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Homework Statement
Cadmium metal is added to 0.350 L of an aqueous solution
in which [Cr3+] = 1.00M. What are the concentrations
of the different ionic species at equilibrium?
What is the minimum mass of cadmium metal required
to establish this equilibrium?
2Cr3+(aq) + Cd(s) <--> 2Cr2+(aq) + Cd2+(aq) where Kc = 0.288
Homework Equations
ICE box, and Kc = [Products] / [Reactants]
The Attempt at a Solution
I know that Cd(s) is not included in the equilibrium expression. I also know that the initial concentration of Cr3+ is 1.00 M. Setting up the ICE box, I get this:
2Cr3+(aq)
I = 1.00M
C = -2x
E = 1-2x
2Cr2+(aq)
I = 0
C = +2x
E = 2x
Cd2+(aq)
I = 0
C = +x
E = x
And setting up my equilibrium expression, I get the following:
Kc = ( [Cr2+]^2 * [Cd2+] ) / [Cr3+]^2
0.288 = ( (2x)^2 * x ) / (1-2x)^2
Unfortunately, going further gives me a cubic function, and my gut is telling me that I have screwed up somewhere or misinterpreted the question, for every other question I have seen in the textbook does not require solving a cubic function. Where did I screw up?