A reaction is second order respect to the reactant A. If the reaction is 85% complete in 12 minutes, how long would it take for the reaction to be 15% complete?
a. 110s
b. 27s
c. 62s
d.130s
e. 22s

e. 22s

Explanation:

Initial Concentration = 100

Final concentration = 15 ( Since the reaction is 85% complete)

Time = 12 minutes = 720 seconds

The integrated rate law for second order reactions is given as;

1 / [A] = (1 / [A]o) + kt

Making k subject of interest, we have;

kt = (1 / [A] ) - (1 / [A]o )

k = (1 / [A] ) - (1 / [A]o ) / t

k = [(1/ 15) - (1 / 100) ] / 720

k = (0.0667 - 0.01 ) / 720

k = 0.0567 / 720

k = 7.875e^-5

How long would it take for the reaction to be 15% complete?

Final concentration = 85 (Since the reaction would be 15% complete)

The integrated rate law for second order reactions is given as;

1 / [A] = (1 / [A]o) + kt

Making t subject of interest, we have;

kt = (1 / [A] ) - (1 / [A]o )

t = (1 / [A] ) - (1 / [A]o ) / k

t = [(1 / 85 ) - (1 / 100) ] / 7.875e^-5

t = (0.0117 - 0.01 ) / 7.875e^-5

t = 0.001765 / 7.875e^-5

t = 22.41 seconds

Corect option = E.