[eskimogenius]

Hi all,

Need assistance solving this consecutive, second order, irreversible reaction in a batch reactor problem.

Initially, 1 mole of A, 2 moles of S. Find mole fraction of X after half of A is consumed. k2/k1 = 2

A + S >k1> X
X + S >k2> Y

Attempted Solution
I formed a system of ODEs for A,Y,S, and X but I don't know where to proceed from here. Furthest I can get is:

Nx' + Ns' = -4 (k1) Nx Ns

Where Ns' = dNs/dt

[mjc123]

I did it this way:
Define fractions α and β such that
[A] = 1-α
[Y] = β
[X] = α-β
[S ] = 2-α-β
Obtain expressions for dα/dt and dβ/dt. Hence obtain an expression for dβ/dα and solve.
In this way I got (laboriously) β = α², and the answer to the question follows easily. I can't help thinking that if the solution is that simple there must be an easier way to get to it, but I may be wrong.
It is of course very easy to solve numerically.