Question

In an aqueous solution at 223.15 K, the diffusion coefficient of Hemoglobin (r=35 A with dot on top ) is 7.6x10-14 cm2s-1 and for O2 (r=2.0 A with dot on top ) is 1.2x10-12 cm2s-1. The rate constant for binding O2 to Hemoglobin is 4.0x107 M-1s-1. Is this a diffusion-controlled reaction? Find necessary parameter and explain your opinion.

Answer 1

then rate constant k=A as activation energy(Ea) of such processes is zero

diffusion coefficient for hemoglobin radius r1 = 35 A = 3.5 x 10-7 cm

diffusion coefficient of O2 radius r2 = 2 A = 0.2 x 10-7 cm

diffusion coefficient for hemoglobin D1 = 7.6 x 10-14 cm2 s-1

diffusion coefficient for O2 D2 = 1.2 x 10-12 cm2 s-1

NA = Avogadro constant =6.022 x 1023

the equation to calculate the rate constant (kd) is

kd = 4 * pi* NA(r1 + r2)(D1 + D2) M-1 s-1

by incorporating the given values we will get

kd = 4 x 3.14 x 6.022 x 1023 (3.5 x 10-7 cm + 0.2 x 10-7 cm)(7.6 x 10-14 cm 2s-1+ 1.2 x 10-12​​​​​​​ cm2 s-1)

kd = 3.57 x 106 cm3 mol-1 s-1

kd = 3.57 x 103 M-1 s-1

since actual rate constant (3.57 x 103 ) is smaller than the diffusion limited rate constant (4 x 107) the reaction is diffusion limited