A powder is to be completely dissolved in an aqueous solution in a large, well-mixed tank. An acid must be added to the solution to render the spherical particle soluble. The particles are sufficiently small that they are unaffected by fluid velocity effects in the tank. For the case of excess acid, C₀ = 2 M, derive an equation for the diameter of the particle as a function of time when
a. Mass transfer limits the dissolution: –W_A = k_cC_A0
b. Reaction limits the dissolution:−rA″=krACA0
What is the time for complete dissolution in each case?
c. Now assume that the acid is not in excess and that mass transfer is limiting the dissolution. One mole of acid is required to dissolve 1 mol of solid. The molar concentration of acid is 0.1 M, the tank is 100 L, and 9.8 mol of solid is added to the tank at time t = 0. Derive an expression for the radius of the particles as a function of time and calculate the time for the particles to dissolve completely.
d. How could you make the powder dissolve faster? Slower?
Additional information:
De=10−10m2/s,k=10−18/sinitial diameter=10−5m