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differential equations - Solving ODES in order to find unknown constants


I am trying to solve a set of ODES which represent a second order consecutive chemical reaction.


eqn = {
   CA'[t] == -k1*CA[t]*CF[t],
   CB'[t] == k1*CA[t]*CF[t] - k2*CB[t]*CF[t],

   CC'[t] == k2*CB[t]*CF[t] - k3*CC[t]*CF[t],
   CD'[t] == k3*CC[t]*CF[t] - k4*CD[t]*CF[t],
   CE'[t] == k4*CD[t]*CF[t],
   CF'[t] == -(k1*CA[t]*CF[t] + k2*CB[t]*CF[t] + k3*CC[t]*CF[t] + 
       k4*CD[t]*CF[t])};

I want to solve these equations either for a generic expression for k1, k2, k3, or k4, or for a particular value with these particular boundary conditions, n.b. not to sure if both t= 1 and t = 4 needs to be used...


bcs = {
   CA[0] == 0.052952,
   CB[0] == 0,

   CC[0] == 0,
   CD[0] == 0,
   CE[0] == 0,
   CF[0] == 0.0226939,
   CA[1] == 0.047442,
   CB[1] == 4.08*10^-3,
   CC[1] == 1.24*10^-3,
   CD[1] == 0.19*10^-3,
   CE[1] == 0,
   CF[1] == 0.0191289,

   CA[4] == 0.043412,
   CB[4] == 5.03*10^-3,
   CC[4] == 3.54*10^-3,
   CD[4] == 0.90*10^-3,
   CE[4] == 0.07*10^-3,
   CF[4] == 0.0151489};

I have tried to use both NDsolve and Dsolve, NDSolve requires that I have initial values for k1, k2, k3, k4 and Dsolve doesn't seem to want to help... the rest of my code for DSolve...


vars = {CA[t], CB[t], CC[t], CD[t], CE[t], CF[t]};


solution[t_] = DSolve[{eqn, bcs}, vars, t]

Any help would be appreciated!! Chemistry is my forte not Mathematica!!


Cheers!




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