If 50% of the reactant that follows first order kinetics is converted into product(s) in 25 min , how much of it would react in 100 min?
For any reaction, time taken for 50% of a reactant to convert into product(s) is called the half life (t12)
For a first order reaction:
t12=ln2k=25 mink=ln225 min−1
k=Rate constant
Also,
For a first order reaction:
A→Products
[A]=[A0]e−kt...(i)
Here,
[A]=Concentration of A at time t
[A0]=Concentration of A initially
Putting t=100 min & k=ln225 in (i)
[A]=[A0]e−ln225×100
[A]=[A0]e−ln24
[A]=116×[A0]
% reacted=[A0]−[A][A0]×100%=[A0]−[A0]16[A0]×100%% reacted=93.75%