Chemical kinetics, reaction order, resistance

[maryghee]

X + Y + Z -> A + C⁺ + B^-

Initial Concentrations Z= 4.1 X 10^-3M, X=2.3 X 10^-1M, Y= 1.2 X 10^-1 M.

http://s121.photobucket.com/user/ma...-1024a2a3f3d5_zpscc804723.jpg.html?sort=3&o=0

3. So my attempt included graphing -R/(R_∞-R) vs. time. which produced a curve. Beyond that I'm not really sure what I am supposed to do. Our example in class had 2 species with matching concentrations. We have no book and we only have hand outs and mostly do derivations in class. I didn't expect it to be this hard honestly and am now way over my head.

So I have this curve and this initial concentrations and need to find the order. Should I take the log of the curve or what? (Also he is not giving help on this assignment until after it is due apparently)

 

[epenguin]

X + Y + Z -> A + C⁺ + B^-

Initial Concentrations Z= 4.1 X 10^-3M, X=2.3 X 10^-1M, Y= 1.2 X 10^-1 M.

http://s121.photobucket.com/user/ma...-1024a2a3f3d5_zpscc804723.jpg.html?sort=3&o=0

3. So my attempt included graphing -R/(R_∞-R) vs. time. which produced a curve. Beyond that I'm not really sure what I am supposed to do. Our example in class had 2 species with matching concentrations. We have no book and we only have hand outs and mostly do derivations in class. I didn't expect it to be this hard honestly and am now way over my head.

So I have this curve and this initial concentrations and need to find the order. Should I take the log of the curve or what? (Also he is not giving help on this assignment until after it is due apparently)

It sounds like you had some idea when you chose to plot that function. Could you say more explicitly what you think it is equal to in terms of the concentrations of interest?

Secondly, looking at the concentrations can you see a useful simplifying approximation?

With these the kinetics becomes fairly simple and standard. Quite likely it is in your handouts.

 

[maryghee]

The handout on this one is very unclear and hard to follow. (These handouts aren't all that awesome, they're hand written, not in order, they jump around a lot, and he's kinda in his 80's)

from what i gather on the hand out (a-x)(b-x) but a~b. In this problem I have 3 species so that would be (a-x)(b-x)(c-x) that are definitely not even close. Should i assume Z doesn't exist since its small?

I used what i used with the R's but that was using what was in the handouts with the assumptions so it could totally be wrong, that all I had so that's why I picked it. but that was derived assuming a~b... so that could actually be totally worthless for me.

i know in general with graphs linear is zero order
ln of that then if its linear is 1st order
then the inverse is 2nd order.

So would I even need to know the initial concentrations? Is he giving us those to throw us off?

 

[epenguin]

from what i gather on the hand out (a-x)(b-x) but a~b. In this problem I have 3 species so that would be (a-x)(b-x)(c-x) that are definitely not even close. Should i assume Z doesn't exist since its small?

Understanding you mean a = X₀ (X at t = 0), b = Y₀, c = Z₀ and x = A = C⁺ = B^-,
and that your (a-x)(b-x)(c-x) is your conjectured expression for dx/dt derived from the assumption that dx/dt = X_tY_tZ_t
OK?
what I was first getting at was, at t = $\infty$ what is the maximum possible x? Hence what are the least possible X₀, Y₀, Z₀ then?

Then you did not answer my previous question.

Also it would be somewhat useful if you produced as well as the table the graph you said you had done.

Can I ask what level you are - is this High School or University? course on what? Specialist?

 

[maryghee]

yes yes that's what i was meaning.

I guess I'm not entirely sure what you are getting at... so time infinity would be the most reacted the reaction will go. So Z would probably be the most reacted since there wasn't much of it to begin with? and there would be more of the other 2 left?

College physical chemistry on chemical kinetics obviously :(

 

[maryghee]

And resistance is the inverse of concentration. I'm a little fuzzy on how I should actually flip the -(Rt/Rinfinity-Rt) on the left part of the graph given that its technically the inverse. I'm not so good at the math which has really been hurting me because I don't understand a lot of this and the whys.

 

[maryghee]

and thank you. I do appreciate any help and would really like to be able to understand this stuff. It just made so much since in class but when i got down to actually doing the work i realized i was in over my head. If there are any good websites online that don't have the changing concentration. i would be happy to look at those. I've been having trouble finding anything useful. Most of these problems involve resistance, initial pressure, half-life, percent of reaction, pressure and some weird reversible processes with (a-b) <-> (b+x)

 

[epenguin]

And resistance is the inverse of concentration. I'm a little fuzzy on how I should actually flip the -(Rt/Rinfinity-Rt) on the left part of the graph given that its technically the inverse. I'm not so good at the math which has really been hurting me because I don't understand a lot of this and the whys.

Don't panic! Don't panic!

