Question

1. A certain first-order reaction (A→products) has a rate constant of 1.00×10−2 s−1 at 45 ∘C. How many minutes does it take for the concentration of the reactant, [A], to drop to 6.25% of the original concentration?

2. A certain second-order reaction (B→products) has a rate constant of 1.15×10⁻³M−1⋅s−1 at 27 ∘C and an initial half-life of 200 s . What is the concentration of the reactant B after one half-life?

please show work

Answer 1

1) rate constant k₁= 1.00×10−2 s−1

   Half life t_1/2 =0.693/k₁

                   =0.693/1x10^-2

    Half life t_1/2 =69.3 secs

To drop 6.25% reactant concentration it takes 4 half lifes

                   =4x69.3

To drop 6.25% reactant concentration it takes =277.2 secs

   To drop 6.25% reactant concentration it takes 4.62 minutes

2)    a rate constant k₂=1.15×10⁻³M−1⋅s−1

     An initial half-life t_1/2= 200 s

              k₂₌[1/at_1/2]

             Initial concentration a=[1/k₂t_1/2]

                               a= [1/(200x1.15×10⁻³)]

                                 a= [1/(2.3x10⁻¹)]

                                a= 10/2.3

                                  a= 4.347   

After one half life reactant concentration is 2.173 mol/l