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In dyeing of wool, some dyes can react quickly and reversibly with wool as dye diffuses into the fiber. Derive the relationship between the concentration of reacted dye (c2) as a function of time (t) and depth from the wool surface (z). Assume: (i) equilibrium relationship between free dye (c1) and reacted dye (c2) or c2 = Kc1; (ii) the reaction will not change the diffusivity of dye (D) in wool; (iii) dye concentration on. the surface is c10