I had not really looked at your measurement parameter till now.

You might assume the conductance (i.e. 1/R) is proportional to the concentration of the products - which are charged. That would make sense wouldn't it? - the more the ion concentration the more the solution will conduct.

There must be more to it because we see the solution conducts even at zero concentration of the products.

So plot instead of resistance, conductance against time. Or if you prefer plot the difference between conductance at time t and that at t = 0.

We are going to assume that this latter parameter is proportional to the concentration of product.

We don't know the constant of proportionality but we will manage without it.

(At risk of confusing by too many considerations, what I just proposed is what we often do - how do we measure products in a chemical reaction? By taking any physical parameter we can that is possible and convenient to measure that depends on it. We hope, and if possible experimentally verify that it is proportional, or else calibrate somehow. I have to say that the proportionality assumption is not that reliable for conductivity measurements. There would be a way of experimentally calibrating to do this rigorously you might think how to do, but this does not seem real experimental data or actual substances would have been mentioned, so just graph as mentioned.)

You seem to have two experiments there, what are they? Different starting concentrations of something?

 

[maryghee]

What i have on the graph is -R/(R∞-R) vs. time.
the other data is straight off the table. i was assuming concentration was inversely proportional to the change in resistance/conductance.

and in that bit you highlighted what i actually was trying to mean was that since the curve wasn't linear it is obviously a different order and seeing as we have the inverse. I am not sure how to go about changing it to get a linear line to prove the order.

 

[epenguin]

The plots I suggested in #8 are just an informative way of presenting the course of the reaction representing something we can believe essentially proportional to product concentration instead of something related in an unobvious and unvisual way. It is for seeing what the reaction time course (also known as progress curve) looks like, not for linearising yet. It seems the second table is for another reactions substance - we should treat and plot both.

 

[epenguin]

I guess I'm not entirely sure what you are getting at... so time infinity would be the most reacted the reaction will go. So Z would probably be the most reacted since there wasn't much of it to begin with? and there would be more of the other 2 left?

Reaction kinetics with three substances are in the general case quite complicated to treat. Except when they aren't because of simplifying factors. Which exist in this case. If all the Z reacts what, in numerically, is its concentration at the beginning and at the end, in the specific case? What are those of X and Y? Simple question, answers should be suggestive.

I don't know what time it is where you are but I have to go and will take this further tomorrow if you have answered.

 

[maryghee]

so initial Z= 4.1 X 10^-3M and Z final would be approximately 0. X is about 2 times the concentration of Y. I figured this one was simplified and not involving 3 substances though we do have a few derivations with 3 substances, we weren't given enough information to deal with a 3 substance problem.

 

[epenguin]

Firstly, what exercises like this have to do with is this.

Kinetics, which is an essential part, though only part, of the study of chemical reaction mechanisms boils down to study of rates, or more generally time courses, of chemical reactions, and the factors influencing them. The main factor studied is concentrations of participants.

You could vary concentration and study how that changed the initial rate of reaction iin say seven different experiments. But as a reaction proceeds concentrations are changing anyway by definition, so in one experiment you can make seven observations at different times. You could draw a graph of extent of reaction against time - which I urged you to do because you don't get a picture of what we are talking about from tables of indirectly related partners - and drawing tangents get the rate (dZ/dt) at different times and concentrations. But it is more satisfactory to fit the observations to a mathematical model where dZ/dT is integrated - simple cases of the sort of thing calculus was invented for.

But with three substances reacting this can be quite complicated in theory and in practice. So often you set up the experiments to make it simpler.

So I asked you about simplifications, asked a question about the concentrations at start and end of reaction, and as you have not answered this question, and this

so initial Z= 4.1 X 10^-3M and Z final would be approximately 0. X is about 2 times the concentration of Y. I figured this one was simplified and not involving 3 substances though we do have a few derivations with 3 substances, we weren't given enough information to deal with a 3 substance problem.

has not actually said the point, I don't know whether you have grasped it or not.

Answer to my very simple question is while Z varies from 4.1 X 10^-3 to 0, X changes from 0.23 M to 0.226 M and Y from 0.12 M to 0.116 M. In other words during the reaction X and Y percent wise let's say do not change concentration significantly. So the slowing of the reactions with time that you are going to see when you have plotted the conductances are due to the change of [Z], on which reaction rate depends. It probably does depend on [X] and [Y] as well but as these are practically constant during the reaction we can for the moment forget them.

All that is the relatively trivial and obvious part that the Prof. and handouts hardly explain maybe.

Then the first thing to try is whether the time course fits first-order kinetics in [Z] - that is explained e.g. at

http://en.wikipedia.org/wiki/Rate_equation

http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Reaction_Rates/First-Order_Reactions

but also in any university level physical chemistry textbook if it has even one chapter on kinetics.