EDTA: Videos & Practice Problems

EDTA, a hexaprotic acid, can exist in multiple forms depending on the pH of the solution, influencing its ability to form metal complexes. The basic form of EDTA is most effective for complexation, with formation constants (K_f) indicating the stability of these complexes. The relationship between pH and the fraction of the basic form is crucial for determining the concentration of free metal ions. The conditional formation constant (K_f') incorporates the fraction of EDTA in its basic form, essential for understanding metal-ligand interactions.

EDTA

Hey everyone. So in this video, we're going to take a look at EDTA. Here, we're going to say in its fully protonated form, EDTA exists as a hexaprotic acid. Here, it has the form of H6 because hexa means 6, protic means 6 protons, y2+. If we take a look here, we have the fully deprotonated form of EDTA.

That's why we have a charge of -four, so EDTA -four. Now, its form can change by the number of H+ it possesses. Okay, so that can increase or decrease depending on the pH of the solution. We're going to say here that remember for biological systems that carboxylic acids are considered strong organic or biological acids. They tend to have pKa values that are lower.

So, here we have a carboxylate group, another one, another one, and another one. Four carboxylate groups, which correspond to these 4 pKas. Then we're going to say that we have these 2 amine groups that can be protonated and therefore have their own pKa values. Those will result in these 2 higher pKas. Remember we've talked about this in the past that if your pH is greater than your pKa then that can result in deprotonation of a group.

And if your pH is less than your pKa then that can just be protonation. The environment is not basic enough to remove an H+ ion. So here the charge can change for EDTA based on the pH of the solution itself that it's submerged in. Now we're going to say in order to form metal complexes these acidic hydrogens must first be removed. We're going to say that EDTA can exist in up to 7 different forms depending on the pH of the solution.

So if we're taking a look here, we're going to say that this is considered the acidic form or fully protonated form. This exists when the pH of the solution is low enough, so it exists in an acidic environment. What we have here is we have basically the removal of protons or H+ over time as the pH of the solution increases. So we have 6 protons, 5, 4, 3, 2, 1, and then none. We're going to say that out of all these forms, this one here is the one that is neutral.

This neutral form is the one that's easiest to keep intact within a solution. So, if we want to transport EDTA over long periods of time submerged in a solution, we typically do it in its neutral form. We keep going and we get to this one here. This form here is our basic form. In this form, the pH is high enough that we've removed all the acidic protons from EDTA, so it exists in this EDTA form that we saw earlier.

We're going to say that this basic form is the ideal form when dealing with metal complexes. Now, if we take a look here at this graph, this graph is basically showing us at different pHs which of the 7 forms predominates. So we're going to say here that let's say for example here, a pH of 6, it aligns with this pKa of 5. This pKa of 5 means that we have kind of an equilibrium with one another, this form and this form of EDTA. At that pH of 6, we would say that we have an even split between them.

So 50% H2Y2- 50% HY3- At this point here, pKa 6, we're going to say that this is when our pH is around 10.37. We're going to say at that pH we have an equal amount of HY3- and the Basic form. Beyond that pH, so higher than 10.37, we'd have the basic form be the dominant or predominant form. Another piece of information that's good to know from this graph is that we can see that below a pH of 3, we can see that 4 of the 7 forms exist. So these are the forms that exist.

So basically, they exist when the environment is a pre-acidic pH of 3 and lower. Now, we can say to calculate the fraction of EDTA in its basic form we can utilize the following equation. So here we have basically the fraction and sub of the basic form equals the concentration of the basic form divided by the concentration of EDTA. So here that would equal the concentration of my basic form. When we say here the concentration of EDTA, we're talking about the concentration of all 7 forms.

Now here this can be expanded further into this lower equation. This lower equation, when we have the fraction of our basic form, is used when the pH of a solution, is given, and we're asked to find the fraction of the basic form because as you can see here, we have concentrations of H+ involved throughout the equation. And remember that if you know pH, you know H+ because H+=10-pH. And we can see also that we have Ka values being involved in this equation. We also know what our Ka values are because remember that Ka equals 10-pKa.

