Question

4. Consider the following sequence of first order reactions: k1 k2 O → M → G Where k1 = 2.50 × 1011 s -1 and k2 = 5.20 × 1010 s -1

a. At what time in seconds will the maximum concentration of M occur? (3 points)

b. If [O]0 = 2.00 M, what will [G] be 9.50 × 10-12 s after the reaction is initiated? (4 points)

Answer 1

O ----> M : K1 = 2.5 x 10¹¹ / s

and M -----> G : K2 5.2 x 10¹⁰ / s

for first order reaction

K = (2.303 / t ) x log [A₀] / [A]

where, [A₀] = initial concentration of reactant

[A] = final concentration of reactant at time t

t = (2.303 / K2) x log [ A0] /[A]

at maximume M product O will zero or minimum

t = ( 2.303 / 2.5 x 10¹¹ / s) x log [ zero]

t = 9.212 x 10^-12 s

b) first complet O ---> M reaction in 9.212 x10^-12 s then after start M -----> G

t = (9.5 x10^-12 s - 9.212 x10^-12 s) = 2.88x10^-13 s

K2 = (2.303 / t ) x log [ M] / [G]

5.2x10¹⁰ /s = (2.303 / 2.88x10^-13 s ) log [2]/[G]

(0.014976 / 2.303 )= log[2]/[G]

[G] = 1.97 M after 9.50 × 10-12 s after the reaction is initiated.