Question: You are interested in dissolving solid sugar crystals in your coffee solution (herefor referred simply as coffee). The maximum solubility of sugar in coffee is
You are interested in dissolving solid sugar crystals in your coffee solution (herefor referred simply as coffee). The maximum solubility of sugar in coffee is 150g/ml, and diffusivity of sugar in coffee can be assumed to be 1.510.5cm2/s. The average diameter of the sugar crystals is 0.8 mm (assuming spherical crystals) and at room temperature the density and viscosity of coffee is 1050kg/m3 and 1.1cP, respectively. Since most of the solvent is water, assume, a molecular weight of solvent of 18g/mol, density of 1000kg/m3 and viscosity of 1cP. The molecular weight of sugar is 342g/mol. Calculate the molar dissolution rate (mol/s) of a single sugar crystal before the crystal diameter decrease as it dissolves (i.e. t=0+t ) For this problem, you can use the following empirical relationship to calculate convective mass transfer coefficient: Sh=DABkLdp=2+0.44(Ndp2)0.504(DAB)0.355 In this relationship, dp is particle diameter and N=1.7, which is the revolutions per second you do when stirring your coffee
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