A batch reactor has neither inflow nor outfow of reactants or products whilst the reaction is being carried out. Suppose that the reaction A→B, the reactor is given by
dt
dA
=−k
1
A
n
,A(0)=A
0
, where A
0
is the initial concentration of the reactant (a) By solving the appropriate differential equation determine how the concentration of the reactant in the reactor depends upon the time since the reactor was started for (i) a first order reaction, [3] (ii) a second order reaction. [3] (b) Hence obtain a formula for the time taken t
R
for the concentration of the reactant to decrease to 10 percent of its initial value for (i) a first order reaction, [2] (ii) a second order reaction. [3] (c) (i) For a given first order reaction k
1
=10
−4
s
−1
. Determine t
R
. [2] (ii) For a given second order reaction k
1
A
0
=10
−3
s
−1
. Determine t
R
. [2]