The Solution Process Model Whether or not a substance will dissolve in another substance depends on the magnitude of the forces between molecules. Cohesive forces: Forces between similar molecules Adhesive forces: Forces between dissimilar molecules Solvent molecules cohesive Solute + solvent adhesive Solute molecules cohesive

The Solution Process Model Step # 1: Removal of solute molecule from the pure solute structure, this results in loss of energy due to breakage of cohesive forces.

The Solution Process Model Step # 2: Creation of a hole in solvent molecules by disrupting intermolecular forces between solvent molecules. This results in loss of energy due to breakage of cohesive forces:

The Solution Process Model Step # 3: Introduction of the solute molecule into the hole in the solvent structure and subsequent solvation of the solute molecule by the solvent. This results in gain of energy from formation of new adhesive forces : In general: Overall gain of energy < loss of energy, solubility will be very high. Overall gain of energy > loss of energy, solubility will be very low.

I. Effect of particle size on solubility of solid in liquid Dissolution rate is a measure of how fast a solid drug dissolves in a liquid solvent. Dissolution is defined as the process of dissolving a solute to form a homogeneous solution as described by Noyes Whitney equation. When a particle of a drug is dissolved in water, the molecules at the very surface of the particles dissolve and saturate the diffusion layer. The dissolved drug particles then diffuse out of the diffusion layer through the less tightly bound water to the bulk (stirred) solution.

The rate of dissolution is given by Noyes-Whitney equation which takes into account the two processes necessary for dissolution to occur which are: Saturation of the diffusion layer and diffusion of drug molecules into solvent. dm/dt =KS (Cs-Ct) K = D/h dm/dt =(D/h)S (Cs-Ct) dc/dt =(K/V) S (Cs-Ct) Where: dm/dt is dissolution rate which is the change in mass of solute per time, unit is mg/second. K = Dissolution rate constant (cm/sec). S = Surface area of exposed solid in square cm. D = Diffusion coefficient (square cm/ sec) of the drug in solvent ( a measure of how fast the drug molecules move or diffuse through the solvent. H = Thickness of the diffusion layer (> 0.05 mm thick). Cs = Saturation solubility (Molar or mg/ml). Ct = Solubility at any time t (Molar or mg/ml). V = volume of solution (ml).

Example: A preparation of drug granules weighing 5.5 gm and having a total surface area of 2800 cm2 is allowed to dissolve in a 500 ml of water at 25oC. After the first minute, 0.76 gm have dissolved. The saturation solubility (Cs) of the drug is 15 mg/ml. a) Calculate the dissolution rate constant (K) dm/dt =KS (Cs-Ct) dm/dt =0.76gm / 60 seconds = 0.01267 gm/sec X 1000= 12.67 mg/sec S = 2800 cm2 Cs = 15 mg/ml Ct = 0.76 gm / 500 ml = 0.00152 gm/ ml X 1000 = 1.52 mg/ml 12.67 mg/sec = K (2800 cm2) (15 mg/ml - 1.52 mg/ml) K = 0.000336 cm /sec b) If the diffusion layer thickness (h) is 0.005 cm, calculate the diffusion coefficient (D). K = D/h D = K X h D = 0.000336 cm /sec X 0.005 cm = 1.6 X10-6 cm2/ sec c) Suppose that surface area was increased to 5000 cm2, what would be the dissolution rate. dm/dt =KS (Cs-Ct) = (0.000336 cm /sec)(5000 cm2)(15- 1.52 mg/ml) dm/dt = 22.65 mg/sec

When surface area is 2800 cm2: dm/dt = 12. 67 mg/sec i.e., surface area leads to increasing dissolution rate. How to utilize Noyes Whitney equation to enhance solubility: dm/dt =(D/h)S (Cs-Ct) Increase surface area by decreasing particle size. Effective surface area is area in direct contact with water. Reduced particle size leads to increased surface area leading to increased effective surface area and increased solubility. Mechanical stirring leads to reduced diffusion layer thickness ( reduced drug concentration in diffusion layer) leading to increased solubility.

Sink and non-sink conditions: dm/dt =KS (Cs-Ct) If Ct is very small (Ct >0.1 Cs), then dissolution rate is directly proportional to the saturation solubility (Cs). This assumes that S is constant which is only true at the very beginning of the experiment when only a small amount (>0.5%) of the solid drug has dissolved. When these two requirements are obeyed, then the system is under sink condition. If either requirements is violated, then non-sink condition operate and rate of dissolution is not directly proportional to saturation solubility. Ct Sink Non-sink Time (hr)