Noob: conversion rates question

[JeffEvarts]

Hello!

I have a question for the chemists out there. Every chemistry book in the world seems to offer a question that runs something like this:

A flask contains X mol of SO2 and Y mol of O2 after equilibrium is reached, how much SO3 will there be?​

Strangely, I can actually answer that one! Given the equilibrium constant at the given temperature and pressure, you divide blah blah blah.

MY question is "How long will it take to reach equilibrium?". The fact that the reaction is thermodynamically favored to the tune of around -100KJ/mol should indicate that the reverse reaction is rare, leading to an increased rate of conversion. Intuitively, increased pressure and temperature should reduce the time as well.

I did Google the question. Most of the answers are about catalyzed reactions, which are advantageous but beside the point. Frustratingly, the remaining answers are all over the place: from 10% to 0.035% conversion of SO2 to SO3 per hour.

So I guess I have two questions:

1. How DO you figure out how long this will take, and
2. Given the importance of this reaction, why isn't an STP value or Pressure/Temperature/Rate table available online?

Thanks in advance,
-Jeff

 

[eigenperson]

The first thing to understand is that the question of reaction rates is quite separate from the question of equilibrium proportions. You can't deduce whether a reaction will occur quickly or slowly from the equilibrium properties of the reaction.

If you take a container containing some water and a gas consisting of 1% methane and 99% air, then put it outside, the equilibrium state will involve all the methane having been oxidized to carbon dioxide and water. This equilibrium will take decades to achieve because the atmospheric lifetime of methane is 12 years or so. So this is an example of a reaction where the products are strongly favored, but the rate is very low.

If you take some water and put some acetic acid into it, only a very small amount of the acetic acid will be hydrolyzed. But, to the extent that it happens, it will happen almost instantly. So this is an example of a reaction where only a small amount of the products exist at the equilibrium, but the reaction rate is very high.

So considerations about the equilibrium state will be unhelpful in estimating the rate.

What you need to do is look up the reaction in a table of chemical kinetics. Try kinetics.nist.gov.

EDIT: Oh, by the way, the reason you couldn't find the table is because the reaction is actually completely unimportant. No one ever does this reaction without a catalyst, so why should anyone bother to do the experiment to find the reaction rate without a catalyst?

 

[JeffEvarts]

Hrm...

"...the reaction is actually completely unimportant". That is a bold statement.

I assume you meant to say "All modern processes for producing sulfuric acid in industrial quantities use the contact process, which involves a catalyst".

There are other reasons to measure SO2->SO3 conversion rates,

-Jeff

 

[Chestermiller]

Maybe eigenperson went beyond what he intended to say. But his main point is correct. You need to dig up the reaction kinetics data for the reaction (or, probably, in this case, sequence of reactions, since the overall reaction is probably not elementary). The first step is to identify the elementary reaction sequence, and then determine reaction rate constants. You can then carry out the time dependent calculation that you desire. The overall equilibrium constant can help in establishing some of the rate constants.

Chet

 

[JeffEvarts]

Chestermiller and (definitely) Eigenperson:
I thank you both for replying. It's not like I'm entitled to answers, and I don't want to seem ungrateful.

I followed Eigenperson's advice and went to kinetics.nist.gov. They even have a "result" for the SO2->SO3 reaction, but it appears to be missing the result (I'm expecting something like mol/s or L/s or g/s as a result, perhaps as a function of pressure and temperature) but the formula given is beyond my current level of knowledge.

Can either of you shed some light on its results?

-Jeff

 

[Chestermiller]

Chestermiller and (definitely) Eigenperson:
I thank you both for replying. It's not like I'm entitled to answers, and I don't want to seem ungrateful.

I followed Eigenperson's advice and went to kinetics.nist.gov. They even have a "result" for the SO2->SO3 reaction, but it appears to be missing the result (I'm expecting something like mol/s or L/s or g/s as a result, perhaps as a function of pressure and temperature) but the formula given is beyond my current level of knowledge.

Can either of you shed some light on its results?

-Jeff

I'm not knowledgeable about chemistry to tell you which of the reactions given comprise the elementary reaction sequence. But I can tell you that the site does give the order of each reaction and the units of the pre-exponential factor A of the reaction rate constant (depending on the order of the reaction), so you can calculate the reaction rate. For a first order reaction, for example, the reaction rate is r = kC, where k is the reaction rate constant given in the table (units of /sec), and C is the concentration of the reactant (units of molecules /cm^3).

Chet

 

[JeffEvarts]

First: The NIST tool looks great. Thank you again for pointing me to it.

I'm still a little lost on the units though. Here's what I get when I tweak the units (to liters and moles rather than cc and molecules)

Can someone give me a hand interpreting these results?

If I have a 1L container at STP and it contains 0.5L of SO2 and 0.5L of O2 which were JUST put into the container, how many seconds will I wait before I reach equilibrium (equilibrium is mostly SO3)

-Jeff

 

[eigenperson]

I'm going to go ahead and assume that the rate is k(T)[SO₂][O₂^*]. This is a dangerous assumption because a free-radical chain reaction is probably involved in the reaction, but it will do for a rough guess. In reality the exponents might be any two numbers that sum to 2. To find the actual equation you'd have to read the paper, which I don't seem to have access to.

Anyway, the units are moles per liter per second. So I calculate that the initial rate will be 260 moles per liter per second. Of course, the rate depends on the concentration, so as the reaction proceeds the rate will decrease since the concentration of the reactants is decreasing. To do the calculation properly you need to solve the differential equation. I'm not going to do that here since I don't even know if I have the expression for the rate correct. The point is that 260 moles per liter per second is really fast -- basically instant.

If this doesn't fit with your intuition about the reactivity of SO₂ with oxygen, that's because this reaction is specifically with singlet oxygen.

 

[JeffEvarts]

Singlet oxygen! <headdesk>

And no other results for O2. Grr. Well, I shall continue to Google and see if I can find a result.

-Jeff

 

[eigenperson]

That's probably because the reaction mechanism is complex and is broken into multiple steps in the NIST database.

I sent you a PM with http://www.researchgate.net/post/Is_there_an_existing_kinetic_model_rate_equation_for_SO3_formation_from_the_reaction_SO2_O2_H2O where John Birks gives a plausible reaction mechanism involving the OH radical.

 

[JeffEvarts]

This has all the earmarks of a "This is too complex to model accurately, so just try it and measure your own situation" kind of thing. I had an earlier question about Sodium bisulfate which had a similar answer. Well at least I'm not asking questions which have OBVIOUS answers. :)

Thank you to everyone who's read and contributed.
-Jeff

 

[Chestermiller]

This has all the earmarks of a "This is too complex to model accurately, so just try it and measure your own situation" kind of thing. I had an earlier question about Sodium bisulfate which had a similar answer. Well at least I'm not asking questions which have OBVIOUS answers. :)

Thank you to everyone who's read and contributed.
-Jeff

If you can identify the elementary reaction sequence, I'm confident I can help you solve this, particularly since the overall reaction is going to be slow.

Chet