What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H2A, HA–, A2–) at pH 7.05?
Not sure how to find k1 and k2 needed for the fraction formulas...please help :(
looking at the structure, the NH3 groups will have the same pka values (9.731). You will have to use the Henderson Hasselbalch equation (pH=Pka +log(A-/HA) to solve. So, at a pH of 7.05 what is the fraction of dissociation?
You can do it using ka=[HA-][H30+]/[H2A] and ka=[A2-][H30+]/[HA-], but I THINK that you can use the Henderson Hasselbalch equation twice and get the same result. I didn't try and plug in the numbers and see.
I got the answer, thanks!
aH2A = [H+]^2/([H+]^2 + [H+]K1 + K1K2)
aHA- = K1[H+]/([H+]^2 + [H+]K1 + K1K2)
aA2- = K1K2/([H+]^2 + [H+]K1 + K1K2)
KA1 and KA2 can be found elsewhere
Ka1 = 4.65×10–6 and Ka2 = 1.86×10–10
To determine the fraction of each form of piperazine at pH 7.05, we need to use the acid dissociation constants (pKa values) of piperazine, denoted as k1 and k2. These values describe the tendency of piperazine to lose successive protons and form the different ionic forms.
Unfortunately, I do not have access to the specific pKa values for piperazine at the moment. However, I can guide you on how to find these values.
Step 1: Search for pKa values
You can search for the pKa values of piperazine in chemical databases, research papers, or textbooks. These sources generally provide pKa values for different compounds. Look specifically for the pKa values of piperazine, which will be given as k1 and k2.
If you are unable to find the exact pKa values, you may consider using an estimated value or assuming them to be similar to those of structurally similar compounds.
Step 2: Determine the pH needed for the fractions
Once you have the pKa values, you need to determine the pH at which you want to calculate the fraction of each form. In your case, the pH is given as 7.05.
Step 3: Calculate the fractions
The fractions of each form can be calculated using the Henderson-Hasselbalch equation, which relates the pH, pKa, and the ratio of two ionic forms. For the three forms of piperazine, the relevant equations are:
1. H2A ↔ HA- + H+
Fraction of H2A: [H2A] / ([H2A] + [HA-] + [A2-])
2. HA- ↔ A2- + H+
Fraction of HA-: [HA-] / ([H2A] + [HA-] + [A2-])
3. A2- ↔ 2H+
Fraction of A2-: [A2-] / ([H2A] + [HA-] + [A2-])
In these equations, [H2A], [HA-], and [A2-] represent the concentrations of the respective forms, which we need to calculate.
Step 4: Substitute the values and calculate
Using the Henderson-Hasselbalch equation with the pKa values of piperazine and the given pH (7.05), calculate the fractions of each form.
[H2A], [HA-], and [A2-] will be expressed as ratios relative to the total concentration of piperazine (usually given as 1M or 1000mM, for example).
Note that the sum of the fractions of each form should add up to 1.
By following these steps, you should be able to determine the fraction of piperazine in each of its three forms (H2A, HA–, A2–) at pH 7.05.