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Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: LaGÅm on April 01, 2021, 02:34:34 PM

Title: Equilibrium calculation of Mg
Post by: LaGÅm on April 01, 2021, 02:34:34 PM

The problem is as follows:
Mg²⁺ +CO₃^2-  ::equil:: MgCO₃
Using the K for the equilibrium, K_f=10^2.88 and the known concentration of MG species C_Mg=53.0 mM one should make an expression for [MG²⁺]

[MgCO₃]/[Mg²⁺][CO₃^2-]=K_f

from this i get
[Mg²⁺]=[MgCO₃]/[CO₃^2-]K_f

I have tried to attack this problem from diffrent angles but still don't arrive at the book solution of:
C_Mg*1/(1+[CO₃^2-]K_f)
Help and ideas would be reatly appreciated

Title: Re: Equilibrium calculation of Mg
Post by: Orcio_87 on April 01, 2021, 04:23:14 PM

Given concentration (53 mmol / liter) is far above solubility of MgCO₃ (1,648 mmol / liter).

Maybe it is the sum of dissolved MgCO₃ and MgCO₃ as suspension.

Title: Re: Equilibrium calculation of Mg
Post by: mjc123 on April 01, 2021, 04:47:49 PM

If you assume C_Mg = [Mg²⁺] + [MgCO₃] you can get the quoted answer. However, I have my doubts about this. I doubt if there is any significant concentration of undissociated MgCO₃ in water. If it is present as the solid (even as a suspension) its activity will be 1.

Title: Re: Equilibrium calculation of Mg
Post by: Orcio_87 on April 01, 2021, 05:24:06 PM

@LaGÅm

K = [Mg²⁺] [CO₃^2-] / [MgCO₃]

and [Mg²⁺] = [CO₃^2-]

and [MgCO₃] = C - [Mg²⁺]

so one way or another it still leads to quadratic equation.

Title: Re: Equilibrium calculation of Mg
Post by: Orcio_87 on April 02, 2021, 05:17:14 AM

@mjc123

I wonder how did you get "correct" answer.

In my opinion:

[Mg]² + K[Mg] = K C

and

K[Mg]² + [Mg] = C       (answer given by author)

are not the same.

Title: Re: Equilibrium calculation of Mg
Post by: mjc123 on April 02, 2021, 05:54:53 AM

C_Mg = [Mg²⁺] + [MgCO₃]
          = [Mg²⁺] + [Mg²⁺][CO₃^2-]K_f
          = [Mg²⁺](1 + [CO₃^2-]K_f)
[Mg²⁺] = C_Mg/(1 + [CO₃^2-]K_f)

Compare the definitions of K_f and your K.

Note that this doesn't assume that [Mg²⁺] = [CO₃^2-].

Title: Re: Equilibrium calculation of Mg
Post by: LaGÅm on April 02, 2021, 06:08:25 AM

I just solved it the same way as above, my mistake was expanding both [Mg²⁺] and [MgCO₃] when only [MgCO₃] needed to be expanded!