How can we determine the net charge of an amino acid at a given pH?
This is a question that comes up quite frequently in class
and is actually a lot easier to solve that may appear at first.
I usually follow the following steps
1. Identify the ionizable groups
2. Determine the pH of the solution and the pKa values for each of those ionizable groups
3. Determine whether each of these ionizable groups will exist predominantly in a protonated
or deprotonated state
and 4. Add up the charges of the ionizable groups to determine the net charge of the amino acid.
I added a 5th step to make things a little bit more interesting in a slightly more complicated scenario where the pH is equal to the pKa
Let's start with a simple example where we are calculating the net charge of a single amino acid like glycine, and work our way up from there.
Here we have a picture of glycine, and let's pretend that we wanted to determine the net charge of glycine at pH 7.
The first step is to identify the ionizable groups on glycine. Glycine has two ionizable groups.
One ionizable group is the amino group which can exist in one of two forms.
It can either be protonated
with a charge of +1 as NH3+, or neutrally charged, and deprotonated as NH2.
Whether not this amino group will exist predominantly in its protonated or deprotonated form
will depend on the pKa of this group and the pH
and this is something that we're going to discuss very soon
the second ionizable group on glycine is the carboxyl group
it can either be protonated with a neutral charge as COOH or negatively charged and deprotonated as COO-.
Again, whether not this carboxyl group will exist predominantly in its protonated for deprotonated form
will depend on the pKa of this group and the pH.
The next step is to clarify the pH of the solution and the pKa values for each of the ionizable groups.
You're told that the pH of the solution is 7
so we've clarified this point and we can move on to the pKa values
that pKa of the carboxyl group of glycine is 2.34
and the pKa of the amino group of glycine his 9.6
The values for the pKa of the carboxyl group are referred to as pK1
while the values for the pKa of the amino group on an amino acid are referred to as pK2
These values can be found in the following table
What you'll notice is that all of the amino acids have roughly the same pK1 and pK2 values.
pK1 is usually roughly somewhere between 2 and 2.3
while pK2 is somewhere between 9 and 10
You may also notice that some amino acids have a pKR.
This is only present if the amino acid has an ionizable R group.
In the case of glycine, which has an R group of the single hydrogen
it does not have been ionizable group and therefore does not have a pKR.
These value should make sense if you think about the properties of these groups.
The carboxyl group has a relatively low pKa
To remember this, I think that carboxyl groups are found on carboxylic acids. Note the word "acid" and hence the relatively low pKa.
On the other hand, the amino group is relatively basic
hence the relatively high pKa
The next step is to determine whether each of these ionizable groups will exist predominantly in a protonated or deprotonated state.
In order to do this, we can compare the pKa of each of these ionizable groups with the pH. As a general rule of thumb,
when the pH is much higher than the pKa the group will be predominantly deprotonated.
When the pH is much lower than the pKa
the group will be predominantly protonated.
We can use the Henderson-Hasselbalch (HH) equation in order to explain how we arrived at these general rules of thumb.
The HH equation shows the relationship between pH, pKa, and the relative amounts of an acid and it's conjugate base.
Now, let's go through an example that follows the criteria of the first general rule of thumb
where the pH is much higher than the pKa.
Let's pretend that the pH of the solution was 8.34
and the pKa of the ionizable group was 2.34.
Using the HH equation, we can determine that under these circumstances
the ratio of conjugate base to acid 10^6 to 1.
This means of an overwhelmingly predominant ratio of this group will exist deprotonated as the conjugate base.
This is why we can apply these general rules of thumb because most
of our ionizable group will exist in its deprotonated form when the pH is much higher than the pKa.
We can apply them very same math to any combination of pHs or pKas.
In most questions, the pH will be different enough from the pKa values of the ionizable groups that
we don't have to make these calculations, and we can simply rely on the general rules of thumb.
OK, back to the glycine example.
We've established the pH to be 7 and we know the pKa values of each of the ionizable groups.
At pH 7, the pH is much lower than the pKa of the amino group at 9.6.
This means that the amino group will be predominantly protonated and exist as NH3+, with a charge of +1
At pH 7, the pH is much higher than the pKa of the carboxyl group at 2.34.
This means that the carboxyl group will be predominantly deprotonated and exist as COO-, with a charge of -1.
Now on to the final step.
Adding up the individual charges of the ionizable groups.
Well, let's see. We have +1 from the amino group and
-1 from the carboxyl group for a net charge of zero.
The net charge of glycine at pH 7 is zero. Question complete!
What we just went through was a very basic scenario
and we can make things more complicated if we've really wanted to so let's do that.
How about a situation where the pH is equal to the pKa of one of the ionizable groups?
Let's apply this to our glycine example.
We know that glycine has a pK1 of 2.34.
Let's pretend that we're asked to determine the net charge of glycine at pH 2.34.
Well, by our general rules of thumb we know that the pH of 2.34 is much lower
than our pK2 of 9.6.
This means there amino group will exist predominantly as NH3+ with a charge of +1.
But what about the carboxyl group?
Here the pH is equal to the pKa of the carboxyl group.
From the HH equation, we know that when pH is equal to pKa then the
concentration of acid is equal to the concentration of conjugate base.
What this means is that half of our glycine in our solution of glycine will have the carboxyl group protonated
with a net charge of 0.
While the other half of the glycine in this solution will be deprotonated and have a net charge of -1.
This means that on average, the carboxyl group of glycine will have a charge of -0.5.
This brings us to our final step,
adding up the individual charges of our ionizable groups.
Here we have +1
plus -0.5
gives +0.5
The average net charge of glycine at pH 2.34 is +0.5
And we've solved our question!