in a 0.01 M solution of 1.4 butanedicarboxylic acid, (Ka1=2.9x10^-5, Ka2=5.3x10^-6), which species is present in the lowest concentration?
Let's call 1,4-butanedicarboxylic acid simply H2B. Then
H2B ==> H^+ + HB^-
HB^- ==> H^+ + B^2-
k1 = (H^+)(HB^-)/(HB)
k2 = (H^+)(B^2-)/(HB^-)
Since both k1 and 2 are small, you know H2B will be the largest of all.
Since the first H to come off is from k1 (k1 is larger than k2 and that's how you can tell) and you can see that H^+ = HB^-. Therefore, both H^+ and HB^- must be smaller than H2B but larger than the B^2-. That makes B^2- the smallest. You also know what B^2- is. It = Ka2.
To determine which species is present in the lowest concentration in a 0.01 M solution of 1,4-butanedicarboxylic acid, we need to compare the concentrations of the different species present using the dissociation constants Ka1 and Ka2.
1,4-butanedicarboxylic acid (C4H6O4) can dissociate into two acidic protons (H+) and two carboxylate ions (C4H5O4-). The dissociation process involves two steps:
Step 1:
C4H6O4 ⇌ H+ + C4H5O4-
Ka1 = [H+][C4H5O4-] / [C4H6O4]
Step 2:
C4H5O4- ⇌ H+ + C4H4O4^2-
Ka2 = [H+][C4H4O4^2-] / [C4H5O4-]
Since the solution is 0.01 M, we assume that the initial concentration of the acid (C4H6O4) is 0.01 M.
Let's calculate the concentrations of the species using the given dissociation constants:
Step 1:
Assuming x is the concentration of [H+] = [C4H5O4-], the concentrations at equilibrium are:
[H+] = [C4H5O4-] = x
[C4H6O4] = 0.01 - x
Applying the dissociation constant:
Ka1 = (x)(x) / (0.01 - x)
Simplifying the equation:
Ka1 = (x^2) / (0.01 - x)
Solving for x, you can use the quadratic equation or approximate methods to find the concentration of [H+] and [C4H5O4-].
Step 2:
Using the concentration [C4H5O4-] obtained from Step 1, we can find the concentration of [C4H4O4^2-]:
[C4H5O4-] = x
[H+] = x
[C4H4O4^2-] = 0
Since there is no [C4H4O4^2-] produced in Step 2, it means that the concentration of [C4H4O4^2-] is negligible compared to the concentration of [C4H6O4] and [C4H5O4-]. Therefore, the species present in the lowest concentration in the solution is [C4H4O4^2-].
In summary, in a 0.01 M solution of 1,4-butanedicarboxylic acid, the species present in the lowest concentration is the dicarboxylate ion (C4H4O4^2-).