4) [25 pt] Compound A diffuses through a 4-cm-long tube and reacts as it diffuses. The equation governing diffusion with reaction is, for concentration given by A: d2A D - kA = 0 dx2 - - At one end of the tube (x=0), there is a large source of A that results in a fixed concentration of 0.1 M. The other end of the tube is impenetrable to species A, so the boundary condition is dA/dx = 0 at x = L = 4 cm. Using the finite difference method with nodes every 0.4 cm, calculate A as a function of distance in the tube. Compare the results with k = 5 x 10-6 5-1 and D = 1.5 x 10-6, 6.0 x 10-6 and 12 x10-6 cm2/s