep in mind, if you're going to utilize this equivalence point volume formula, to keep an eye out for the number of H+ ions in our acid and also the number of our basic anions for the base. So that would be in the form of OH-, H-, O2-, and H2- respectively.

Intro to Acid-Base Titration Curves Example

Here it says consider the titration of 40 MLS of 0.0550 molar of carbonic acid with 0.160 molar aluminum hydroxide. How many milliliters of 0.160 molar aluminum hydroxide are required to reach the equivalence point? So here we're talking about the complete neutralization between our acid and our base.

So here we're going to say M_acid times V_acid equals M_base times V_base. Here we have to take in consideration how many H⁺ ions our acid has. Carbonic acid has 2H⁺ ions, so we'd have to multiply this concentration by two. So its real concentration will be 110 molar, so the volume of our acid is 40 mills.

Then here we have to figure out the molarity of our base. Aluminum hydroxide has three hydroxides in it, so we multiply the concentration times 3, so it would be 480 molar and we're looking for the volume of our base. So that's what's missing. Divide out the 48 molar here molarities cancel out and we'll have our answer in milliliters.

When we plug that in, we're going to have 9.17 milliliters of our aluminum hydroxide base.

Shape of a Titration Curve

In our further discussion of acid-based titration curves, we can say that the parts and overall shape of the titration curve depend on the type of titrate and titrant used. Whether they're both strong or a combination of weak and strong can have a vast effect on the overall shape of our titration curve. Here we're going to say sigmoidal. This is the shape of the titration curve when both the titrate and titrant are strong, kind of like an S, almost like a more straightened-out shape.

Now here, this is an example of a strong-strong titrate, strong titrant curve. It gives us a sigmoidal shape. And when it comes to this typical type of acid-base titration curve, there are some key features you need to keep in mind. So here we're going to say our pure titrate. This is just the beginning of the titration before any titrant has been added. So here we have zero mL of our titrant that has been added. This is our starting point, and that's what we have, just the pure titrate by itself.

Then we have what's called the equivalence point. The equivalence point is just the middle region of the curve that has the steepest incline. So we see that it sharply increases once we hit around 60 mL. It kind of shoots up the middle of that. That's our equivalence point. And then finally, we're going to have after the equivalence point. This is just the region where excess titrant is being added. So once we've gone beyond this equivalence point, this is where we have excess titrant that's continuously added, and then we reach a plateau over time.

So keep in mind when we're dealing with the strong titrate, strong titrant curve, these are the three key features you should keep in mind when looking at a typical curve.

Intro to Acid-Base Titration Curves Example

Based on the image of the titration curve provided below, what is the potential identity of the titrate? Alright, so if we take a look here at this curve, we have a sigmoidal shape just in the opposite direction. So it's still between a strong tight ranked and strong tight trained. Remember, if we want to find the identity of the titrate, look at the beginning of the titration curve.

We're going to say the beginning starts before we've added any titrate. So we're starting right here. Now, what can we say about this starting point? Well, we can say that this starting point has a pH of 12, so it's 8 that greater than 7, meaning that our titrate is a basic compact. Remember bases have pH is greater than 7.

So if we take a look here, which one of these will represent a base? The first one is nitric acid. It is an OXY acid, so it wouldn't count. Then we have hydrofluoric acid, a binary acid. That doesn't count either potassium hydroxide. This is an example of a strong base, so this could be our answer.

Next we have acetic acid doesn't work, and then finally we have a positively charged amine. Remember, positively charged amines are acidic, so they would have PHS less than 7. So out of all the options, option C is the correct choice. Potassium hydroxide represents a strong base and it would represent the identity of my titrate.

