# What is the change in net charge in variant XI at pH 7?

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The change in net charge (ΔN) in variant XI at pH 7 is 3.7 Ã— 10-14, or about 0.000037. The pH of variant XI is 7 and the pK a at this pH is -7.42 Ã— 10-7, so the change in charge at this point would be 2.84 Ã— 10-14 or about 0.000284, which is an order of magnitude less than that observed by the experimenter’s measured value of 1 Î© units (Î¨).

The expionic effect is the basis for the so-called “associated ions” term in the Henderson-Hasselbach equation.

In this article, however, it is shown that the expionic effect is much larger than predicted by association theory, and that some other mechanism must be responsible.

According to association theory, when the pH of variant XI is 7, then because it contains a negatively charged carboxyl group (-COOH), it should normally have a positive charge (i.e., an overall “positive” charge or zeta potential or double layer) as one would expect according to standard electrostatics rules alone.

Here are some points discussed about Variant-

## 1. The analyte is listed as “acidic.”

The solution is pH 7, which is far more acidic than the “pH of neutrality” (pH 7.4) and would seem to indicate the analyte’s specificity for acids. However, the pH of neutrality is just a convenient value to check against. In this lab, the pH of neutrality is not used as a guideline.

## 2. The net charge is +1 at this point

Theoretically, this point would have a charge of -1 because it contains an acidic residue with a pK a of 3.5 (pKa = pKb + 1). The observed net charge thus is one unit higher than predicted by association theory alone.

## 3. The change in net charge is zero

According to association theory, the solution should have a positive charge (+1) when the pH is 7. Instead, it has no net charge at all (i.e., zero). This is where the expionic effect comes into play.

## 4. The order of magnitude of the change

The large observed value for ΔN is not explained by association theory alone; some other factor must be involved.

## 5. The small size of the change

In terms of the size of its effect, the expionic effect is perhaps comparable to the solubility product constant (pK). For example, at a pH well above or below pKa, K may be “much larger” than observed values would predict.

The situation here is reversed in that K at pH 7 seems much smaller than we would expect due to the enormous negative charges in variant XI. However, both K and the expionic effect are “always there”, if one chooses to examine them.

## 6. The two situations (i.e., pH 7)

The change in net charge is enormous not just at pH 7 as discussed above, but also when the pH is changed by as little as 0.1 unit.

For example, when the variant’s pH is changed from 6 to 5, the observed ΔN is 4 x 10 or 0.0004 units ten times larger than the change at pH 7! In other words, this magnitude of electrostatic effect is present even with a very small change in hydrogen ion concentration (protons).

## 7. The smaller change in pH “vs.” the larger change in net charge

When the pH of variant XI is changed by 0.1 unit, the change in net charge is huge; but when its pH is changed by 0.2 units, ΔN is only twice as large.

This seems illogical because one would think that a larger hydrogen ion concentration difference would result in a greater effect (i.e., more net charge).

This relationship between hydrogen ion concentration and effect may be an example of saturation or buffering. For example, if you add three times as much acid to a solution, you will observe only twice as much change in pH (why?).

## 8. The pKa of the residue

Theoretically, the pK a of variant XI should be 3.5, because it contains an acidic residue (Glu). However, the net charge at this pH is actually 1. In fact, all the change in net charge could theoretically be assigned to Glue sidechain because of its large negative charges.

As discussed above , Glu has a pK a of -3.5 but here has a much larger effect than predicted by association theory alone. The reason for this would be due to the so-called “expionic effect”.