Repost:: sorry couldn't understand it

What is the concentration of C2O4^-2 in a 0.370M oxalic acid solution? Ka1=5.6x10^-2 and Ka2=5.1x10^-5

This is what Dr. Bob222 gave you as an answer in your previous post:


Here is what I would do.
.......H2C2O4 ==> H^+ + HC2O4^-
I.......0.370......0.......0
C........-x.........x......x
E......0.370-x......x......x

BUT there is no need to solve the equation. We simply note that (H^+) = (HC2O4^-) and move on to k2.

k2
.......HC2O4^- ==> H^+ + C2O4^2-
I.....x(from above)..0.....0

k2 = (H^+)(C2O4^2-)/(HC2O4^-)
BUT from k1 we saw (H^+) = (HC2O4^-); therefore, H^+ in the numerator cancels with HC2O4^- in the denominator so that k2 = (C2O4^2-)

You can do this for several reasons. Note that we assumed the total H^+ = just H^+ from k1. We can do that because the H^+ supplied by k2 is 1000 times less than that supplied by k1. And we can assume HC2O4^- we used for k2 is the same as (H^+) because only 1/1000 of those HC2O4^- ions will ionize further.

To find the concentration of C2O4^-2 in a 0.370M oxalic acid solution, we first need to understand the dissociation reactions involved.

Oxalic acid (H2C2O4) has two acidic hydrogen atoms. It can dissociate in two steps, each with its own equilibrium constant (Ka).

The dissociation reactions are as follows:
H2C2O4 ⇌ H+ + HC2O4^- (Ka1)
HC2O4^- ⇌ H+ + C2O4^-2 (Ka2)

The first equilibrium constant, Ka1, is given as 5.6x10^-2, and the second equilibrium constant, Ka2, is given as 5.1x10^-5.

Now, let's assign variables to the unknown quantities:
Let x represent the concentration (in M) of C2O4^-2 in the solution.

Using the equilibrium expressions, we can set up the following equations:

For the first dissociation:
[H+][HC2O4^-] / [H2C2O4] = Ka1

For the second dissociation:
[H+][C2O4^-2] / [HC2O4^-] = Ka2

We also know that the initial concentration of oxalic acid (H2C2O4) is 0.370M.

To solve for the concentration of C2O4^-2, follow these steps:

Step 1: Use the initial concentration and the first equilibrium expression to find the concentration of HC2O4^-:
[HC2O4^-] = (Ka1 * [H2C2O4]) / [H+]

Step 2: Substitute the concentration of HC2O4^- from Step 1 into the second equilibrium expression to solve for the concentration of C2O4^-2:
[C2O4^-2] = (Ka2 * [HC2O4^-]) / [H+]

Substitute the concentration values and equilibrium constants given to solve for [C2O4^-2].

[C2O4^-2] = (5.1x10^-5 * [(Ka1 * [H2C2O4]) / [H+]]) / [H+]

Hope this helps!