Equilibrium problem involving cube root

[kasse]

Homework Statement

The reaction 2Fe³⁺ + Ni(s) = 2Fe²⁺ + Ni²⁺ has equilibrium constant K = 1.5E34. What is the concentration of Fe³⁺ at equilibrium if a lot of Ni(s) is added to a 0.1 M solution of Fe³⁺ that initially contains no Fe²⁺?

The Attempt at a Solution

K = 4x³/(0.1-2x)²

My plan is to find x. [Fe³⁺] is then 0.1-x, but how do I solve this problem involving a cube root?

 

[GCT]

Disregard the 2x portion in the denominator and the solve for x - if the value of 2x is negligible relative to the 0.1 than you've got a good approximation of the actual answer - read in your text or confer with your teacher to find out what constitutes "negligible".

 

[eli64]

Disregard the 2x portion in the denominator and the solve for x - if the value of 2x is negligible relative to the 0.1 than you've got a good approximation of the actual answer - read in your text or confer with your teacher to find out what constitutes "negligible".

May I suggest double-checking the equilibrium constant value. GCT's suggestion will apply if the K is very small. However as written, K is very large and may affect what is negligible.

 

[kasse]

K is correct.

I found this in the solutions manual:

K = [Fe²⁺]²[Ni²⁺]/[Fe³⁺]² = 1/[Fe³⁺]²

but why is [Fe²⁺]²[Ni²⁺] = 1 ??

 

[eli64]

K = [Fe²⁺]²[Ni²⁺]/[Fe³⁺]² = 1/[Fe³⁺]²

but why is [Fe²⁺]²[Ni²⁺] = 1 ??

It is a curious approximation. I'm not sure how to explain it.

Another approach: If K is so large, how does adding the Ni(s) reactant shift the equilibrium, and what does that indicate about [Fe3+] and its initial concentration?

There is an approximation that could be made but I would look at the [0.1 - 2x]2 term and think about the change the equilibrium.

 

[Borek]

but why is [Fe2+]2[Ni2+] = 1 ??

No idea. I would say it is 5*10^-4. To get this number simply follow eli64 advice. If K is so large, where is the equilibrium? How much Fe³⁺ is left?