So when it comes to EDTA, it has a lot of different forms, and those forms are determinant on the pH of the solution in which our EDTA structure is submerged. Remember, the basic form is the best form when it comes to dealing with metal complexes themselves.

EDTA Calculations 1

So here it states, the formal concentration of EDTA is 1.50 millimolar. Now we're asked, what is the concentration of the basic form at a pH of 5.0? Alright. So we need to determine what the concentration of our basic form will be at this given pH. And here we have the overall concentration of EDTA.

Out of this total concentration, a portion of it belongs to the basic form. We're going to say that the concentration of my basic form equals the initial concentration of EDTA as a whole times the fraction of EDTA that exists in the basic form which we designate as alpha. Here, we're going to change our concentration to molarity. You could keep it in millimolar but I'll just change it to molarity. Remember here that 1 millimolar is equal to 10^-3 molar.

Here we have 1.50 × 10 - 3 molar. And here we're dealing with a pH of 5. What we have here are all our pH values set to a temperature of 25 degrees Celsius and an ionic strength of 0.10 molar. Remember, what do we notice? As the pH is increasing, as we go from 0 to 14, look at the fraction that exists in the basic form.

We can see that it's increasing. And this makes sense because on the previous page, we saw that chart with the waves and the lines, and we saw that as the pH increased, a greater percentage or a greater fraction of my total EDTA solution exists in the basic form. And what this is telling me is that once I get to pHs of 13 and 14, it's so basic that 100% of my total EDTA solution is in the basic form. All we do now is we just have to look up 5 for pH and here is my alpha for the basic form at that particular pH. We're just gonna plug that value in.

When we multiply that, we get 4.35 × 10 - 10 molar. What that answer is telling me, it's telling me that the total amount of EDTA with all 7 forms together totals 1.50 × 10 - 3 molar. Out of that amount, this is how much of it exists in the basic form at that pH of 5. So just remember, this goes in hand with the graph that we saw on the previous page with the waves. As the pH is increasing, the basic form becomes more and more a predominant part of my overall solution.

Now that we've seen this, take a look at example 2. Once you've attempted it or even if you don't attempt it, don't worry. Just come back and see how I approach example 2.

EDTA Calculations 1

For example 2, we need to determine the fraction of our EDTA that exists in the basic form when the pH is 8.50. Now from our chart given here, 8.50 would lie somewhere between 89 of course. We should expect our answer to be somewhere between 4.2 times 10^-3 and 0.041. Remember, if they're asking us to determine what our fraction of the basic form of EDTA is and all they give us is the pH, then the formula that we utilize is alpha, our fraction of the basic form equals k_a1·k_a2·k_a3·k_a4·k_a5·k_a6 H⁺6 + 5·k_a1 + H⁺4·k_a1·k_a2 + H⁺3·k_a1·k_a2·k_a3 + H⁺2·k_a1·k_a2·k_a3·k_a4 + H⁺·k_a1·k_a2·k_a3·k_a4·k_a5 + k_a1·k_a2·k_a3·k_a4·k_a5·k_a6 . Remember, EDTA in its fully protonated form is a hexaprotic acid. Therefore, it has 6 K_a values or 6 p_Ka values.

Now, they give us pH. So with pH, we know what the H⁺ is because remember, H⁺ equals 10^-pH. So it'll be 10^-8.50. And then, here we have our p_Ka values that were: p_Ka3 was 2, p_Ka4 was 2.69, p_Ka5 was 6.13, and then p_Ka6 was 10.37.

If you know your p_Ka value, then you know what your K_a value is. So here, we'd say that k_a1 equals 10^-p_Ka1. So 10^-1.50, 10^-2.00, 10^-2.69, 10^-6.13, and finally, this would be 10^-10.37. So all we do here is we plug in these values that we have here into each one of the spaces that we have here. It's a long arduous process but this is the formula we'd have to utilize in order to figure out our fraction of the basic form of EDTA.

