Kinetics: pseudo order reactions

Question

If you have a reaction A+B--->C, and [B] >> [A], you can assume that the [B] will remain mostly constant and the rate=k'[A]^m. If A and B are both first order reactions (overall second order reaction) which integrated rate equation would you use to find the amount of time it would take for an initial concentration to reach a final concentration. Would it be considered first order overall because it's a pseudo first order? Would you use the ln[A]final = ln[A]initial -kt and solver for t? Or because it's a second overall, would you use 1/[A]final = 1/[A]initial+kt. Please help!

Answer 1

Hi Kellie F.,

As I see it, the designation "pseudo-first-order" is a term of convenience. The overall reaction is still second order (or whatever, you indicated rate = k'[A}]^m ?? If m .not.= 1, then overall reaction won't likely be second order, either!), but for convenience of solution, since B(final)~=B(initial), that term is included in your new k' coefficient, and you may use the first-order equation to solve. If you couldn't, then the problem would have been stated as B>A, not B>>A. The solution as "first-order" may just be easier, and if you are obtaining rate constants from experimental data over time, maybe less subject to error from noise in the data.

Now, you seem to have made an unjustified assumption, regarding your 2nd order plot: if you really needed that for an accurate solution, then you would have to have included calculation for B in the solution, not just for A.

By the way, using data to graphically determine physically significant variables in a problem, is an extremely useful technique. For instance, in my career as a lab chemist, I used first-order type plots to find out what were the limiting physical variables for drying of thin films of adhesive on a Tyvek supporting surface. For this, the assumed plot for mass vs. time should be an exponential decay to a constant value (i.e. to the mass of the totally dried film), and you should be able to figure out how that should graph as a semi-log plot (assuming a value for the constant value). Why ever would one go to the trouble of doing that sort of measurement, if you might just dry the film and be done with it? Because, if the time to completely dry different film samples differs greatly among samples, you might spend much less time only partially drying each, and using data for mass vs. time for each to extrapolate the completely dried mass. The graph will tell you (1) if there is an initial period where the gradient conditions are being set up for the eventual smooth drying; that period will not conform to a straight plot line as a semi-log graphing (2) when a significant period of exponential-decay water loss has taken place; that plot portion will enable you to pick an accurate completely-dried-mass value, and (3) if any degradations, etc. are taking place which make the overall loss into a bi-exponential curve (or worse!). You can detect all that, just from the (appropriately plotted!) mass vs. time data, no chemical analyses needed! Such is the power of math, and graphs.

I've only sketched out the procedure here; if you'd like to examine more closely, comment back and I'll arrange (eventually) to send you a journal article reprint.

-- Cheers, -- Mr. d.