A first order reaction has a specific reaction rate of 10-2 s-1. How much time will it take for 20 g of the reactant to reduce to 5 g?
138.6s
For a first order reaction,
Rate constant (k)=2.303tlogaa−x
Where, a =initial concentration
a–x =concentration after time ‘t’
t =times in sec.
Given, a =20 g, a - x =5 g, k=10−2
∴t=2.30310−2log205
=138.6s
Alternatively,
Half –life for the first order reaction,
t12=0.693k=0.69310−2=69.3s
Two half –lives are required for the reduction of 20 g of reactant into 5 g.
20gt12→10gt12→5g.
∴ Total time =2t12=2×69.3=138.6s