When you plug in all those values, so when we plug in all the K_a values and we multiply them with each other, what we would get as a result is 2.04174 times 10^-23. Then, we could plug in all the values we have for each one of these here. So when we do that for each one of them, we'd get a bunch of different values. So I'll write them here: 1.0 times 10^-51 + 3.16228 times 10^-43 + 3.16228 times 10^-36 + 1.0 times 10^-29 + 6.54 times 10^-24 + 1.51356 times 10^-21 + 2.04174 times 10^-23.

So when you add up all of that on the bottom, you still have what you have on the top. Divided by all of those units added together on the bottom gives us a grand total of 1.54043 times 10^-21. So here, when we plug that into our calculators to get our final answer, we get an answer of 0.0133, which is a reasonable answer. Technically, we should only have 2 significant figures for the most part because the majority of those numbers have 2 significant figures. So we say 0.013, which is a reasonable answer because it is a number that falls in between these two values of 4.2 times 10^-3 and 0.041. Remember, as our pH is increasing, the fraction of the basic form of EDTA is increasing in amount. And remember, we use this version of the formula when we're only given the pH of the solution.

We use this form to figure out the fraction of the basic form. If they had given us the form of each of the 7 major forms of EDTA, then we'd use the original equation to figure out the fraction of basic form of EDTA. Like both formulas are pretty complex and long, so make sure you carefully plug in the right numbers step by step in order to find the final answer.

Now that you've seen this, answer this practice question that's left on the bottom. This one is much more straightforward. I've given us a graph which you'll have to utilize to find your answer. Once you attempt that, come back and see if your answer matches up with mine.

Determine the pH where αY4– equals 0.20.

• A. pH ≈ 11.1
• B. pH ≈ 12.5
• C. pH ≈ 9.80
• D. pH ≈ 9.00

Answer: (C)

EDTA Complexes

So, with EDTA complexes comes the discussion of formation or stability constants, which represent the equilibrium constant for the reaction between a ligand and a metal. Here, the formation or stability constant is shown by this variable. Now, the ligand in question that we are dealing with is EDTA. The general formula is our metal ion.

Here, we don't know what its charge is, so we say n⁺ to represent a metal with a +1 charge, or a +2 charge, or a +4 charge, or +3 charge, plus Y^-4. Y^-4 represents EDTA. This is the basic form of EDTA and is the predominant form that is usually used when dealing with a metal ion, although other forms of EDTA could also form ligand connections with the metal. It's just that this is the one in particular that is usually used.

Now, when they combine together, we get our EDTA complex. So here it's M_n^-4. For example, if you're dealing with calcium, which has a +2 charge, and we're dealing with EDTA, so calcium is +2, EDTA would be -4 here, so the overall net charge would be -2. We'd say CaEDTA^2-. If we're dealing with, let's say, iron 3 with EDTA, so this is +3, this is still -4.

So, overall, this would be -1. That's how the overall charge works, and here we're dealing with an equilibrium that's being established because we have the reversible arrows and just like with any equilibrium constant, we'll say that our formation or stability constant K_F equals products over reactants. Thus it would equal the EDTA complex divided by the concentration of the free metal ion times the concentration of EDTA. This formula itself is useful in determining the concentration of the free metal ion within the solution. Not every ounce or amount of the free metal will connect with EDTA. There will be some free-floating metal ions that haven't combined with every single EDTA molecule.

This expression can be used to determine the amount of free metal ion existing within the solution. Now, we're going to say the formation constants for metal-EDTA complexes are given below. Realize that some of them have superscripts of a and b. So, when it's a, that means the temperature is 20 degrees Celsius, and our ionic strength is 0.1 molar, and for the one labeled with a subscript of b, it is 20 degrees Celsius still, but now our ionic strength is 1 molar.

What we should realize here is that the common trend is the higher our charge becomes, the greater the affinity between the ligand and the metal, and the higher your K_F value will be. Again, the more positive the charge, the stronger the connection between the ligand and the metal. The higher your K_F, the more products would be favored, so the more your EDTA complex would be formed. Now, we are going to say only a portion of EDTA exists in its basic form, and the lower the pH, the more the other forms predominate.

