The reaction A → B is first order in [A]. Consider the following data.

Question

Time (s): 0.0 ; 5.0 ; 10.0 ; 15.0 ; 20.0

[A] (M): 0.20 : 0.14 ; 0.10 ; 0.071 ; 0.050

The concentration of A is ________ M after 40.0 s.

Answer 1

Inspecting the data, we can see that at 10 seconds, the [A] is 1/2 of what it was initially, i.e. it went from 0.20 M to 0.10 M in 10 seconds. Thus, we can say the half time (or half life, t1/2) is 10 seconds. For a 1st order reaction, the fraction remaining at any time (t) is equal to 0.5 raised to the number of half lives elapsed. Written in mathematical form, we have...

fraction remaining = 0.5ⁿ

In this example, n = 4 half lives since 40 seconds represents 4 half lives.

fraction remaining = 0.5⁴

fraction remaining = 0.0625

Thus, the concentration of A after 40 seconds would be 0.0625 x 0.20 M = 0.0125 M = 0.013 M