Ascorbic Acid is an organic diprotic acid, H2A, that is found in many natural materials. KA1=7.94x10^-5 and KA2=1.62x10^-12. If you start with a 0.75 M solution of H2A, what is the concentration of ALL species in the solition at ph=3.8?

I have no idea how to even start this equation. Please help!

This is done just like a monoprotic acid but just do one acid at a time and reason it through. The pH is 3.8 so what is (H^+)? pH = -log(H^+) so (H^+) is about 1.6E-4

............H2A ==> H^+ + HA^-
I..........0.75..1.6E-4...0
C...........-x......x......x
E.........0.75-x. 1.6E-4+x..x

Substitute the E line into Ka1 and solve for x and the others; thata gives you H2A, H^+, and HA^-. That leaves only A^2-.

Now set up Ka2 the same way.
...........HA^- ==> H^+ + A^2-

Substitute the E line into Ka2 expression and solve for A^2-.

To solve this problem, you need to consider the dissociation of ascorbic acid (H2A) and its two acid dissociation constants (Ka1 and Ka2). Let's break down the steps to solve this equation:

1. Determine the dissociation reactions:
H2A ⇌ H+ + HA- (Reaction 1)
HA- ⇌ H+ + A2- (Reaction 2)

2. Write the expressions for the equilibrium constant (Ka) for each reaction:
Ka1 = [H+][HA-] / [H2A] (Equation 1)
Ka2 = [H+][A2-] / [HA-] (Equation 2)

3. Determine the expression for the concentration of each species in terms of x, the degree of dissociation:
[H2A] = (0.75 M - x) (Concentration of H2A)
[HA-] = x (Concentration of HA-)
[H+] = x (Concentration of H+)
[A2-] = x (Concentration of A2-)

Note: In this case, x represents the degree of dissociation, assuming the concentration of H2A is significantly larger than the value of x.

4. Use the equations and expressions to set up an overall expression for Ka1 and Ka2:
Ka1 = (x)(x) / (0.75 M - x)
Ka2 = (x)(x) / x

5. Solve for x using the Henderson-Hasselbalch equation:
pH = pKa + log([A-] / [HA-])
Subtracting both sides by pKa, we have:
pH - pKa = log([A-] / [HA-])
Convert the equation using the antilog:
[A-] / [HA-] = 10^(pH - pKa)
Since [A-] = x and [HA-] = x:
x / x = 10^(3.8 - pKa1) (pKa1 is the logarithmic value, not the decimal)

6. Calculate x using the obtained equation:
x = 10^(3.8 - pKa1)

7. Calculate the concentration of each species:
[H2A] = (0.75 M - x)
[HA-] = x
[H+] = x
[A2-] = x

Note: Ensure that x is less than 0.75 M to validate the assumption made in step 3.

By following these steps, you can determine the concentrations of all species in the solution at pH 3.8.