Question

The Noyes-Whitney equation is often used to predict the rate at which a solid substance dissolves into water. One form of this equation is: dC/Dt = k(CS-C) where k=DA/Vh . Here D is the diffusivity of the dissolving substance in the electrolyte, A is the area of the sample dissolving, h is the thickness of the diffusion boundary layer, V is the volume of electrolyte, C is the time-dependent concentration of the substance in the electrolyte and Cs is the saturation concentration of the substance in the electrolyte. This equation is often used in the pharmaceutical industry to predict the kinetics of drug release.

At 20 °C acetylsalicylic acid (aspirin) has a solubility, Cs = 2 mg/mL. Consider a tablet of aspirin in the form of a disk, 0.4cm in diameter and 0.1cm thick. (A) Determine the time-dependent dissolution rate of aspirin at 20 °C in a total volume of water of 5 mL using the parameter values below. Plot your results as dC(t)/dt versus t. (B) Determine the time-dependent concentration of dissolved aspirin. Plot your results as C(t) versus t. Does the dissolved aspirin ever reach saturation and if so when? Molecular mass of aspirin =180 g/mol. Density of aspirin = 1.4 g/cm³ D = 10-6 cm²/sec h = 0.01 cm.

Answer 1