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  Noyers Whiter Equation for Calculating Dosage Rates

 

Calculus is often employed in the field of pharmacology to determine the best dosage forms that provide a steady rate of dissolution of the administered drug. In many cases, a tablet that is taken passes into the aqueous solution of the stomach where it slowly dissolves.

Dosage forms must tighly regulated and controlled, because the rate of dissolution for each drug is different.If a drug is supplied in a form that dissolves too quickly or dissolves too slow it may yeild a toxic or ineffective effect on a patient. Thus medicine must meet the compliance of a theraputic range which is effective, safe, and provides for a long period of realease as opposed to immediate release  which have sharp peaks and drops in the blood concentration.

The Noyes–Whitney is used to determine the dosage rates of varying dosage form:

                          
                           

Where:

  •  represents the dossage rate
  • A is the surface area  of the solid.
  • C is the concentration of the solid in the bulk dissolution medium.
  • Cs is the concentration of the solid in the diffusion layer surrounding the solid.
  • D is the diffusion coefficient
  • L is the diffusion layer thickness.

The Noyes-Whitney equation essentialy represents a surfance area problem.  The rate of dissolution of compound is dependent on its surface area. An adjustment to the surface area exposed to the outer basic or acidic enviroment will change the bioavailability of the compound in the patients circulatory system. 

DRAFT: This module has unpublished changes.
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DRAFT: This module has unpublished changes.

Example using the Noyes-Whitney equation

Calculate the dissolution rate of a hydrophobic drug having the following physicochemical characteristics:

surface area = 2.5 x 103  cm2

saturated solubility = 0.35 mg/mL (at room temperature)

diffusion coefficient = 1.75 x 10-7 cm2/s

thickness of diffusion layer = 1.25 µm

Concentration of drug in bulk = 2.1 x 10-4  mg/mL

 dW  = DA(Cs-C)

    dt            L 

 

   dW   =          (1.75 x 10-7)(2.5 x 103)( 0.349 mg/mL)

   dt                                   1.25E-4

 

 

dW

 

=

  

(1.75E-7)(2.5E3)( 0.35 mg/mL - 2.1E mg/ml) 

dt

 

1.25E-4

 

 

  

dW

 

=

 

1.53 x 10-4

 

= 1.22 mg/sec

dt

 

1.25 x 10-4

 

DRAFT: This module has unpublished changes.