Consider a homogeneous spherical bacterium with a radius of 10 cm. A substance A diffuses into the bacteria and a first-order reaction takes place there. In the steady state, ignoring the term convective transfer; a) Derive the differential equation that gives the change in substance A concentration .
Consider a homogeneous spherical bacterium with a radius of 10 cm. A substance A diffuses into the bacteria and a first-order reaction takes place there. In the steady state, ignoring the term convective transfer; a) Derive the differential equation that gives the change in substance A concentration .
Biochemistry
9th Edition
ISBN:9781319114671
Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Publisher:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Chapter1: Biochemistry: An Evolving Science
Section: Chapter Questions
Problem 1P
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Consider a homogeneous spherical bacterium with a radius of 10 cm. A substance A diffuses into the bacteria and a first-order reaction takes place there. In the steady state, ignoring the term convective transfer;
a) Derive the differential equation that gives the change in substance A concentration .
b) Solve the differential equation you found in part (a) using the boundary conditions given below.
(Reaction rate constant, k=0.8 s-1 and diffusion coefficient, D=0.2 cm2/s)
Boundary Conditions;
SK1: r = 0.01 cm CA = 0 mol/cm3
SK2: r = 1 cm CA= 10 mol/cm3
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