Pressure and Equilibrium of Decomposition

[Moose100]

Homework Statement

SO3 decomposes on heating:
2SO2(g)

2SO2(g) + O2(g)
A sample of pure SO3 was heated to a high temperature T. At equilibrium, the mole ratio of SO2 to
SO3 was 0.152 and the total pressure was 2.73 atm. If the piston was pushed into cut the volume in half what is the new pressure?
[/B]

Homework Equations

I tried using the ratio to get the pressures on the left. 0.414 and 2.32 respectively.Also tried multiplying 2.73 by 2 but don't think this is the way. [/B]

The Attempt at a Solution

See above. I got to "an endpoint" with the problem but feel like it's wrong want to learn a general approach. Sorry these are my weakspot![/B]

 

[Bystander]

Can you write an equilibrium constant for the reaction?

 

[Moose100]

Can you write an equilibrium constant for the reaction?

With or without the numbers I found that I was using that ratio they gave me wrong.

 

[Borek]

You didn't found that, you were told that ;)

 

[Moose100]

Which means it was found out. ;) Like some of this makes sense some of it doesn't. It's not a typical ICE problem nor do I think it really applies in this instance? But I am lost so..

 

[Bystander]

ICE

"ICE" is what? Intro. Chem. Eng.?

 

[Moose100]

Initial CHange equilibrium.

 

[Bystander]

"ICE? RICE?" Oh, brother --- there's no way to break this to you gently --- there is one thread in the forum on "ICE," --- and, the method seems to be something of a joke/farce/disaster --- looking at "ICE/RICE" in Wiki, I'm inclined to agree. https://www.physicsforums.com/threads/rice-tables.170018/#post-1329914

Have you had any conventional chemistry training/instruction on reactions and equilibrium constants? What they are and what they can do for you? I'd really rather not get tangled up in an edu-babble religious ritual trying to make a failed instructional approach make sense to you if we can find some way around it.

 

[Moose100]

"ICE? RICE?" Oh, brother --- there's no way to break this to you gently --- there is one thread in the forum on "ICE," --- and, the method seems to be something of a joke/farce/disaster --- looking at "ICE/RICE" in Wiki, I'm inclined to agree. https://www.physicsforums.com/threads/rice-tables.170018/#post-1329914

Have you had any conventional chemistry training/instruction on reactions and equilibrium constants? What they are and what they can do for you? I'd really rather not get tangled up in an edu-babble religious ritual trying to make a failed instructional approach make sense to you if we can find some way around it.

Lol yes I have I am actually studying for the MCAT and am doing problems. Have a bachelor in mS in bio. LOOONG time since I took chem and analytical.

I felt that ICE wasnt useful.

To come clean. I looked at the solution and had issues with how to arrive at the molarities. I know I- is 0.1M I also "know" that I2 is 0.0013M but why use this at all? Is there a reason we use the saturation molarity in water only AND that of it in KI? this loses me.

Im pretty sound on the constant.

 

[epenguin]

Have threads got mixed up? I know there was another one about iodine precipitating. #1 is about sulphur oxides and oxygen.

You ask about a general approach. Do you know/remember the law of chemical equilibrium, what an equilibrium constant is? Even if you don't, look it up and find It's nothing very difficult. Then what is the relation relating concentrations of these three substances in this case? Already asked in #2!

Then mass conservation laws mean that however they vary in the closed vessel when you vary the pressure or volume, neither the number of sulphur atoms, nor the number of oxygen atoms varies. Here you start from SO₃ (g) (please correct your formula) and the result is that once you know the concentration, we'll call it C₀ of your starting SO₃, and the concentration, call it x, of any of the gases at equilibrium, you easily know concentrations of all three, in terms of x and C₀. (It will be a bit simpler if you let x be [O₂].)

So rewrite your equilibrium equation in terms of x and C₀. Solve it. Then when you halve the volume what do you know that changes how?

 

[Moose100]

Equilibrium conc of:

SO3: 2.73-2x
SO2: 2x
O2 : x

2x/2.73-2x=0.152

x=0.180

Eventually I get to the point where K= 0.00415

Am I in the ballpark here?

 

[Bystander]

Start with the reaction: 2SO₃ = 2SO₂ + O₂.

K = [SO₂]²[O₂]/[SO₃]²

If I give you that much, can you get where you need to go?

 

[Moose100]

Excuse me but i got that already.

 

[Bystander]

got that already.

Good.

2x/2.73-2x=0.152

You have three gases contributing to the total pressure. You have a mole ratio for two of them, and a stoichiometric ratio for a different pair.

 

[epenguin]

Not enough working shown. You needed to write explicitly the equation of #12, and then express it In terms of different quantities as I suggested - explicitly. I think your expression lacks the necessary brackets and in the end there should be x² terms in it, even x³, and where is C₀?