Consider the titration of 100.0 mL of 0.40 M HCl with 0.40 M NaOH. If sodium hydroxide is the titrant, which volume would place it in excess? 

a) 70.0 mL                    b) 25.0 mL                    c) 100.0 mL                   d) 110.0 mL                   e) 9.0 mL

• A. 70.0 mL
• B. 25.0 mL
• C. 100.0 mL
• D. 110.0 mL
• E. 9.0 mL

Here’s what students ask on this topic:

When comparing the titration curves for the titration of a strong acid with a strong base and the titration of a weak acid with a strong base, which portion of the curves will be the most similar?

When comparing the titration curves of a strong acid with a strong base to that of a weak acid with a strong base, the most similar portion will be the vertical section of the curves that represents the rapid rise in pH. This section corresponds to the equivalence point where the amount of acid equals the amount of base added. At this point, the solution contains only the salt and water, and the sharp increase in pH reflects the neutralization reaction that has just occurred.

For both strong and weak acids, once you've added enough strong base to reach the equivalence point, the pH will rise quickly due to the excess hydroxide ions (OH^-) present. However, before and after the equivalence point, the curves will differ significantly because a weak acid does not dissociate completely in water, leading to a buffer region and a more gradual initial pH rise compared to a strong acid, which dissociates completely.

Which statements about titration curves are correct? Select all that apply:

• Is the pH at the equivalence point of the titration of a strong acid with a strong base 7.00?
• Is the pH at the equivalence point of the titration of a weak acid with a strong base greater than 7.00?
• Does the pH increase rapidly past the equivalence point, since there is excess hydroxide added?
• Is the starting pH of a weak acid titrated with a strong base lower than the starting pH of a strong acid titrated with a strong base?

In a titration of a strong acid with a strong base, the pH at the equivalence point is indeed 7.00. This is because the strong acid and strong base neutralize each other to form water and a salt, and the resulting solution is neutral if the salt does not affect the pH.

For the titration of a weak acid with a strong base, the pH at the equivalence point is greater than 7.00. This is because the conjugate base of the weak acid is formed in the reaction, which can react with water to produce hydroxide ions (OH-), making the solution basic.

Yes, the pH does increase rapidly past the equivalence point in any titration involving a strong base, including the titration of a weak acid with a strong base, because any additional strong base added will remain largely unneutralized, significantly increasing the pH.

The starting pH of a weak acid titrated with a strong base is indeed lower than the starting pH of a strong acid titrated with a strong base. Weak acids do not dissociate completely in solution, resulting in a higher initial pH compared to strong acids, which dissociate completely and thus have a lower initial pH.

How can the equivalence point on a titration curve be found?

The equivalence point on a titration curve can be determined by finding the point where the amount of titrant added reacts exactly with the amount of the substance being titrated. This is characterized by a sharp change in the pH of the solution. In an acid-base titration, the equivalence point is typically where the curve shows a steep rise or fall in pH value, depending on whether the titrant is an acid or a base.

To find this point, you can:

1. Plot the pH of the solution against the volume of titrant added.
2. Look for the section of the curve that shows the most significant change in slope, which indicates a rapid change in pH.
3. The equivalence point is at the inflection point of the curve, which is the midpoint of the vertical part of the curve.

For more accuracy, a pH indicator or a pH meter can be used. The indicator changes color at the equivalence point, while the pH meter will show a sudden change in the electrical potential. Alternatively, a derivative plot can be drawn, where the equivalence point corresponds to the peak of the curve.

How can pKa be determined from a titration curve?

To determine the pKa from a titration curve, you need to locate the point on the curve where the pH changes most gradually in response to the addition of titrant; this is the buffer region where the concentration of the weak acid and its conjugate base are equal. The pKa is the pH value at the midpoint of this buffer region. This midpoint corresponds to the point where exactly half of the acid has been neutralized and is therefore present in its conjugate base form.

On the titration curve, this is typically the flattest part of the curve before the steep rise of the pH that indicates the equivalence point. The equivalence point is where the amount of titrant added equals the amount of the substance being titrated. In a titration curve of a weak acid with a strong base, the pKa is found at the center of the vertical part of the curve. For a weak base titrated with a strong acid, it's the same principle but mirrored.