'advanced' maths.

Former MemberFormer Member Posts: 1,876,329 The Mix Honorary Guru
I put the advanced in inversed comas, because it might be easy for someone who learnt it in some kind of advanced school, but I reckon most people who are not studying something technical won't be familar with it.

Basically. I need to find a differential equation for the following problem.

A chemical reaction reacts from substance A to substance E, whereas substance E reacts further to endproduct B, so A----> E ----> B

Both reactions have the 1. order (so no powers). The rate constants k1 (for A--->E) and k2 (for E--->B) are known. but, k1 ≠ k2

The question is, how much of each concentration a, e or b is there to any kind of given moment.

Since we were only having differential equations with 2 variables, it will be a f(x,y), or f(x,y,y') function.

So basically I need to find a diff.eq. for the concentration in dependence of the time t., maybe they ask for 3 equations, resepctively for "a" in dependence of the time, e i.d. of t, etc.

I hope anyone has a faint idea somewhere.

Comments

  • Former MemberFormer Member Posts: 1,876,329 The Mix Honorary Guru
    Give me 2 weeks, I just started calculus II and we're just about to learn about d.e. with 2 variables :p
  • Former MemberFormer Member Posts: 1,876,329 The Mix Honorary Guru
    ShyBoy wrote:
    Give me 2 weeks, I just started calculus II and we're just about to learn about d.e. with 2 variables :p

    (obvious movie response), "I'll give you two days!"

    Not possible, bud. On thursday I have math excersises, and I need to have it done then :S

    thanks tho.
  • Former MemberFormer Member Posts: 1,876,329 The Mix Honorary Guru
    I learnt this at university but promptly forgot it. Sorry.
  • Former MemberFormer Member Posts: 1,876,329 The Mix Honorary Guru
    Randomgirl wrote:
    I learnt this at university but promptly forgot it. Sorry.

    and there is no way to get that ol' brain all oiled up and get the toothed wheels in gear again, or find handwritings of lectures back then?

    :(
  • Former MemberFormer Member Posts: 1,876,329 The Mix Honorary Guru
    E= k1 dA/dt

    B= k2 dE/dt ---> = k2 k1 d(dA/dt) / dt

    ---> B= k1k2 d^2(A)/dt^2

    more nicely

    E=k1 A'
    B=k2 E' = k1k2 A''

    edit: one assumes in this case that

    A=f(t)
    E=f(A,t)
    B=f(E,t)

    as the constants are irrelevant to the structure of the functions really. (or if one assumes both constants = 1)

    but then I guess A is also dependant on how much has reacted into E...

    I dunno, I'm no chemist, but it's a start. (maybe) also, this could be completely wrong.
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