The Solution Process Model

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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
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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.

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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

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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 lt loss of energy,
  solubility will be very high.
• Overall gain of energy gt loss of energy,
  solubility will be very low.

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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.

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• 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)
• 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 (gt 0.05 mm
  thick).
• Cs Saturation solubility (Molar or mg/ml).
• Ct Solubility at any time t (Molar or mg/ml).

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• 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

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• When surface area is 2800 cm2
  dm/dt 12. 67 mg/sec
• When surface area is 5000 cm2
  dm/dt 22.65 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.