Isoelectric and Isoionic pH: Videos & Practice Problems

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

The isoelectric point (pI) of a polyprotic acid, particularly amino acids, is the pH at which the molecule carries no net electrical charge, making it neutral. At this point, the amino acid exists as a zwitterion, characterized by a positively charged ammonium group and a negatively charged carboxyl group, which balance each other out. The alpha carbon, adjacent to the carboxyl group, is connected to an alpha hydrogen and is central to the structure of the amino acid, which can vary due to the presence of 20 different R groups.

When an amino acid zwitterion is placed in an acidic solution (below the isoelectric point), the carboxyl group becomes protonated, losing its negative charge and resulting in a cationic form of the amino acid. Conversely, in a basic solution (above the isoelectric point), the ammonium group loses a proton, leading to a negatively charged anionic form. This behavior illustrates the principle that cations are attracted to negatively charged plates in an electric field, while anions are attracted to positively charged plates, due to the attraction between opposite charges.

Understanding the isoelectric and isoionic points is crucial for grasping the behavior of amino acids in different pH environments, particularly in biochemical contexts. The zwitterionic form at the isoelectric point is significant as it indicates a state of neutrality, where the amino acid does not migrate in an electric field. This foundational knowledge sets the stage for further exploration of calculations related to these points and their implications for the behavior of amino acids and other compounds.

Isoelectric and Isoionic Points

At the isoionic point, a polyprotic acid exists in an intermediate state, which is crucial for understanding its behavior in solution. For diprotic acids, there are three forms: the acidic form, the intermediate form, and the basic form. The concentration of hydrogen ions (H⁺) for the intermediate form can be calculated using the equation:

H⁺ = \sqrt{K_{a1} \cdot K_{a2} \cdot [HA]} + \frac{K_{a1} \cdot K_w}{K_{a1} + [HA]}

where K_w is the ion product of water, equal to 1.0 × 10^-14 at 25°C. In the case of triprotic acids, which are common polyprotic acids, there are two intermediate forms, leading to two distinct equations for calculating H⁺ concentrations. The pH values corresponding to these forms are defined as:

pH = pK_a1 for the first intermediate form,

pH = pK_a2 for the second intermediate form, and

pH = pK_a3 for the basic form.

The isoelectric point (pI) is the pH at which the concentrations of the acidic and conjugate base forms are equal, resulting in a net charge of zero. For diprotic acids, the pI can be calculated using the formula:

pI = \frac{1}{2}(pK_{a1} + pK_{a2})

For polyprotic acids, the calculation depends on which intermediate form is being considered. The equations are:

pH = \frac{1}{2}(pK_{a1} + pK_{a2}) for the first intermediate form,

pH = \frac{1}{2}(pK_{a2} + pK_{a3}) for the second intermediate form.

Isoelectric points are particularly relevant in the context of amino acids, which typically have three pK_a values. For acidic amino acids, such as aspartic acid (Asp, D) and glutamic acid (Glu, E), the two lower pK_a values are used to determine the pI. Conversely, for basic amino acids like arginine (Arg, R), histidine (His, H), and lysine (Lys, K), the two higher pK_a values are utilized.

In summary, understanding the relationships between pH, pK_a values, and the forms of polyprotic acids is essential for accurately determining the isoelectric points of amino acids and their behavior in biochemical contexts.

Isoelectric and Isoionic Points Calculations 1

To calculate the isoelectric point (pI) and isoionic pH of glutamine, which has a concentration of 0.025 M, we first note that glutamine is a neutral amino acid with two pKa values: pKa₁ = 2.19 and pKa₂ = 9.00. The isoelectric point can be determined using the formula:

pI = \frac{1}{2} (pKa₁ + pKa₂)

Substituting the values, we find:

pI = \frac{1}{2} (2.19 + 9.00) = 5.60

Next, to find the isoionic pH, we consider the zwitterionic form of glutamine, which is a diprotic system. The formula for calculating the concentration of hydrogen ions (H⁺) is given by:

H⁺ = \sqrt{K_a1 \cdot K_a2 \cdot [A]} + \frac{K_a1 \cdot K_w}{K_a1 + [A]}

Where K_a1 and K_a2 are calculated as:

K_a1 = 10^-pKa₁ = 10^-2.19

K_a2 = 10^-pKa₂ = 10^-9.00

Substituting the values into the formula, we have:

H⁺ = \sqrt{(10^{-2.19}) \cdot (10^{-9.00}) \cdot 0.025} + \frac{(10^{-2.19}) \cdot (1.0 \times 10^{-14})}{(10^{-2.19}) + 0.025}

Calculating the numerator:

Numerator = 1.61478 \times 10^{-13}

And the denominator:

Denominator = 0.031457

Thus, we find:

H⁺ = \sqrt{\frac{1.61478 \times 10^{-13}}{0.031457}} \approx 2.26566 \times 10^{-6} \text{ M}

To find the pH, we take the negative logarithm of the H⁺ concentration:

pH = -\log(2.26566 \times 10^{-6}) \approx 5.64

It is important to note that for diprotic or polyprotic systems, the isoelectric point and isoionic pH values are typically close to each other. However, the isoionic pH is generally more accurate due to its dependence on the actual concentration of the amino acid.

For further practice, consider the example of aspartic acid, which is an acidic amino acid with three pKa values. At a pH of 9.82, determine the predominant form of aspartic acid by analyzing its pKa values and the resulting charge states. This exercise will enhance your understanding of amino acid behavior in different pH environments.

Isoelectric and Isoionic Points Calculations 1

Aspartic acid is an acidic amino acid characterized by three pKa values, which are essential for understanding its behavior in different pH environments. The pKa values are as follows: pKa₁ = 1.88, associated with the alpha carboxylic acid group; pKa₂ = 3.65, related to the carboxylic acid group in the side chain (R group); and pKa₃ = 9.60, corresponding to the ammonium group.

At a pH of 9.82, which is above the pKa₃, aspartic acid predominantly exists in its deprotonated form. This means that all acidic hydrogens have been removed due to the basic environment. The process of deprotonation occurs sequentially as the pH increases past each pKa value. Initially, at pH = pKa₁, the first acidic hydrogen is lost from the alpha carboxylic acid group. As the pH rises to pKa₂, the second hydrogen is removed from the side chain carboxylic acid. Finally, when the pH exceeds pKa₃, the last acidic hydrogen is removed from the ammonium group, resulting in a neutral form of the amino acid.

In summary, at pH 9.82, aspartic acid exists as a fully deprotonated species, represented as NH₂ for the ammonium group, with both carboxylic acid groups in their deprotonated forms. This illustrates the relationship between pH and pKa, where a pH greater than the pKa indicates a sufficient basic environment to remove acidic hydrogens.

To further explore the properties of aspartic acid, one can calculate its isoelectric point (pI), which is the average of the pKa values surrounding the zwitterionic form. This is a valuable exercise to deepen understanding of amino acid behavior in various pH conditions.

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

Answer: (A)

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

Answer: (C)

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.