Posted by C on Tuesday, March 19, 2013 at 7:57pm.
H2A+ H2O----H3O+ HA^-2
HA^-2+ H2O-----> H3O + A-
Let x=HA^-2
Let y=A-
So, for the following reaction
H2C2O4 + H2O----H3O+ HC2O4
H2C2O4...........H3O....HC2O4
I0.40M..............0 ........ 0
C-x.....................x............ x
E0.40-x.............x.............x
Solve for x,
ka1=[x][x]/[0.40-x], which turns into,
ka1=[x][x]/[0.40]
sqrt*(ka1*0.40)=x=5.4 x 10^-3
HC2O4 + H2O-----> H3O + C2O4
HC2O4...........H3O....C2O4
I.......Y..............0 ............ 0
C....-z...............z.............z
E....y-z..............z.............z
But since it is a diprotic acid and x=H3O+ y= H3O+, the charts become
H2C2O4 + H2O----H3O+ HC2O4
H2C2O4...........H3O....HC2O4
I0.4M..............0 ........ ..0
C-x..............,,..x............ .x
E0.4-x.........x+Y..........x-y
HC2O4 + H2O-----> H3O + C2O4
HC2O4..................H3O...............C2O4
I...5.4 x 10^-3.........x.....................0
C..-y......................x+y.....................y
E...5.4 x 10^-3-y...x+y.....................y
So, ka1=[5.4 x 10^-3+y][5.4 x 10^-3-y]/[0.370]
and
ka2=[5.4 x 10^-3+y][y]/[5.4 x 10^-3]
We solved for x, so solve for y.
I believe this is how you tackle this problem.
See the above.
Change H2C2O4 to H2A, HC2O4 to HA^2, and C2O4 to A-. Everything else is okay.