Non-steady state chemical dissolution

Consider the chemical dissolution of a slightly soluble solid reactant A in a liquid with excess reactant B, This type of reaction is encountered frequently in organic syntheses. This situation resembles the solid surface reaction that was treated in section 5,3,2,2, but the difference is that now the solid dissolves first and then reacts in the liquid phase (therefore the solid reactant is now denoted as A). When the reaction is relatively slow (tp 0.3), eq. (5.21) is to be applied here. For the situation where the rate is completely determined by mass transfer of the slightly soluble A into the solution with a large excess of B, the effective rate constant is now the mass transfer coefficient of A, and the calculations similar to those in section 5,3,2,2 apply here also. The mass balance for n particles per unit volume is then 

This has to be combined with eq. (5.21). Let us consider two simple cases. 

Chemical kinetics can only be rate determining, as long as there is still a certain quantity of undissolved reactant A present, to guarantee that the solution is saturated with A, For this situation eqs. (5.21) and (5.23) yield 

The time t required for total dissolution is then found from 1 r 1 + P 

Note that the dissolution time goes to when P 0, but this is not a realistic situation. A certain excess of B was a prerequisition for this reasoning. 

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