Compound A diffuses through a 4 cm long tube and reacts as it diffuses. The equation governing diffusion with reaction along the distance x of the tube (in cm) is given by: d?A dx2 - kA = 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.5: Properties Of Logarithms
Problem 60E
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Compound A diffuses through a 4 cm long tube and reacts as it diffuses. The equation
governing diffusion with reaction along the distance x of the tube (in cm) is given by:
d² A
D
dx?
- kA = 0
At one end of the tube, there is a large source of A at a concentration of 0.1 M. At the other
end of the tube there is an adsorbent material that quickly absorbs any A, making the
concentration of A zero. If D = 1.5 × 10-6 cm² s-1 and k= 6 x 10-6 s-1,
What is the general solution for the concentration of A as a function of distance in the
tube?
What would be the concentration of A at lcm distance from the source?
Transcribed Image Text:Compound A diffuses through a 4 cm long tube and reacts as it diffuses. The equation governing diffusion with reaction along the distance x of the tube (in cm) is given by: d² A D dx? - kA = 0 At one end of the tube, there is a large source of A at a concentration of 0.1 M. At the other end of the tube there is an adsorbent material that quickly absorbs any A, making the concentration of A zero. If D = 1.5 × 10-6 cm² s-1 and k= 6 x 10-6 s-1, What is the general solution for the concentration of A as a function of distance in the tube? What would be the concentration of A at lcm distance from the source?
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