Question

The reaction A - B is first order in A. Initially, [A]=0.800 M and after 54 min., [A] = 0.100 M. At what time (in minutes) is [A] = 0.040?

Answer 1

Sol .

For a first order reaction ,  

kt = ln ( [A]o / [A]t )  

where k = rate constant

t = time  

[A]o = initial concentration of A

[A]t = concentration of A at time t

Here t = 54 min , [A]o = 0.8 M , [A]t = 0.1 M

So , k × 54 min = ln ( 0.8 M / 0.1 M ) = 2.0794

k = 2.0794 / 54 min-1 = 0.0385 min-1  

Now , [A]t = 0.04 M , k = 0.0385 min-1 , [A]o = 0.8 M

0.0385 min-1 × t = ln ( 0.8 M / 0.04 M ) = 2.9957

t = 2.9957 / 0.0385 min = 77.81 min

Therefore , answer is   77.81 min