3. The phenomenon of autocatalysis is the catalysis of a reaction by the product
ID: 871330 • Letter: 3
Question
3. The phenomenon of autocatalysis is the catalysis of a reaction by the products. For example, in a reaction A --> P it may be found that the rate law is v=k[A][P] and so the reaction rate increases as products are formed. (The reaction gets started because there are usually other reaction routes for the formation of some P initially, which then takes part in the autocatalytic reaction). Starting with an initial concentration of A0 (starting material) and P (product) derive an integrated expression that describes concentration of product, [P] as a function of time (t).Explanation / Answer
Assuming that this is a reversible reaction, the sistem A<-->P
It shows that "A" direct reaction disappears, but is created in the inverse reaction. therefore the overall rate equation is:
d[A]/dt=-k1[A]+k-1[P]
la variacion de la concentracion de "A" y "P" no es independiente, sino que ambas estan relacionadas con el grado de avance:
delta[A]/-1=delta[P]/+1= epsilon/V=x
where:
[A]=[A]0-x
[P]=[P]0+x
d[A]/dt=-dx/dt
dx/dt=(k1[A]0-k-1[P]0)-(k1+k-1)x
if alpha= (k1[A]0-k-1[P]0) and beta=(k1+k-1), then:
dx/dt=alpha+beta*x
the integral will be:
1/beta*ln((alpha+beta*x(t))/(alpha+beta*x(0)))=t
but x(t=0)=0 and with the originals variables we will get:
ln((k1[A]-k-1[P])/(k1[A]0-k-1[P]0)=-(k1+k-1)t
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