Remember, we have to go to pHs of 13 and 14 for 100% of my solution to be in the basic form. If my pH is less than that, then portions of the solution will exist in the other six forms of EDTA. Now, here, we're going to say, under a fixed pH, the fraction of the basic form of EDTA becomes a constant and can be used to determine the conditional formation constant. So our conditional formation constant is here. So, it's K_F', which represents the formation of our EDTA complex at any pH value. Here, our conditional formation constant equals the fraction of your EDTA in basic form times your formation or stability constant and that still equals products over reactants. It's still the EDTA complex divided by the concentration of free metal ion times the concentration of EDTA. We'll have to utilize these different expressions, equations, and values to answer the following questions when it comes to EDTA complexes. So, click on to the next video and see how we approach the question where we are asked to find the concentration of the free barium ion within our EDTA complex that's formed when it reacts with EDTA itself.

EDTA Complexes

So here we have to basically discover the amount of free barium ion that exists when we've already formed our EDTA complex. So we're going to utilize this equation here within the question, and substitute in barium for that unknown m. So we're going to have Ba2++EDTA. Remember, EDTA, we're dealing with its basic form, so its charge is minus 4. So minus 4 plus 2 from the barium, so the net charge at the end will be minus 2.

So that's how we came up with BaY2-. Now, we're going to have our initial, our change, and our amount at equilibrium. Here they give me an initial concentration for the barium EDTA complex as being 0.10 molar. We don't have any initial amounts for the EDTA and the barium, 2+ ion. Since we have an initial amount for our complex, it's going to be decreasing over time, so this is minus x.

These 2 would be plus x. Bring down everything, so this is plus x, plus x, 0.10 minus x. Alright. So with any ice chart setups, or which we have to figure out equilibrium amounts, we need to know what our formation constant will be in this case, and not just our formation constant, but our conditional formation constant.

So we're going to have to utilize this portion here. So our conditional formation constant equals the fraction of EDTA that exists in its basic form times our formation or stability constant. So they're telling us that the pH is 10. Remember in our previous videos, we said that when the pH is 10, if we look on the chart from a few pages ago, we know that the value of our basic form of EDTA would be 0.30. Now, we need to figure out what our Kf is.

Well for barium ion, here it is right here, The log of Kf of barium is 7.88. So log of Kf for barium ion equals 7.88, but I don't want the log of Kf, I just want Kf. So I take the inverse of the log function. So now, Kf of barium ion equals 10^7.88. So that is what my Kf would equal.

When I multiply those 2 together that gives me 2.28 times 10^7. Now that I have my conditional formation constant, which is based on the pH given, We're going to say that this constant, like all other constants, equals products over reactants. So my barium complex divided by my barium ion times EDTA. All we're going to do now is we're going to plug in the values that we know. So we know that our conditional formation constant, we calculated it as 2.28 times 10^7 equals, at equilibrium, this is 0.10 minus x divided by both of these multiplying each other on the bottom is x squared.

So we're going to have to solve for x, so we're going to multiply both sides now by x squared. So 2.28 times 10^7 x squared equals 0.10 minus x. So this x variable has the largest power, so it's the lead term. So everything has to be moved over to its side. So my equation now is 2.28×107x2+x-0.10.

Next, we're going to use the quadratic formula in order to isolate our x variable. So here it'll be negative 1 plus or minus the square root of 1 squared minus 4 times 2.28 times 10^7 times negative 0.10, divided by 2a, which is 2 times 2.28 times 10^7. Alright. So here, when we solve, remember this is going to be plus or minus whatever all of this comes out to be. So when we do the math, we're going to say x equals negative 1 plus, so when I multiply, when I do all the functions inside, and then I take the square root, that's going to give me 301 divided by 4.56 times 10^7, or x equals negative 1 minus 303019.93 divided by 4.56 times 10^7.

So we get 2 possible values for x. So here for the first one, x would be 6.62 times 10^-5 molar, or x would be negative 6.62 times 10^-5 molar. Remember, at equilibrium, your final concentrations cannot ever be negative. It's not possible. So this cannot be the answer for x.

This would be my answer for x, and at equilibrium, x represents the concentration of both EDTA and barium ion. Here we don't care about the EDTA. We're focused on the barium ion free-floating barium ion concentration. So this would be our answer. So when it comes to determining the amount of free-floating metal ion, this is the approach we must take.

