Isoelectric and Isoionic pH - Online Tutor, Practice Problems & Exam Prep

The isoelectric point (pI) of amino acids is the pH at which they exist as zwitterions, having both positive and negative charges that cancel out, making them neutral. Below the pI, amino acids act as cations, while above it, they behave as anions. For diprotic acids, the pI can be calculated using the average of the two pKa values: $pH=(1/2)(pK₁+pK₂)$. Understanding these concepts is crucial for grasping acid-base reactions and the behavior of polyprotic acids in solution.

Isoelectric and Isoionic Points

We're going to say here that our isoelectric or isoionic points represent the pH where a polyprotic acid doesn't migrate to an electric field because it's neutral. Traditionally, when we talk about isoelectronic and isoionic points, we refer to amino acids. Now a lot of the amino acids have 2 pKa values because of their acidic carboxyl group and their amino group that can be protonated to act as an acid as well. At the isoelectric point, we have an amino acid that has a negatively charged carboxyl group and a positively charged ammonium group. Overall, the amino acid is neutral because the negative end and the positive end cancel each other out.

We're going to say at the isoelectric point, your amino acid exists as a zwitterion ion. We have our carboxyl group here, our ammonium ion group here. Here, the carbon that is next to the carboxyl group is referred to as our alpha carbon. The alpha carbon has connected to it an alpha hydrogen; there are 20 different amino groups or amino acid groups because there are 20 different R groups when it comes to amino acids.

If we dump this zwitterion in a solution that is more acidic, we're going to protonate this carboxyl group. By protonating it, it no longer has that negative charge. It has this newly acquired H⁺ group, and all that remains is this positive charge. Below our isoelectric point, where the solution is more acidic, we exist as a cation. If we go the opposite way and throw the zwitterion into a more basic solution, we're going to deprotonate the ammonium group.

As a result, it becomes NH₂ which is neutral. Overall, the charge of our amino acid would be negative. We'd say that in a more basic solution, which is above the isoelectric point of my amino acid, my amino acid would exist as an anion, a negative ion. As a cation or an anion, they would be affected by an electric field. The cation, being positive, would be attracted to the negative plate of an electric field.

The anion, which is negative, would be attracted to the positive plate of an electric field because, remember, opposite charges attract one another. At the isoelectric point as a zwitterion for an amino acid, it's neutral overall and is not attracted or repelled by an electric field. Now that we've gotten the basic idea behind isoelectric and isoionic points, click on the next video to see the calculations that are involved with both of these two points and how they relate to the zwitterion or intermediate forms of compounds.

Isoelectric and Isoionic Points

Here we say that at the isoionic point, the polyprotic acid exists as an intermediate. We can utilize past equations to determine the concentration of H⁺. Now remember, for a diprotic system or diprotic acid, we have 3 forms. We have the acidic form, we have the intermediate form, and we have the basic form. Here, we only have one intermediate form.

The concentration of H⁺ for that intermediate form equals the square root of K_a1 times K_a2 times the formal concentration of my diprotic acid plus K_a1 times K_w which remember is \( 1.0 \times 10^{-14} \) at 25 degrees Celsius divided by K_one plus the formal concentration again. For a polyprotic acid, traditionally, triprotic acids are the most common polyprotic acids discussed. We have the acidic form. We have the 1st intermediate form. We have the 2nd intermediate form, and then we have our basic form.

Here we have 2 intermediate forms which is why we have 2 different equations. So remember, here we'll be dealing with H⁺ for the 1st intermediate form, and here we'd be dealing with H⁺ for the 2nd intermediate form. Remember that pK pH here equals pKa 1. pH here equals pKa 2. And then here, pH equals pKa 3.

Depending on where your pH lands in terms of being in here or being in here can help us determine, which equation really is useful in terms of determining pH or H⁺ in this case. Now the isoelectric point is the pH where the acid form is equal to the conjugate base form. Therefore, the average charge is equal to 0. Now again, if we're dealing with a diprotic acid, diprotic acids have 2 K_a values, K_a1 where we remove the first acidic hydrogen to give us our intermediate form, and then K_a2 which gives us our basic form. Also remember here that K_a2 would be connected to K_b1 and then K_a1 would be connected to K_b2.

