How Do Ks0 Values of MnCO3(s) Differ in Freshwater and Estuarine Waters?

[spooky01]

Homework Statement

compare the Ks0 values of MnCO3(s) in fresh water (I=0) and in estuarine waters (I=0.08) at 25°C. If each of the waters contained a concentration of CO32- equal to 10-6M and MnCO3(s) controls the Mn solubility, what is the Mn2+ concentration in each water? What is the Mn2+ activity in each water?

Homework Equations

MnCO3 (s) = Mn2+ (aq) + CO32- (aq)

Ks0 = {Mn2+}{CO32-} / {MnCO3 (s)}

Ks0 = yMn2+[Mn2+] yCO32-[CO32-]

The Attempt at a Solution

Not sure how to start. Any suggestions are greatly appreciated!

 

[spooky01]

Maybe I'm just not understanding what the problem means. Does it mean if [CO32-] is 10-6M and the ratio of CO32- to Mn2+ is 1:1 in the chemical equation then [Mn2+] is also 10-6M? Is this how others are interpreting the problem?

 

[Borek]

Calculate concentration of Mn²⁺ assuming solution is saturated AND concentration of CO₃^2- is 10^-6.

 

[spooky01]

Then an ICE table should be used? Something like this?
____________MnCO3 (s)__________Mn2+ (aq)________CO32- (aq)

Initial___________solid______________0_______________10-6M

Change__________-x_______________+x__________________+x

Equilibrium______-x_______________+x______________10-6M + x

 

[Borek]

No, no need for ICE table.

Write formula for Ksp. You know Ksp value, you know concentration of CO₃^2-, the only unknown is the concentration of Mn²⁺. And solving for the concentration of Mn²⁺ is trivial.

 

[spooky01]

Ksp = [Mn2+][CO32-]
Ksp = [x][x]
x= 10-6M
Ksp = (10^-6M)(10^-6M)
Ksp = 1.0x10^-12

Is this right?

 

[Borek]

No, you are doing strange things. That means you are completely confused about something.

First - find Ksp value in the Ksp tables. What is the value?

 

[spooky01]

Ohh I see what you're saying not, Ksp is 2.2 x 10-11.

 

[Borek]

Now plug the Ksp and CO₃^2- concentration into Ksp formula, and solve for the only unknown.

 

[spooky01]

Gotcha, that's simple! I was over thinking it. Thank you oh mighty chemistry guy. So in my above equation Ks0 = yMn2+[Mn2+] yCO32-[CO32-], can Ksp be put in for Ks0?

2.2x10^-11 = [Mn2+] (10^-6M)
2.2x10^-5 = [Mn2+]

 

[Borek]

As far as I can tell Ksp and Kso are different symbols used for exactly the same constant.

Just in case someone wonder what your equation means. I guess it is

K_{sp} = \gamma_{Mn^{2+}}[Mn^{2+}]\gamma_{CO_3^{2-}}[CO_3^{2-}]