We have to set up a basic ice chart, look at the stoichiometric relationship between EDTA and the free-floating ion in the formation of our EDTA complex. Remember, we have a polydentate EDTA that forms a 1 to 1 ratio with the free-floating metal ion. So for every 1 mole of the free-floating metal ion, we have 1 mole of EDTA. You also have to determine the conditional formation constant and use that at the particular pH given to determine your final concentration at the end. So, keep in mind the approaches that we used here to find the answer for free-floating metal ions.

EDTA Complexes Calculations 1

So for this question, it asks us to determine the conditional formation constant for this EDTA complex at a pH of 8.0. Now remember our conditional formation constant is k′f. It is equal to the fraction of the basic form of EDTA, which we'll designate as alpha, times my formation or stability constant. Now here, if we take a look, remember EDTA itself is minus 4 in terms of its charge when dealing with the basic form. The overall charge is minus 1.

For that to occur, cobalt here would have to have a charge of plus 3. We're dealing with cobalt 3 ion interacting with EDTA to produce this EDTA complex. Now, here they're telling us that our pH is 8.0. Remember, in the chart that we saw a few pages ago, when the pH is 8.0, then the fraction of the basic form of EDTA gives us a value of 4.2×10−3. Here when we're dealing with whole integers in terms of pH, so 0 to 14, we can simply look at that chart and pick the value that we see for the fraction of the basic form of EDTA.

Now remember, if our pH is a value that is not a whole integer, so let’s say we had, 6.15 instead of 8.0, we’d have to utilize the equation that we've used before to figure out the fraction of the basic form. So remember, that was the one where we had ka1 all the way to ka6 on top, divided by H+6, plus all the other portions of the denominator. So that one would be a longer process in order to figure out the fraction of the basic form of our EDTA species. But again, we're dealing with whole numbers so we can simply look at the chart and pick the value that we see. Alright.

Now we have that. Then when we're dealing with cobalt 3, well, the log of kf for cobalt 3 ion equals 41.4. But we don't want the log of kf, we just want kf. So we're gonna take the inverse log function. So that's kfofcobalt 3 ion equals 1041.4.

So we'll put 1041.4 here. And then multiply those two values together, gives me an answer of 1.05×1039 as the conditional formation constant at that exact pH. Now, remember your k value, it's greater than 1. That means that products are highly favored which would mean that when Cobalt 3 ion comes into contact with EDTA, there is a high propensity or high desire to form this complex here. That's what our kf value was telling us here.

And remember, the more positive the charge of the metal ion, the greater the affinity the EDTA molecule or ligand has for the positive ion. The more they're going to combine together to help make this complex here. Now that we've seen this simple example, move on to example 2. Remember and utilize some of the techniques that we used in the previous page to help figure out the amount of free tin 2 ion within this example given. So good luck, guys.

EDTA Complexes Calculations 1

Here in this question, it states that the concentration of Tin(II) ions is 0.20 M and the potassium EDTA complex is at pH 9.00. First, we will split this complex. We have a Potassium ion, which represents our spectator ion, and then, from here, we have SnEDTA. The '2' here came from this complex, so this would be 2-. Now, moving forward, we have to think about the relationship between our Tin and EDTA.

Here, we're still looking at free Tin(II) ions, so we'd have Tin(II) ion + EDTA with a charge of -4, which explains why this ended up being -2. Here, we'd set up our ICE chart: Initial, Change, Equilibrium. We have an initial amount for this complex of 0.20 M. We don't have anything for Tin(II) ion or EDTA, initially, so they're both 0. Since we have an initial amount of this complex, this will decrease over time, thus minus x.

