Question

Use this equilibrium equation to complete the next question: 4 SO4^2- + 4 Co^3+ <---> S2O8^2- + 4Co^2+

If the equilibrium constant is 9*10 ^-9

Find all concentrations of the initial Co^3+ concentration is 0.5 M and the initial SO4^2- concentration is 0.3 M

Answer 1

Well, first of all lets rewrite the equation , as it is wrong balanced the way you wrote it. The equation correctly balanced is:

2 SO₄^-2 + Co⁺³ <--------> Co⁺² + S₂O₈^-2   

now, it is useful to write the equilibrium constant for this reaction:

K = [Co⁺²]  [S₂O₈^-2 ] / [SO₄^-2 ]² [Co⁺³]= 9x10^-9

The best here is to use the ICE method:

[SO₄^-2 ] : initial: 0.3M , change: -2X, equilibrium: 0.3M - 2X

[Co⁺³] : initial: 0.5M , change: -X , equilibrium: 0.5M - X

[Co⁺²]: initial: 0 , change: X, equilibrium: X

[S₂O₈^-2 ]: initial: 0, change: X , equilibrium: X

Now we rewrite the equilibrium constant replaceing the equilibrium concentrations.

K = [Co⁺²]  [S₂O₈^-2 ] / [SO₄^-2 ]² [Co⁺³]= 9x10^-9 = X* X / (0.5M-X ) (0.3M-2X)²

X² / (0.5 - X) (0.09 - 0.12X + 4X²) =  9x10^-9

X² /(0.045 - 0.06X - 0.09X - 2X² + 0.12X² - 4X³ =  9x10^-9

0.045 - 0.06X - 0.09X - 2X² + 0.12X² - (1/ 9x10^-9 )X² - 4X³ = 0

- 4X³ -111111112 X² - 0.15X + 0.045 = 0

The roots of the polynomial are:

x1=2.0E?5

x2=?2.0E?5

x3=?27777778

As the X cannot be a negative number, X = 2x10^-5 . Then:

[SO₄^-2 ] : equilibrium: 0.3M - 4x10^-5

[Co⁺³] : equilibrium: 0.5M - 2x10^-5

[Co⁺²]: equilibrium: 2x10^-5

[S₂O₈^-2 ]:equilibrium: 2x10^-5