Here, we really don't need to worry about the K_b values. Just realize for diprotic acid, pH for the isoelectric point which sometimes is written as Pi equals half the pKa 1 plus the pKa 2. With polyprotic acid, we run into the issue again of are we talking about the 1st intermediate form or the second intermediate form? So we have 2 different equations. Here we have pH equals half pKA 1 plus pKA 2 when we're dealing with the 1st intermediate form.

Then here we have pH equals half pKA 2 plus pKA 3 when dealing with the 2nd intermediate form. Traditionally, when we talk about isoelectric points, we relate them to the amino acids. For this first isoelectric point where we're dealing with the 2 lower pKa values, this is traditionally used for the acidic amino acids. So the acidic amino acids have 3 pKa's. Here, we'd use the two lower pKa values that they have out of the three. Examples of our acidic amino acids would be aspartic acid which has a 3 letter code of ASP and the one letter code of D, and glutamic acid. Glutamic acid has a 3 letter code of GLU and the one letter code of E. If we're dealing with determining the isoelectric point of aspartic acid or glutamic acid, they both have 3 pKa values but we'd use the 2 lower pKa values to find the isoelectric point. Here, we're dealing with the 2 larger pKa values, pKa2 and pKa3. This is traditionally used for the basic amino acids.

Like the acidic amino acids, they also have 3 pKa's but we're focusing on the 2 larger pKa values to find the isoelectric points. Your basic amino acids would be arginine, It's arginine, which has a 3 letter abbreviation of ARG, one letter abbreviation of R. We also have histidine which has a three letter abbreviation of HIS and one letter abbreviation of H. And then lysine would be the last basic amino acid. Here, it'd be LYS and K.

Remember, when we're talking about isoelectric points, we traditionally refer them to amino acids. When we're talking about polyprotic acids, we're talking about amino acids with 3 pKa values. Diprotic acids, those are just the normal amino acids that are not acidic or basic. They only have 2, pKa values that we can use, so there's only one equation for them. And then also remember that when we're talking about the isoelectric point, we're really referring to the intermediate form of your diprotic acid or your polyprotic acid.

We're calling the equations for the intermediate forms for a diprotic system and a polyprotic system as essential on our path to determining what our pH will be. Keep in mind these different definitions and how they relate to these different formulas.

Isoelectric and Isoionic Points Calculations 1

So here we're told to calculate the isoelectric and isoionic pH of 0.025 molar glutamine. Here, glutamine has 2 pKa values. pKa₁ equals 2.19 and pKa₂ equals 9.00. This is neither an acidic nor a basic amino acid. That's why a third pKa is not given.

Now here, to determine our isoelectric point, we can say here that pH is equal to half of pKa₁ plus pKa₂. So that's half of \(2.19 + 9.00\) which gives me a final pH of 5.60. For the isoionic pH, anytime we have to find the isoionic pH, we assume that we're dealing with the zwitterion of the amino acid, its intermediate form. It only has 2 pKa values, so it is a diprotic system. In that case, \(H^+\) would equal

( 10 - 2.19 ∗ 10 - 9.00 ∗ 0.025 ) + ( 10 - 2.19 ∗ 1 . 0 ∕ 10 - 14 ) ( 10 - 2.19 + 0.025 )

Here, when we work out the problems on top and on the bottom, we're gonna get \(1.61478 \times 10^{-13}\) on top, divided by 0.031457 on the bottom.

When we take the square root of that ratio, we're gonna get as our final concentration for \(H^+\) as \(2.26566 \times 10^{-6}\) molar. So that represents the concentration of \(H^+\). Taking the negative log of it will give me my pH. Here, my pH equals approximately 5.64. Realize here that when it comes to determining the isoelectric and isoionic pH of a diprotic or polyprotic system, the values will be very close to one another.

Here, the isoionic pH because it involves the use of more values and the actual concentration, will be closer to the actual pH of my diprotic or polyprotic system. The isoelectric point, although close, usually is not as accurate. But don't worry, both of the values should be very close to one another anytime you do both of these processes. Now that we've seen this, attempt to do example 2. Draw the structures and charge of aspartic acid at a pH of 9.82.

So aspartic acid represents an acidic amino acid. Therefore, it's gonna possess 3 pKa values. Based on those pKa values, determine which form would predominate at the given pH. Once you've done that, come back and see if your answer matches up with mine.

Isoelectric and Isoionic Points Calculations 1

Here it says, draw the structures in charge of aspartic acid at pH equal 9.82. Aspartic acid represents an acidic amino acid. It possesses 3 pKa values. Its pKa one value equals write them up here. pKa 1 equals 1.88.

