Someone computes the diffusion-limited rate constant for a target of radius with as…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Biophysics & Medical Physics · Physical foundations of the living cell

Forces, Machines and Signals, Ch Diffusion: friction, capture and the crowded cytoplasm

Problem

Someone computes the diffusion-limited rate constant for a target of radius a=2.0 nma = 2.0\,\mathrm{nm} with D=1.0×10−9 m2 s−1D = 1.0\times10^{-9}\,\mathrm{m^2\,s^{-1}} as follows: "k=4πDa=4π(1.0×10−9 m2 s−1)(2.0×10−9 m)=2.51×10−17 m3 s−1k = 4\pi Da = 4\pi(1.0\times10^{-9}\,\mathrm{m^2\,s^{-1}})(2.0\times10^{-9}\,\mathrm{m}) = 2.51\times10^{-17}\,\mathrm{m^3\,s^{-1}} per molecule. Converting to molar units, k[M−1 s−1]=k[m3 s−1]×NA=(2.51×10−17)(6.022×1023)=1.51×107 M−1 s−1k[\mathrm{M^{-1}\,s^{-1}}] = k[\mathrm{m^3\,s^{-1}}]\times N_A = (2.51\times10^{-17})(6.022\times10^{23}) = 1.51\times10^{7}\,\mathrm{M^{-1}\,s^{-1}}." ((a)) Find the error in this working. ((b)) Give the corrected molar rate constant.

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