 

[Moose100]

That's the value of the ratio given in the problem.

2.73-2x is the equilibrium value (or so I hope) for SO3. 2x is that of SO2. I set this ratio SO2: SO3 equal to 0.152 to get x and subsequently the new equilibrium values. Then I use these to get k by using the equilibrium expression.

Hopefully this is OK and makes more sense?

 

[Borek]

2.73-2x is the equilibrium value (or so I hope) for SO3. 2x is that of SO2.

Lasciate ogni speranza.

2.73 is a sum of three pressures - that of SO₃, that of SO₂ and that of O₂. If 2x is SO₂, and 2.73-2x is SO₃, sum of their pressures is 2.73-2x+2x=2.73 - so where is the oxygen?

No matter what question you solve, all the time you are ignoring the fact amounts of different substances is combined because of the stoichiometry of the reaction. You make the same mistake over and over.

 

[epenguin]

If you set out your working explicitly and used the formula quoting and using the formula given you in #12 we could help you more and you could help yourself. It is not clear if you use the square of the ratio. This squared ratio equals something invovling three parameters, C, x and K. No idea how you got any of them. You need to get C from info you are given, then x from stoichiometry, only then can you get K from the ratio given, only after that can you get a new value for new C.

(As far as I can see that will involve solving a nasty equation but all the more we need explicit clarity; we'll talk about that if we get there.)

 

[Moose100]

I know how to apply the equilibrium formula but that ratio is throwing me.

 

[Borek]

Assume partial pressures of gases to be p_SO2, p_SO3 and p_O2. Express the ratio and total pressure using these unknowns. What does the reaction equation tell you about the p_SO2 and p_O2? Are they linked somehow? Can you express this dependency with a third equation?

 

[epenguin]

We haven't seen you take first or second step of anything anyone has suggested to you,

 

[Moose100]

I'm trying it just doesn't make sense to me at the moment.

 

[Moose100]

Assume partial pressures of gases to be p_SO2, p_SO3 and p_O2. Express the ratio and total pressure using these unknowns. What does the reaction equation tell you about the p_SO2 and p_O2? Are they linked somehow? Can you express this dependency with a third equation?

They are linked by their stoichiometry.

When you say the ratio you mean the 0.152? Or their stoichiometry ratios?

 

[Bystander]

Forget numerical values for total pressure. Borek has told you that P_total is the sum of three partial pressures. The original problem statement gives you one relation between the equilibrium pressure of the reactant and one of the products. The balanced equation for the reaction gives you a second relation between the equilibrium pressures of the two products. Write those relationships, each as a separate equation.

 

[Moose100]

Ok I was thinkkng about that.

Ptot=pO₂+pSO₃+pSO₂

 

[Bystander]

Okay, that's the "zeroth" equation. Now write an equation relating p_SO3 to p_SO2.

 

[Moose100]

pSO₂/pSO₃=0.152 ?

 

[Bystander]

Good enough for the moment. Now an equation relating p_SO2 to p_O2.

 

[Moose100]

I think I see where you are going..(hopefully )

pO₂=1-pSO₂

pSO₂=0.152pSO₃

 

[epenguin]

I know how to apply the equilibrium formula but that ratio is throwing me.

I think I see where you are going..(hopefully )

pO₂=1-pSO₂

No! I thought you had at least that right before.

 

[Bystander]

pO2=1-pSO2

What's the stoichiometric relationship from the equation for decomposition?

 

[Moose100]

2:2:1

 

[Moose100]

Yknow what I will be back. I'm split between this and work. I will concentrate better and save you all some aggravation.

 

[Borek]

How many moles of O₂ are produced per each mole of SO₂?

 

[Moose100]

1 mole of O₂ for 2 moles of SO₂

 

[Borek]

How are their pressures related?

 

[Moose100]

IM not able to do much at the moment I said that earlier.

 

[Borek]

Write the equation that combines these pressures

 

[Moose100]

Ptotal=pO₂+pSO₃+pSO₂

pSO₂/pSO₃=0.152

pO₂/pSO₂= 0.5

Ptotal= 0.5pSO₂ +pSO₂/0.152 + pSO₂

Ptotal=8.08pSO₂

pSO₂=2.73/8.08=0.0338
pSO₃=0.338/0.152=2.22
pO₂= 0.169

k=[pSO₂]²[pO₂]/[pSO₃]²

k=[0.338]²[0.169]/[2.22]²
k=3.9 × 10^-3

 

[Moose100]

1. If they are correct the equilibrium values become the initial values upon the change in condition. I.e. Moving the piston in halfway.

