Solubility Notes - Summary PHYSICAL PHARMACY – Pharmaceutics PDF

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Solubility Textbooks: Aulton- ‘Pharmaceutics: The Science of Dosage Form Design’. Florence and Attwood- ‘Physiochemical Principles of Pharmacy’. Sinko- ‘Martin’s Physical Pharmacy and Pharmaceutical Sciences’. Definition of Terms:  Solution- a mixture of two or more components that forms a single phase which is homogenous down to the molecular level. Mixing is spontaneous, mixtures are thermodynamically stable, inhomogeneties on molecular levels, properties of solution are independent on the way they are prepared.  Solvent(s)- Dissolves the solute. Determines the phase of solution. Usually constitute the largest proportion of the system.  Solute(s)- Dissolved in the solvent(s)- dispersed as molecules throughout the solvent.  Dissolution- the transfer of molecules from a solid state into a solution.  Solubility- of a substance is the amount of the solute that passes into solution when the equilibrium is established. The solution that is obtained under these conditions is saturated.  Unsaturated- less than max. amount of solute dissolved in solvent.  Supersaturated- solutions that are formed by dissolving the solute to a level in excess of its solubility in a particular solvent with the aid of heat.  Miscibility- 2 gases or 2 liquids. Solutions, colloids and suspensions:  Solutions- mixtures with particle sizes at the molecule/ion level. Dimensions- 0.1-2nm (1Á-20Á). Typically transparent.  Colloids- mixtures with particle size that consist of clumps of molecules. Dimensions- 2-1000nm. May look homogeneous to the naked eye- exhibit Tyndall Effect.  Suspensions- mixtures with particles that have diameters greater than 1000nm. Particles are visible to the naked eye. Expressions of Concentration:  Quantity per quantity- the weight/volume of solute that is contained in a given weight/volume of the solution. E.G. 1g/L, 0.1g per 100mL.  Percentage- used with one of the four different meanings according to circumstances: % w/w, % w/v, % v/v and % v/w.  Parts- number of ‘parts’ of solute dissolved in a stated no. ‘parts’ of solution, e/g/ ppm and ppb.  Molarity- no. moles of solute in 1L of solution. Unit= mol/L.  Molality- no. moles of solute divided by the mass of the solvent. Unit= mol/kg.  Equivalent- mass (in g) of a substance that reacts with 6x1023 (Avogadro’s Number). It is equal to the amount of substance in moles divided by the valence of the substance. For monovalent ions, 1 equivalent (Eq) = 1 mole. For divalent ions, 1Eq = 0.5 mol -> 2Eq = 1 mole.  Normal solutions- no. equivalents (in g) in 1L of solution. E.G. 1Eq/L (1N).  Ratio- no. g or mL of solute in g of mL of solution -:- w/w, -:- w/v, -:- v/v, -:- v/w. E.G. 1:1000 w/v (1g solute in 100mL preparation). Sources of Solubility Data: E.P., B.P., U.S.P., Martindale, Pharmaceutical Codex, Merck Index, Beilstein Database.

Summary of units

Expression

Symbol

Definition

Percent by weight

% w/w

Grams of solute in 100 g of solution

Percent by volume

% v/v

Millilitres of solute in 100 ml of solution

Percent weight in volume

% w/v

Grams of solute in 100 ml of solution

Molarity

M

Moles of solute in 1 litre of solution

Normality

N

Gram equivalent weights of solute in 1 litre of solution

Molality

M

Moles of solute in 1000 g of solvent (!)

