[Sonntag]

Hi,

do you know a text where I can look up integrated rate laws for standard reactions?

I would like to integrate the following differential rate law. If you can give me any tipps without case differentiation I would be very glad.

[tex] \frac{d[A]}{[dt]}  = -k_1~[A]~[D]_0~exp(-k_1~[A]~t]) - k_2~[A]~[C]_0~exp(-k_2~[A]~t])  [/tex]

Sonntag

[Corribus]

This isn't a typical rate expression form for a "standard reaction".

E.g., for second order reaction, -d[A]/dt = k[A]²

What is the origin of this differential equation?

[Sonntag]

I would like to have that parallel reaction, little bit more advanced, but not that unusual:

A + D             rate constant: k₁
A + C             rate constant: k₂

[Corribus]

So then you are looking for a solution to something like

-d[A]/dt = k₁[A][D] + k₂[A][C]

Yes?

(Unfortunately, there is no "generic" solution to differential equations. You can look up common ones, but for more unique reaction mechanisms, you'll have to solve each case uniquely. Which is why, if you're going to be doing a lot of chemical kinetics, a background in differential equations is very useful. Or at least, have access to a strong mathematical software package.)

[Sonntag]

Yes, your equation was my start equation. I've thought similiar about my last outcome. Nonetheless, I've hoped that I've just missed one point and the solution is not that far away.

[Babcock_Hall]

What about starting with the known solution to the parallel reactions problem and guessing the solution to yours?  In my very limited understanding of differential equations, it is OK to guess, as long as you verify that your guess is correct:  http://www.dummies.com/how-to/content/checking-differential-equation-solutions.html

[Enthalpy]

If you need a numerical solution once, you may consider a simulation (mis)using Spice. Inspiration there
http://www.chemicalforums.com/index.php?topic=73837.msg274163#msg274163
Spice can model nonlinear networks too.

[Enthalpy]

And in case you really need an algebraic solution but have no intention to learn how to find it, several pieces of software do that.
Maple, for sure.
I suspect Mathcad does it as well. Its algebraic capabilities may include this.
Mathematica, necessarily - though I haven't used it.
Matlab?