Consider a reaction that proceeds autocatalytically with the kinetics v=k*a*b. At which concentrations of A reaction will be fastest? Also what will be the concentration of B?
The reaction you are analyzing is a simplified scheme of the auto-catalytic reactions A -> B, A + B -> 2B or A + (n-1)B -> nB. For n = 2 the kinetic equation has the form (elementary reactions) rA = k1cA + k2cAcB => rA(cA) = k1cA + k2cA(cAo - cA + cBo). After differentiating and equating the derivative to zero, you get cA* = (k1 + k2 (cAo + cBo))/2k2, cB* = cAo - cA* + cBo Of course, this is the value (cA*) for which the function rA(cA) reaches the maximum (the second derivative is negative). Regards,
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