Question

A first-order reaction has a half-life of 17.3 minutes. What is the time required for the reactant concentration to decrease to 2.0% of it's origional value?

Thank you!

Answer 1

For a first order reaction rate constant , k = ( 2.303 /t )x log ( M_o / M)

Where

M_o = initial concentration

M= Mass left after time t = 2.0 % M_o = (2/100) x M_o = 0.02 M_o

t = time = ?

k = rate constant = 0.693 / t _1/2

t_1/2 = half life of the reaction = 17.3 min

       = 17.3 min x 60 (s/min)

      = 1038 s

k = 0.693 / 1038 s

   = 6.68x10^-4 s^-1

Plug all the values we get   k = ( 2.303 /t )x log ( M_o / M)

                                           t = ( 2.303 /k )x log ( M_o / M)

                                          t = ( 2.303 /(6.68x10^-4 s^-1) )x log ( M_o / 0.02M_o)

                                            = 5857 s

                                            = 5857 s x ( 1/60) ( min/s)

                                           = 97.6 min