Question 18.11: In aqueous solution at 25°C and pH 7.4 the diffusion coeffic...

Thermodynamics, Statistical Thermodynamics, & Kinetics

In aqueous solution at 25°C and pH 7.4 the diffusion coefficient for hemoglobin (radius =35 Å) is $7.6 × 10^{-7} cm^{2} s^{-1}$ , and the diffusion coefficient for $O_{2}$ (radius =2.0 Å) is $2.2 × 10^{-5} cm^{2} s^{-1}$ . The rate constant for the binding of $O_{2}$ to hemoglobin is $4 × 10^{7} M^{-1} s^{-1}$ . Is this a diffusion -controlled reaction?

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Assuming the reaction is diffusion controlled, the rate constant is expected to be

k_{d}=4\pi N_{A}\left( r_{A}+r_{B} \right)D_{AB}

=4\pi N_{A}\left( 35 ×10^{-8}  cm +2.0×10^{-8}  cm\right)

\left( 7.6 ×10^{-7}  cm^{2}  s^{-1} +2.2×10^{-5}  cm^{2}  s^{-1} \right)

=6.4 ×10^{10}  M^{-1}  s^{-1}

The diffusion-controlled rate constant is significantly greater than the experimentally measured rate constant; therefore, the binding of $O_{2}$ to hemoglobin is not diffusion controlled.

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