Order of Reaction (in my nightmares) [Chemistry]

ceres

I knew this problem was going to be hand-crafted to show up in my nightmares when I saw that time was given in years and concentration for the reactant in moles per unit [/i]furlong[/i]. As time increases, concentration of the sole mentioned reactant decreases.

Basically, the problem is to find the oder of reaction with respect to the reactant and graph it over time. It seems pretty simple once you realize that units of concentration, no matter how bizarre, aren't really important.

Except the data... it doesn't line up to *mean* anything at all. From the data given, it's obviously a rate of decay problem. It doesn't seem to be first-order, and the numbers don't line up for half-life. I can't get a straight line 1/[concentration], making me think it's not second order. Numbers don't seem to work for zero order, and in fact the only hint I can think of that he's given us for how we might deal with this is that reactions can be any order at all, even fractional orders, but he didn't tell us how to figure that out.

I really, really don't want answers posted for me, but I'm out of ideas on how to approach the problem. Any ideas, rate formulae, explanations, or new ways of looking at it are appreciated. I'll post all the data if I have to, but if I can do it without I'd prefer to.

Dropping Loads

Unless you are required to think of a mechanism, this is more of a math problem than a chemistry one. I'm assuming you were just given a list of time points and concentrations? Paste in your graphing program of choice and simply grab whatever equation it spits out. Could you post a picture of the graph you obtain?

If you do need to think of a mechanism, those tend to come out after you have a reaction order. Did he provide a chemical formula / structure?

ceres

We specifically need to figure out the order of the reaction with respect to the reactant.

I'll try to make a graph of the data to post.

Dropping Loads

In that case I'd just go with the mathematical answer and not worry about the chemistry so much. There are a number of decompositions that have a non-integer order, either in the presence or absence of catalyst. Unfortunately I can't help you with the graphing as much as I could the mechanism.:?

ceres

But.. that's what I'm trying to DO. That's the problem. "Find the order of the equation with respect to [reactant]." I am not sure how to look at this data to make it fit into something I know. None of the numbers seem to add up to the standard first, second, or zero order reactions. I am looking for new ways to approach the math to make the numbers make any sense. There is no catalyst. It's straight decomposition, I'm just not sure on what order, and that's what I need to know. How do I figure out the the order of a non-integer order reaction?

edit: Here is a rough graph of the data.

Daenris

Can you post the numbers used to generate that graph? By just eyeballing it and playing with some things, it looks like it could match a half-life curve, depending on the period of the half-life.

ceres

basically,

Time in Years:
0
2
4
6
8
10

Concentration in moles per cubic furlong:
.15
.099
.073
.047
.028
.022

I did a whole bunch of math to see if it was a half-life problem, and the numbers for half-life just don't seem to add up. What am I missing?

Daenris

Hmm... apparently my eyeballing was terrible... with the actual numbers you're right, it doesn't work out. It comes close to matching the curve for a halflife of 3.556 years, but it's not an exact fit.

Unfortunately I don't really have any other suggestions at the moment on how to solve it.

Dropping Loads

What program are you using to make the graph? Can't you get the program to make a regression line FOR you, and have it spit out an equation? That should give you the approximate order of the reaction. It's not likely to be a smooth curve on it's own b/c it's just not that much data, so having the computer fit the equation instead of trying guess-and-check might help.

Rook

It looks like first order with not perfect data, which is pretty much what you expect if you ever do things for real. Taking the natural log seems to give a pretty good straight line.

ceres

I was thinking half-life. It really *looks* like half-life. I kept thinking maybe there was some trick. Maybe there is, and that trick is that it's supposed to resemble what you might get with field data.

Daenris, how did you work it out to 3.556? Without the time for a concentration of .075, I was unsure how to proceed. Rounding the .073 up to .075 I could say it was about 4 years, but that was the best I did and at 2 half-lives there would only be 18% left instead of 25. :P

Daenris

ceres wrote: »

I was thinking half-life. It really *looks* like half-life. I kept thinking maybe there was some trick. Maybe there is, and that trick is that it's supposed to resemble what you might get with field data.

Daenris, how did you work it out to 3.556? Without the time for a concentration of .075, I was unsure how to proceed. Rounding the .073 up to .075 I could say it was about 4 years, but that was the best I did and at 2 half-lives there would only be 18% left instead of 25. :P

Well, since it seemed to visually fit a half-life curve so well, I just put it into Matlab's non-linear fitting function, with the equation for half-life and the data you gave, and it uses a least squares method to estimate the best fitting value for your coefficient of interest (in this case, the period of the half-life). I'm not actually too big on chemistry, so I'm not sure what formulas you would use to calculate this normally.

ceres

Alright.. thanks guys. I think what I needed was just reassurance that is it most likely a half-life curve. Looking at the problem, he doesn't actually ask specifically for any math.. just what is the order of the reaction, and plot the curve to back up the speculation.

What I'm going to do is say that I think it's a first-order reaction because it's pretty clearly a half-life curve, include a graph, and turn it in. He might want some sort of math to back it up, but if he does it's math I don't think we've learned yet. And then I'm not going to stress about it.

Fuzzy Cumulonimbus Cloud

Yeah, fit a line for it or do a log scale.
It should be pretty clear what it is, then.

When in doubt, run a curve and always post your R-square value. Should be in the high .9s if it is good.
Welcome to chemistry, enjoy your stay, try not to hate it.

ceres

LOGS. That would be what I was forgetting. I knew it was going to be something simple.

This is why I'm a bio major and not a chem major. You people and your iterative equations and your equilibria and your ICE tables...

Thanks for all your help everyone, I have an answer (and even a graph!) I feel I can be somewhat confident in. This thread can be locked now.