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### Topic: Simple Equilibrium Question - Conceptual  (Read 5938 times)

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#### [V]

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##### Simple Equilibrium Question - Conceptual
« on: April 20, 2014, 02:36:46 AM »

I'm trying to understand this conversion (this is the Claus process btw). At lower temperatures we have better conversion, because we are favoring the S_8 allotrope, but at higher temperatures we have the S_2 allotrope.

Im trying to figure out how my ln(K) expression relates to the %conversion vs TEMP graph I have drawn.

Can someone please explain conceptually how this shape can fit that expression I have written? If I am solving for K at different temperatures, I wouldn't imagine the shape of the graph to look like that.

is my Standard Free Energy ALSO changing while I change temperature? Would I need to be calculating the standard free energy of different mixtures of S_2 & S_8 for each temperature?

Im just looking for a conceptual explanation behind this!

Thank you!

#### [V]

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #1 on: April 21, 2014, 12:42:16 PM »
Anyone?

Am I wrong to think delta G = 0 at equilibrium?

#### Corribus

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #2 on: April 21, 2014, 03:26:37 PM »
I can't see the embedded image, so I don't have much comment. But no, you aren't wrong to think that ΔG = 0 at equilibrium. This is practically the definition of equilibrium.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### [V]

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #3 on: April 21, 2014, 04:46:42 PM »
« Last Edit: April 22, 2014, 04:24:35 AM by Borek »

#### [V]

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #4 on: April 22, 2014, 02:40:17 AM »
Can anyone help me with the rest of this question?

#### Big-Daddy

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #5 on: April 22, 2014, 01:07:37 PM »
ΔG=ΔG°+RTln(Q)

#### Big-Daddy

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #6 on: April 22, 2014, 01:09:12 PM »
And for the degree of conversion, you'll have to express that in terms of K and then K in terms of T and a constant thermodynamic state function. So kick out ΔG° in favour of ΔH°-T*ΔS° first of all.

#### [V]

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #7 on: April 22, 2014, 02:54:06 PM »
Thank you big daddy.

Since we are probably making different ratios of S_8 :S_2 allotropes, can we say our
delta_H_not and delta_S_not are both changing with temperature?

If a computer were to generate this, are these the two values we are calculating to infer K at different temperatures?
« Last Edit: April 22, 2014, 03:06:55 PM by [V] »

#### Big-Daddy

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #8 on: April 22, 2014, 04:55:19 PM »
Thank you big daddy.

Since we are probably making different ratios of S_8 :S_2 allotropes, can we say our
delta_H_not and delta_S_not are both changing with temperature?

If a computer were to generate this, are these the two values we are calculating to infer K at different temperatures?

This seems like a textbook problem so a lot depends on what information you have. If it's up to you to collect as much web data as you can and need, there are of course various levels you could solve it at. But I'm myself not that comfortable with trying to treat this question using temperature-dependent ΔS° and ΔH° (I mean your function for K in terms of T would include an exponential raised to the power of an integral ... uncomfortable stuff, though surely not unplottable) so maybe you can just consider them constant? Then look their values up. Using ΔG°=-RTln(K) you should then be able to find the function for K in terms of T. Then express a Cartesian function containing degree of dissociation and K and substitute in K(T) for K to find the Cartesian function for degree of dissociation with T. Unlikely on the face of it that you'll be able to solve explicitly for degree of dissociation in terms of T.

#### Corribus

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #9 on: April 23, 2014, 09:37:00 AM »
@V

I'm not really clear on what you're asking here. Are you asking for an explanation of your plot? Well, let's start with: where did you get the plot from? You've mentioned S2 allotrope, but that's not in the chemical equation you provide in your image. So what conversion are you actually referring to?

If you clear up what you're asking for, you are more likely to get better quality assistance.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### Big-Daddy

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #10 on: April 23, 2014, 12:14:44 PM »
I'd also like to add to Corribus' post that it isn't clear whether you are referring to the percentage conversion of SO2 or H2S. The shape of the plot would probably be the same but I'd feel more comfortable doing the problem if it were better-defined.

#### Big-Daddy

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##### Re: Simple Equilibrium Question - Conceptual
« Reply #11 on: April 23, 2014, 05:46:06 PM »
Also if I'm not wrong I think we need to know volume, temperature (to find the total pressure at equilibrium) and initial number of moles of each reactant, to model the problem correctly.