Question

In aqueous solution at 298 K and pH 7.4, the diffusion coefficient for hemoglobin (radius = 3.5 nm) is 7.6 x 10-^7 cm^2/sec, and the diffusion coefficient for O2 (radius = 0.2 nm) is 2.2 x 10^-5 cm^2/sec. The rate constant for the binding of O2 to hemoglobin is 4 x 10^7 M^-1 sec^-1. Is this a diffusion-controlled reaction?

Answer 1

If given reaction is a diffuscion controlled reaction then rate constant k = A, as activation energy (E_a) of such processes is zero (A= Arhenius constant )

And A_diff = 4(r_m + r_n) (D_m + D_n) N_o / 1000

here r_m, r_n, are  radii and D_m, and D_n are diffusion coefficients

N_o is Avagadro’s number = 6.022 x 10²³

A_diff = {4(3.2 + 0.2) (7.6 x 10^-7 + 2.2 x x 10^-5) 6.022 x 10²³}/ 1000

= 5.85 x 10²² M^-1 s^-1.

Since this value is not equal to given rate constant value, the reaction is not diffusion-controlled reaction