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Topic: Equilibria and Mass Balance  (Read 22397 times)

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Offline Borek

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Re: Equilibria and Mass Balance
« Reply #30 on: February 19, 2012, 06:38:56 PM »
10^1 = [Mn 2+]/( [NH3] * ([Mn^2+] -( [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4] )))

[Mn2+]/(...) or [Mn(NH3)2+)/(...)? Or is it just a typo?

Even if it is a typo, I don't see how these equations reduce to "functions of [Mn(NH3)4]". Could be it is possible to eliminate other variables - that would be OK, as it would probably mean they can be calculated once you find the value of the [Mn(NH3)4]. Somehow I find it unlikely.
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Offline mx4ly

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Re: Equilibria and Mass Balance
« Reply #31 on: February 20, 2012, 03:25:40 PM »
10^1 = [Mn 2+]/( [NH3] * ([Mn^2+] -( [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4] )))

[Mn2+]/(...) or [Mn(NH3)2+)/(...)? Or is it just a typo?

Even if it is a typo, I don't see how these equations reduce to "functions of [Mn(NH3)4]". Could be it is possible to eliminate other variables - that would be OK, as it would probably mean they can be calculated once you find the value of the [Mn(NH3)4]. Somehow I find it unlikely.

[Mn(NH3)n].  Yes, that was a typo.  Sorry about that.

I can't work out analytically how it reduces down either, as Matlab is doing all of the equation solving.  However when I solve the system with italicized bits replaced with [Mn 2+] it works out correctly to the previous (incorrect) method I was using.  So the overall system is set up correctly, except for the modifications I am making to take into account that the complex formation uses up the [Mn 2+].

I can't seem to identify the error.  Do you see what is wrong with the system of equations?

Offline Borek

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Re: Equilibria and Mass Balance
« Reply #32 on: February 20, 2012, 04:15:50 PM »
10^(-12.70) = [Mn 2+] * OH^2

That would mean presence of solid, I think we already checked there will be no solid at pH 6.
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Offline mx4ly

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Re: Equilibria and Mass Balance
« Reply #33 on: February 20, 2012, 04:56:12 PM »
10^(-12.70) = [Mn 2+] * OH^2

That would mean presence of solid, I think we already checked there will be no solid at pH 6.

Ok, let's ignore that equation if we are doing the low pH case.  We eliminate that equation and one variable because [Mn(OH)2] = 0.  It's still does not work out in Matlab - meaning the system of equations is still incorrect when no solid is present

Offline Borek

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Re: Equilibria and Mass Balance
« Reply #34 on: February 21, 2012, 08:31:07 AM »
2 = ( [Mn^2+] -( [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4] )) + [Mn(OH)2] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]

I think I know what have happened. This is incorrect, you are mixing formal and equilibrium concentrations. It should be

2 = [Mn2+] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]  + [Mn(OH)2] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]
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Offline mx4ly

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Re: Equilibria and Mass Balance
« Reply #35 on: February 24, 2012, 08:02:37 PM »
2 = ( [Mn^2+] -( [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4] )) + [Mn(OH)2] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]

I think I know what have happened. This is incorrect, you are mixing formal and equilibrium concentrations. It should be

2 = [Mn2+] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]  + [Mn(OH)2] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]

Hmmm, I don't really understand what you mean here.  It looks like you are counting each of the complex molecules as double in terms of solving for the manganese concentration - but I don't understand why that would be.  Essentially you have: 2 = [Mn 2+] + [Mn(OH)2] + 2*[complex].  It seems to be working though - would you mind explaining the logic behind it?  I'll try to extrapolate now to cases where there is complex present.

Another plus - I found a better equation solver than Matlab's default.  The problems I was having before stemmed from a few numbers getting too small for Matlab to keep track of.  I'm able to find the correct solution now that values are actually being returned.

« Last Edit: February 24, 2012, 08:47:36 PM by mx4ly »

Offline Borek

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Re: Equilibria and Mass Balance
« Reply #36 on: February 25, 2012, 04:37:28 AM »
Sorry, my mistake. They should be listed only once.

Note that in your original equation

2 = ( [Mn^2+] -( [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4] )) + [Mn(OH)2] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]

complexes concentrations cancel out, leaving just

2 = [Mn^2+] + [Mn(OH)2]

Equation as I wrote it was wrong, but was "relatively" correct - that is, it was correct in logical terms, just the coefficient had incorrect value - so it was working better than equation that was in no way related to the situation in the solution.
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Offline mx4ly

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Re: Equilibria and Mass Balance
« Reply #37 on: February 25, 2012, 11:36:08 AM »
Sorry, my mistake. They should be listed only once.

Note that in your original equation

2 = ( [Mn^2+] -( [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4] )) + [Mn(OH)2] + [Mn(NH3)] + [Mn(NH3)2] + [Mn(NH3)3] + [Mn(NH3)4]

complexes concentrations cancel out, leaving just

2 = [Mn^2+] + [Mn(OH)2]

Equation as I wrote it was wrong, but was "relatively" correct - that is, it was correct in logical terms, just the coefficient had incorrect value - so it was working better than equation that was in no way related to the situation in the solution.

Ok, that makes sense. 

Now we get to the case with [Mn(OH)2] formation.  This begins pH ~ 7.5 (a peak in [complex]).  I am trying to use this additional equation, relating the free manganese and total complex to the solubility product.  I assume this is wrong because the resulting values are not correct, yet this makes logical sense to me:

([Mn 2+] + [complex]) * [OH-]^2 = 10^-12.70

The complex resulting from this system of equations should equal the case where solid = 0 at pH 7.5, which is unfortunately not happening.  Additionally, the concentration of complex flattens out much more quickly then when pH is increasing up to that point.  The total amount of complex at pH 8 is ~.072 calculated this way.  At pH 7 the concentration of complex is around .095, and at the peak pH 7.5 it is around .23 (using [Mn(OH)2] = 0).  The concentrations should be equal equidistant from the peak concentration, which is not the case.

Offline Borek

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Re: Equilibria and Mass Balance
« Reply #38 on: February 25, 2012, 12:52:18 PM »
For Mn(OH)2 presence of the complex doesn't matter. All that matters are equilibrium concentrations of Mn2+ and OH-. We have discussed it extensively before.
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