2. V₂=V₁/2
P₁V₁=P₂V₂
P₁V₁=V₁P₂/2
2P₁=P₂

3. 2SO₃ 2.22-2x
2SO₃ 0.338+x
O₂ 0.169-x



Ok this is where I spent many hours last night. One because I seem to be stuck at factoring the 2P1 concept and also I am still shaky if these are the right pressures. When using the equilibrium constant to solve for the new pressures.

k=[pSO2]²[pO2]/[pSO3]²3.9 ×10^-3=[pSO2]²[pO2]/[pSO3]²

 

[epenguin]

First check results for consistency.
You say pO₂/pSO₂= 0.5 but it isn't in your conclusions. - only a decimal point mistake or other?

Then I would like to say that - I don't know that this is always followed, but In my book equilibrium constants have to have units.
Well for reactions like A ⇔ B, or A + B ⇔ C + D the eq, constant is dimensionless, but in your case it has the dimensions of pressure and units of atm. Somebody else might use torr etc. but it could also have been concentrations and M (as I was assuming in my sketch). You could have done the whole thing in terms of concnetrations but I think it is equivalent reasoning and only units and their numbers different - hope this will be clear to you.

If and when this is right, I have not checked everything, you have done the first two steps of #14.

The next will be step 3. I think the equation is not as horrible as I first thought, but you can begin formulating that.

 

[Moose100]

Ive done so last night. I took note of you saying that its a nasty equation that has a cubed power in it lol. Before I do that do we take the ratios and modify them due to the new conditions? Theres is where I am stuck. Multiply them by two so to speak. Also you mean the ratio of O2 to SO2 doesn't work? Or are you saing the ratio is wrong all the way around?

 

[Moose100]

Ahh I see what you mean the ratio is inflated by 10.

 

[epenguin]

Yes - similarly check other ratios agree with your starting ones. For rest I have to take short break now.

 

[Moose100]

Oops got my notes out it was a typo.

 

[Moose100]

First check results for consistency.
You say pO₂/pSO₂= 0.5 but it isn't in your conclusions. - only a decimal point mistake or other?

Then I would like to say that - I don't know that this is always followed, but In my book equilibrium constants have to have units.
Well for reactions like A ⇔ B, or A + B ⇔ C + D the eq, constant is dimensionless, but in your case it has the dimensions of pressure and units of atm. Somebody else might use torr etc. but it could also have been concentrations and M (as I was assuming in my sketch). You could have done the whole thing in terms of concnetrations but I think it is equivalent reasoning and only units and their numbers different - hope this will be clear to you.

If and when this is right, I have not checked everything, you have done the first two steps of #14.

The next will be step 3. I think the equation is not as horrible as I first thought, but you can begin formulating that.

The K I got is then 3.9 × 10^-3atm

 

[Moose100]

[0.338+2x]²[0.169+x]/[2.22-2x]²=3.9×10^-3atm

At equilibrium under the new conditions P₂=2P₁

That means we multiply these equilibrium expressions in the brackets by two:

(0.676+4x)²(0.338+2x)²/(4.44-4x)²=3.9*10^-3

Eventually, we get x= -0.032atm

so

0.676+ 4(-0.032)=0.548atm
0.338+ 2(-0.032)=0.274 atm
4.44 + 4(-0.032)= 4.568 atm

= 5.39 atm

 

[Moose100]

If this is correct o this isn't a fluke thank you everyone for the help. I may come back with some questions about general approach after I've scrutinized some more.

 

[epenguin]

I don't usually check peoples' arithmetic but often notice anomalies like that.

I'll assume no more mistakes. Actually figures sound to me reasonable.

Parts 1 and 2 of the problem are things I'd say should be expected of you with your background - fairly elementary physical chemistry calculations. Part 3 is more challenging. Before we get into that - and it is too late night for me to concentrate - I think equally to be expected of you is you can translate those pressures (including the eq constant) into molarities. Especially if you are preparing for an exam, plus two other reasons.

I at least find it not simple to imagine what happens to pressures when you halve the volume. It is easy to imagine what happens to total concentration of something in all its forms. If the substances were not reacting your PV laws would hold, but if they react? Also I think your work here suffered from lack of explicitness. If you had written out things like the equilibrium equation you would have saved time and mistakes in the immediate, and also in the long run as when you revise you (as well as us) may not understand why you wrote something. It would be good to write out a couple of equations connecting molarities e.g. of [O₂] (= x) and the other things.

 

[Moose100]

That's what's troubling me I tripped up early on with the ratios. Like I had no clue on how to use them for some reason to even use them at all. I am looking to do more reading on this as well. Is the 0.152 ratio..this isn't a mole fraction ratio is it? That would be a fraction of the total so probably not?

The Ptotal formula should have been easy too. It just didn't dawn on me at all. Any advice on what to read to furnish more understanding in addition to what I am looking to read I am totally open to.