Descriptive term

Approximate volume of solvent in millilitres per gram of solute

very soluble

less than 1

App.% >50

freely soluble

from 1

to 10

50 - 9.1

soluble

from 10

to 30

9.1 – 3.2

sparingly soluble

from 30

to 100

3.2 – 1.0

slightly soluble

from 100

to 1,000

1.0 – 0.1

very slightly soluble

from 1,000

to 10,000

0.1 – 0.01

practically insoluble

more than 10,000

Diclofenac + Sodium. Stoichiometry- drug:counterion = 1:1, therefore, 1 mole of drug gives 1 mole of salt. 1 mole of salt gives mole of drug upon dissociation in solution. 318g of salt gives 295g of drug upon dissociation in solution. •Salbutamol sulphate -> Salbutamol + Sulphate. Stiochiometry- drug:counterion = 2:1, therefore 2 moles of drug gives 1 mole of salt. 1 mole of salt gives 2 moles of drug upon dissociation in solution. 577g of salt gives 472g of drug upon dissociation in solution. Co-Solvation: (used to improve solubilities- only in liquid formulations).  Weak electrolytes and non-polar molecules frequently have poor aqueous solubilities.  Solubility in water can be increased by co-solvency (the addition of water miscible solvents in which the drug has good solubility) (the added solvents = co-solvents).  The solubilising effect by co-solvency is primarily dependent upon the polarity of drug with respect to solvent and co-solvent. Mechanism of Action of Co-Solvents:  Drug-Water Interactions (adhesive forces)- hydrophilic hydrogen bonding groups ensure water miscibility while their hydrophobic hydrocarbon regions interfere with water’s hydrogen bonding network, reducing the overall intermolecular attraction of water  Water-Water Interactions (cohesive forces)- co-solvents make the polar water environment more polar like the solute. Co-Solvents:  Can increase solubility of the non-polar drug up to several orders of magnitude compared to its aqueous solubility.  Co-solvent must meet certain requirements (such as non-toxicity, compatibility with blood, be nonsensitising, non-irritating, physically and chemically stable and inert).  Disadvantages of using a co-solvent- toxicity, poor taste of a formulation (corn syrup, citric acid anf fructose are often added when co-solvents are used). Polarity:  Measure of polarity- dielectric constant (ε), solubility parameter (δ), surface tension (γ), octanol-water partition coefficient (Kow).  The best solvent for a particular solute is the one which most closely matches its polarity.  Non-polar – less polar than either solvent component.  Polar – more polar than either solvent component.  Semi-polar – polarities between the polarities of the solvent and co-solvent.

Non-Polar Solutes: Yalkowsky’s Log-Linear Model – Assumptions:  The mixed solvent’s solubilisation power changes as a log-linear composition-weighted mixture of its pure components (the molar solubility of a solute in a mixed solvent system is a linear combination of its molar solubilities in the pure component solvents).  The solute is not altered in any way by changes in the solvent.  The volume contribution from dissolved solute is negligible and can be ignored.



The log-linear model describes an exponential increase in a non-polar drug’s solubility with a linear increase in co-solvent concentration: logSmix = logSw + σ . fc Where Smix = the total solubilities in the co-solvent-water mixture, Sw = solubility in water, σ = the cosolvent solubilisation power for the particular co-solvent-solute system, fc = the volume fraction of the co-solvent in the aqueous mixture.



Co-solvent power: σ = log





Values of σ can be positive, near zero or negative, depending on the relative polarity of water, cosolvent and solute. Order of solvating power: Ethanol > Propylene Glycol > PEG 400 > Glycerol (N.B. 2011 JF Exam Question: “List 3 co-solvents that can be used in liquid formulations for the oral use”). Solubilisation of a non-polar solute by ethanol, glycol and glycerine:

Semi-Polar  Semiparabolic  solute by glycerine.

 

Sc Sw

Solutes: polar drugs usually have log solubility vs. co-solvent composition curves. Solubilisation of a semi-polar ethanol, propylene glycol and

2 > logKow > -1 logSmix = logSw + σ’.fc + τ.fc2 Where σ’ and τ = constants for each solvent. Semi-polar drugso Have poor aqueous solubility due to strong crystalline interactions. o Rarely have large activity coefficients in water (they tend not to be solubilised greatly by cosolvents). o There is an appreciable amount of structuring of the solvent molecules in the vicinity of the solute.

Polar solutes:

   

Most can dissociate in aqueous solutions. Tend to be soluble in water. Addition of a less polar solvent decreases solubility, thus polar solutes tend to have gradually decreasing solubilisation curves. Solubilisation of polar solute by ethanol propylene glycol and glycerine:

Ibuprofen: Calculation Mw Ibuprofen- 206g/mol.  Solubility in water = 1g/595mL  Solubility in ethanol = 1g/18mL  Using ethanol as the co-solvent- 200mg/5mL solution is needed.  1. Use the log-linear model for non-polar solutes. 2. Calculate the molar solubility of Ibuprofen in water Sw and in ethanol Sc as well as the final concentration of Ibuprofen in formulation Smix. 3. Calculate σ (σ = log

Sc ) Sw

4. Calculate fc- logSmix = logSw + σ . fc...