Kc is 1.67 × 1020 at 25°C for the formation of iron(III) oxalate complex ion:
Fe3+(aq) + 3 C2O42-(aq) [Fe(C2O4)3]3-(aq).
If 0.0200 M Fe3+ is initially mixed with 1.00 M oxalate ion, what is the concentration of Fe3+ ion at equilibrium?
867687
Well, if you want to know the concentration of Fe3+ ion at equilibrium, I suggest you call it "Fe3+ equilibrium-ion". It sounds much more official that way, don't you think?
But seriously, to find the concentration of Fe3+ ion at equilibrium, we can use the expression for the reaction quotient, Qc, which is similar to the equilibrium constant Kc. In this case, Qc would be calculated as [Fe(C2O4)3]3- / [Fe3+][C2O42-]³.
Since we know the initial concentrations of Fe3+ (0.0200 M) and C2O42- (1.00 M), we can plug these values into the expression. However, we don't know the concentration of Fe(C2O4)3]3-, so let's call it x M.
So, our expression becomes x / (0.0200 * (1.00)³). And since we know that Kc = 1.67 × 10²⁰, we can set up the equation Kc = Qc and solve for x:
1.67 × 10²⁰ = x / (0.0200 * (1.00)³)
Multiply both sides of the equation by 0.0200 * (1.00)³ to isolate x:
x = 1.67 × 10²⁰ * (0.0200 * (1.00)³)
Now, just plug the numbers into your trusty calculator to find the value of x, which would be the concentration of Fe3+ equilibrium-ion at equilibrium.
Remember, it's all about those equilibrium-ions!
To find the concentration of Fe3+ ion at equilibrium, we can use the equation for the equilibrium constant (Kc) and the initial concentrations of Fe3+ and C2O42-.
The equilibrium constant expression for the given reaction is:
Kc = [Fe(C2O4)3]3- / [Fe3+] [C2O42-]^3
Given:
Kc = 1.67 × 10^20
[Fe3+]initial = 0.0200 M
[C2O42-]initial = 1.00 M
Let's assume the change in concentration of Fe3+ is x M. This means the change in concentration of C2O42- is 3x M.
At equilibrium, the concentrations will be:
[Fe3+]equilibrium = [Fe3+]initial - x
[C2O42-]equilibrium = [C2O42-]initial - 3x
Using these values, we can rewrite the equilibrium constant expression as:
Kc = [Fe(C2O4)3]3- / ([Fe3+]initial - x) ([C2O42-]initial - 3x)^3
Substituting the given values into the equation, we have:
1.67 × 10^20 = ([Fe(C2O4)3]3-) / (0.0200 - x) (1.00 - 3x)^3
To solve for x, we can rearrange the equation:
([Fe(C2O4)3]3-) = 1.67 × 10^20 (0.0200 - x) (1.00 - 3x)^3
Now, we need the initial concentration of Fe3+:
[Fe3+]initial = 0.0200 M
Substituting this value into the equation, we have:
[Fe(C2O4)3]3- = 1.67 × 10^20 (0.0200) (1.00 - 3x)^3
Simplifying the equation, we have:
[Fe(C2O4)3]3- = 0.0334 (1.00 - 3x)^3
Now, let's solve for x by using the quadratic formula. We will rearrange the equation to isolate (1.00 - 3x)^3:
(1.00 - 3x)^3 = [Fe(C2O4)3]3- / 0.0334
Taking the cube root of both sides to eliminate the exponent:
1.00 - 3x = ( [Fe(C2O4)3]3- / 0.0334 )^(1/3)
Now, solve for x:
x = (1.00 - ( [Fe(C2O4)3]3- / 0.0334 )^(1/3)) / 3
Using the given equilibrium constant expression, we can calculate the concentration of Fe3+ at equilibrium by substituting the calculated value of x back into the equation:
[Fe3+]equilibrium = [Fe3+]initial - x
Note: The value of x in this equation is expected to be very small since we assume that the reaction goes to completion. This assumption is based on the fact that the equilibrium constant (Kc) is very large (1.67 × 10^20), indicating that the reaction strongly favors the formation of the complex ion [Fe(C2O4)3]3-. Therefore, [Fe3+]equilibrium will be approximately equal to [Fe3+]initial.
To determine the equilibrium concentration of Fe3+ ion, we can use the equilibrium expression and the given initial concentrations of the reactants.
The equilibrium expression for the reaction is:
Kc = [Fe(C2O4)3]3- / ( [Fe3+] x [C2O42-]3 )
Given:
Kc = 1.67 × 10^20
[Fe3+]initial = 0.0200 M
[C2O42-]initial = 1.00 M
Let's assume the change in concentration of Fe3+ at equilibrium is x M. Since 3 moles of oxalate ion are consumed for every 1 mole of Fe3+ ion, the change in concentration of oxalate ion is 3x M.
At equilibrium:
[Fe3+] = [Fe3+]initial - x
[C2O42-] = [C2O42-]initial - 3x
Substituting these values into the equilibrium expression, we get:
Kc = [Fe(C2O4)3]3- / ( [Fe3+] x [C2O42-]3 )
1.67 × 10^20 = ([Fe3+]initial - x) * ( [C2O42-]initial - 3x)3
Simplifying the equation and rearranging, we get:
1.67 × 10^20 = (0.0200 - x) * (1.00 - 3x)3
Expanding and solving the equation for x will give the equilibrium concentration of Fe3+ ion. However, this equation involves a complex calculation and may require numerical methods or software programs to obtain the accurate value of x.
Therefore, the final concentration of Fe3+ ion at equilibrium can be found by solving the equilibrium expression equation using numerical methods or software programs.
This is a problem that almost has to be worked "backwards" to make it work.
.....Fe^3+ + 3C2O4^2- ==> [Fe(C2O4)3]^3-
I....0.02....1.00...........0
C....-0.02..-0.06..........0.02
E......0.....0.94..........0.02
What I have done above is to look at the size of Kc (a huge number) and assume the reaction will go essentially to completion. I know Fe^3+ won't be zero at equilibrium although it will be very very small; therefore, you can't calculate how much is left because all most all of it is gone. The way you handle a problem like this is to let it go to completion, then take the E line amounts and let those be initial amounts in another ICE chart and that way the small number can be calculated. Like this.
....Fe^3+ + 3C2O4^2- ==> [Fe(C2O4)3]^3-
I.....0.......0.94..........0.02
C.....x.......3x.............-x
E.....x......0.94+3x.......0.02-x
Then substitute the E line into the Kc expression and solve for x = (Fe^3+)