# Equilibrium problem involving cube root

## 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
Homework Helper
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".

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.

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 ??

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
Mentor
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?

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