Question:
Derive an expression to calculate the time required for completion of the zero-order reaction.
Solution:
Consider a reaction,
R → P t=0
Here R is the reactant and P is the product.
Rate = k[R]0 t=t
(Instantaneous rate) –dR/dt = k , dR =-kdt
On integrating both sides,
ʃDr = -k ʃdt
[R] = -kt + I
At t = 0,
[R]= [R0] which makes I= R0
[R] = [R0]– kt. ……………(i)
Here [R] = concentration of reactant at time ‘t’.
[R0] = initial concentration of the reactant.
This reaction is known as the integrated rate equation of zero order.
After completion of zero order reaction [R]= 0
Using [R]= 0 in (i)
[R0]=kt
t=[R0]/k
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