Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

252 EXPERIMENTAL METHODS FOR HETEROGENEOUS REACTIONSRates of mass transfer to the catalyst surface and pore diffusion can be calculatedby the methods of Section 2.2.2 if the diffusion coefficients are known. However,the molecular theory of diffusion in liquids319- 321 is relatively undeveloped andit is not yet possible to treat diffusion in liquids with the same rigour as diffusionin gases. The complicating factors are that the diffusion coefficient varies withconcentration and that the mass density is usually more constant than the molardensity of the solution. An empirical equation, due to Wilke and Chang322, whichapplies in dilute solution, giveswhere T is the temperature ("K), X is an empirical association parameter of thesolvent, M, is the molecular weight of the solvent and p is the solution viscosity(poises). V, is the molar volume of the diffusing solute (cm3.g-'.mole-')obtained from Kopps Lawla'. For large molecules, the above equation does nothold and the Stokes-Einstein equation must be used. The diffusion coefficientin liquids at ordinary temperatures is about lo-* times that for gaseous systems atatmospheric pressure. A recently published modification of the above equation32is claimed to be more widely applicable.A mass transfer coefficient can be derived from the equation324K,dp/D = 0.991(Np,)'for NPe > 500, where NPe is the Peclet number and dp is the particle diameter.At low fluid velocities K,d,lD + 2.3.3 NON CATALYTIC REACTIONSThe effects of diffusion in solid-liquid systems have been discussed in the previoussection. Dissolution of sodium chloride is an example of a diffusion controlledreaction. In a dilute solution, the rate of dissolution R is given byR = KSwhere S is the total surface area. By Fick's law, the dissolution rate in mole. cm-2.sec'l is D(C,- C)/T, where D is the diffusion coefficient, C, the concentration at thesurface, C the concentration in the bulk of the solution, and T the residence time.Then