And that is for its alpha carboxylic acid group. So that's the carboxyl group that's connected ammonium group connected to the alpha carbon. And then finally, pKa 3 equals 3.65. That is for our R group. Here, we're gonna say that the first way we can draw this structure is we have a carboxylic acid, which is my R group.

Here is my ammonium group that's connected to my alpha carbon, and here's the other carboxylic acid group. Here, we're talking about pKa 1. Well, pH equals pKa 1. Once we pass this line here, it becomes basic enough for us to remove the most acidic hydrogen, which is the hydrogen with the lowest pKa value. That means that we're losing this hydrogen here.

Here, it would look like this now. Here, when we cross when we get to this line, pH equals pKa 2. Once we pass this line, we're going to remove the next acidic hydrogen, most acidic hydrogen, which would be this hydrogen. So now we'd have this form of my amino acid. And then finally, while we're dealing with pKa 3, we have pH equals pKa 3.

And beyond this point, we're basic enough to remove the last acidic hydrogen which is one of these hydrogens here for the ammonium group. Now, we have this neutral form, NH₂. Here, the value would be 1.88. Here would be 3.65 and here is 9.60. The pH is 9.82.

We've gone beyond this line here. The predominant form of the amino acid would be this form where all the acetic hydrogens have been removed. This is the view of the amino acid once the pH hits 9.82. Remember, this is dealing with amino acids but it's piggybacking off of concepts we've seen before where we're relating pH to pKa. If the pH is greater than the pKa, we have enough of a basic environment to remove an acidic hydrogen.

Now that we've seen this example, attempt to do practice question 1. We're asked to figure out what our pI value is for the given amino acid. Once you've attempted this, come back and see if your answer matches up with mine.

Calculate the pI value for histidine. pK_a1 (carboxyl group) = 1.60, pK_a2 (ammonium group) = 9.28, pK_a3 (R-group) = 5.97. 

• A. 7.63
• B. 1.65
• C. 5.44
• D. 3.74
• E. 5.62

Calculate the pI value for gluatamic acid. pK_a1 (carboxyl group) = 2.16, pK_a2 (ammonium group) = 9.96, pK_a3 (R-group) = 4.30. 

• A. 6.06
• B. 7.13
• C. 3.23
• D. 5.47
• E. 7.00

Here’s what students ask on this topic:

What is the isoelectric point (pI) of an amino acid?

The isoelectric point (pI) of an amino acid is the pH at which the amino acid exists as a zwitterion. At this pH, the amino acid has both positive and negative charges that cancel each other out, making it electrically neutral. For amino acids with two pKa values, the pI can be calculated using the average of these values:

$\mathrm{pI}=\frac{({\mathrm{pK}}_1}{2}$

How do you calculate the isoelectric point of a diprotic acid?

To calculate the isoelectric point (pI) of a diprotic acid, you need to know the two pKa values of the acid. The pI is the average of these two pKa values. The formula is:

$\mathrm{pI}=\frac{({\mathrm{pK}}_1}{2}$

This calculation gives the pH at which the diprotic acid exists as a zwitterion, with no net charge.

What happens to an amino acid below and above its isoelectric point?

Below its isoelectric point (pI), an amino acid acts as a cation because the carboxyl group is protonated, and the amino group remains positively charged. Above its pI, the amino acid acts as an anion because the amino group loses a proton, becoming neutral, while the carboxyl group remains negatively charged. At the pI, the amino acid exists as a zwitterion, with both positive and negative charges that cancel each other out, making it neutral.

What is the difference between isoelectric and isoionic points?

The isoelectric point (pI) is the pH at which a molecule, such as an amino acid, has no net charge and exists as a zwitterion. The isoionic point, on the other hand, is the pH at which the concentration of the zwitterion form is at its maximum, and the molecule exists as an intermediate form in a polyprotic system. While the isoelectric point focuses on the net charge being zero, the isoionic point considers the specific intermediate form of the molecule.

How do you determine the isoelectric point of a polyprotic acid?

For polyprotic acids, the isoelectric point (pI) depends on the specific intermediate form being considered. For a diprotic acid, the pI is calculated as:

$\mathrm{pI}=\frac{({\mathrm{pK}}_1}{2}$

For triprotic acids, the pI can be calculated using the two lower pKa values for acidic amino acids or the two higher pKa values for basic amino acids. The specific formula depends on the intermediate form being considered.