As these are going to increase over time: plus x and plus x. Bringing down everything: 0.20 minus x, plus x, plus x. Now we need to figure out our conditional formation constant, \( K'_{f} \). We say this equals our fraction of the basic form times our formation constant \( K_{f} \). Based on the pH, when we look at our table, we'd determine that it will come out to be 0.041. By consulting our table that relates the complex to the logarithm of \( K_{f} \) with our metal ion, which is Tin(II), it tells us that \( \log K_{f} \) is equal to 18.3. Taking the antilog of both sides, \( K_{f} \) would be:

K f 2 = 10 18.3

Plugging this value in, we obtain our conditional \( K'_{f} \), which comes out to be \( 8.18 \times 10^{16} \). This value will now be used within our equilibrium expression:

8.18 × 10 16 = 0.20 - x x 2

The above equation simplifies to:

8.18 × 10 16 x x 2 = 0.20 - x

To find a solution for this quadratic equation, we use the quadratic formula, leading us to:

x = - 1 ± 1 2 - 4 × 8.18 10 16 × - 0.20 2 × 8.18 10 16

Once solved, \( x = 1.56 \times 10^{-9} \) M, which is the concentration of free Tin(II) ions at equilibrium within this given scenario. This value becomes the answer as at equilibrium, negative concentrations are not possible.

Find the concentration of free Na ⁺ in 0.15 M Li ₃[Na(EDTA)] at pH = 10.00. 

• A. 0.024 M
• B. 0.13 M
• C. 0.063 M
• D. 0.22 M

Answer: (C)

Here’s what students ask on this topic:

What is EDTA and how does it function as a hexaprotic acid?

EDTA (Ethylenediaminetetraacetic acid) is a hexaprotic acid, meaning it can donate six protons (H⁺). In its fully protonated form, it is represented as H₆Y. The structure of EDTA includes four carboxylate groups and two amine groups, each with their own pKa values. The form of EDTA changes with the pH of the solution, affecting its protonation state. At low pH, EDTA is fully protonated, while at high pH, it is fully deprotonated, existing as Y^4-. This deprotonated form is most effective for forming metal complexes, as it can bind to metal ions through its multiple donor sites.

How does pH affect the different forms of EDTA?

The pH of a solution significantly affects the form of EDTA. At low pH (acidic conditions), EDTA is fully protonated (H₆Y). As the pH increases, protons are gradually removed, leading to forms like H₅Y^-, H₄Y^2-, and so on, until it reaches the fully deprotonated form Y^4- at high pH (basic conditions). The neutral form (H₂Y^2-) is often used for transport in solutions. The basic form (Y^4-) is ideal for forming metal complexes, as it can effectively bind to metal ions.

What are formation or stability constants (K_f) in the context of EDTA complexes?

Formation or stability constants (K_f) represent the equilibrium constant for the reaction between a ligand (like EDTA) and a metal ion. The general formula for this reaction is Mⁿ⁺ + Y^4- ⇌ MY^(n-4)-. The K_f value is calculated as the concentration of the EDTA-metal complex divided by the product of the concentrations of the free metal ion and EDTA. Higher K_f values indicate stronger and more stable complexes. The K_f values vary with the charge of the metal ion and the pH of the solution.

How do you calculate the fraction of EDTA in its basic form?

The fraction of EDTA in its basic form (Y^4-) can be calculated using the equation:

$\frac{{\alpha }_Y}{\mathrm{EDTA}}=\frac{{\mathrm{[Y]}}_{\mathrm{4-}}}{\mathrm{[EDTA]}}$

Here, [Y^4-] is the concentration of the basic form, and [EDTA] is the total concentration of all forms of EDTA. This can be expanded to include pH and pKa values, as:

$\frac{{\alpha }_Y}{\mathrm{EDTA}}=\frac{{\mathrm{[Y]}}_{\mathrm{4-}}}{\mathrm{[EDTA]}}=\frac{{\mathrm{[H]}}_{\mathrm{+}}{n}^{-}}{K_a}$

where n is the number of protons removed, and K_a values are the dissociation constants.

What is the conditional formation constant (K_f') for EDTA complexes?

The conditional formation constant (K_f') accounts for the fraction of EDTA in its basic form (Y^4-) at a given pH. It is calculated as:

$K_{\mathrm{f\text{'}}}={\alpha }_Y\times K_f$

Here, α_Y is the fraction of EDTA in its basic form, and K_f is the formation constant. This allows for the determination of the stability of EDTA-metal complexes at different pH levels, considering that not all EDTA will be in the Y^4- form at lower pH values.