[Chaste]

4th ed; P8-11B: reference here http://my.safaribooksonline.com/book/chemical-engineering/9780132317191/multiple-reactions/331#X2ludGVybmFsX0ZsYXNoUmVhZGVyP3htbGlkPTk3ODAxMzIzMTcxOTEvMzMx

Terephthalic acid (TPA) finds extensive use in the manufacture of synthetic
fibers (e.g., Dacron) and as an intermediate for polyester films (e.g., Mylar).
The formation of potassium terephthalate from potassium benzoate was stud-
ied using a tubular reactor [Ind. Eng. Chem. Res., 26, 1691 (1987)].
It was found that the intermediates (primarily K-phthalates) formed from
the dissociation of K-benzoate over a CdCl2 catalyst reacted with K-tereph-
thalate in an autocatalytic reaction step.

A :rarrow:R :rarrow:S     Series
R+S  2S            Autocatalytic
rate constants are k₁,k₂,k₃ chronologically.
Where A =k-benzoate, R = lumped intermediates(K-phthalatis, etc) and S = K-terephthalate. Pure A is charged to the reactor at a pressure of 110kPa, The specific reaction rates at 410oC are k₁=1.08 x 10^-3 s^-1 with E₁=42.6kcal/mol,k₂=1.19 x 10^-3s^-1with E₂=48.6kcal/mol,k₃=1.59x10^-3dm³/mol.s with E₃=32kcal/mol
(A)plot the concentrations of A, R, and S as a function of time in a batch reactor at 410^oC noting when the maximum of R occurs
(B)Repeat(A) for temepratures of 430^oC and 390^oC

These are my following equations that I inserted into polymath. my problem is I don't know where to insert a temperature parameter or if there's any equation relating to temperature.
k3 = 1.59*10^-3
k2 = 1.19*10^-3
k1 = 1.08*10^-3
d(ca) / d(t) = ra
ca(0) = 10
t(0) = 0
t(f) = 1000
d(cs) / d(t) = rs
cs(0) = 0
d(cr) / d(t) = rr
cr(0) = 0
rr = k1*ca-k2*cr-k3*cr*cs
rs = k2*cr+k3*cr*cs
ra = -k1*ca

Please help.