Ascorbic acid, H2C6H6O6, is a diprotic acide with a K1= 7.9 E-5 and a K2=1.6E-12. In a .005 M aq solution of ascorbic acid which of the following species is present in the lowest concentration.
1. H2O
2. H3O+
3. H2C6H6O6
4. HC6H6O6-
5. C6H6O6-2
To determine which species is present in the lowest concentration in a .005 M aqueous solution of ascorbic acid, we need to compare the concentrations of the different species based on their equilibrium constants.
Ascorbic acid, H2C6H6O6, is diprotic, meaning it can lose two protons. The first equilibrium constant, K1, represents the dissociation of the first proton from ascorbic acid:
H2C6H6O6 ⇌ H+ + HC6H6O6-
The second equilibrium constant, K2, represents the dissociation of the second proton from ascorbic acid:
HC6H6O6- ⇌ H+ + C6H6O6-2
To find the concentrations of the species, we need to use the equilibrium expression for each dissociation reaction and calculate their concentrations based on their respective equilibrium constants.
For the first dissociation:
K1 = [H+][HC6H6O6-] / [H2C6H6O6]
For the second dissociation:
K2 = [H+][C6H6O6-2] / [HC6H6O6-]
Since we are given a concentration of .005 M for ascorbic acid (H2C6H6O6), we can assume the initial concentration of H2C6H6O6 is equal to .005 M. From there, we can calculate the concentrations of other species using the equilibrium expressions and the given equilibrium constants.
Let's start with the first dissociation (K1). Since we have only one unknown concentration (HC6H6O6-), we can solve for it:
K1 = [H+][HC6H6O6-] / [H2C6H6O6]
7.9E-5 = [H+][HC6H6O6-] / .005
[H+][HC6H6O6-] = 7.9E-5 * .005
[H+][HC6H6O6-] = 3.95E-7
Now, let's move on to the second dissociation (K2). Again, we only have one unknown concentration (C6H6O6-2):
K2 = [H+][C6H6O6-2] / [HC6H6O6-]
1.6E-12 = [H+][C6H6O6-2] / [HC6H6O6-]
[H+][C6H6O6-2] = 1.6E-12 * [HC6H6O6-]
[H+][C6H6O6-2] = 1.6E-12 * (3.95E-7) (Substituting the value of [HC6H6O6-] from the previous calculation)
[H+][C6H6O6-2] = 6.32E-19
Now, we can compare the concentrations to determine which species is present in the lowest concentration.
[H2O] and [H3O+] are not part of the dissociation reactions of ascorbic acid, so their concentrations are not relative to the equilibrium constants.
Comparing the concentrations we calculated:
[H2C6H6O6] = .005 M (initial concentration of ascorbic acid)
[HC6H6O6-] = 3.95E-7 M (from calculation using K1)
[C6H6O6-2] = 6.32E-19 M (from calculation using K2)
From the comparison, we can see that the species present in the lowest concentration is C6H6O6-2 (option 5).