A spherical particle is dissolving in a liquid. The rate of dissolution is first order in the solvent concentration, C. Assuming that the solvent is in excess, show that the following conversion-time relationships hold.

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Rate-Limiting Regime Conversion-Time Relationship Surface reaction Mass transfer Mixed 1-(1-X)1/3=atDi Di2D*[1-(1-x)2/3]=atDi [1-(1-X)]1/3+Di2D*[1-(1-x)2/3]=atDi