Pharmaceutical calculations GPAt | Study notes Pharmacy

PHAR1822(Notes(

Pharmaceutical(calculations(

𝑑=

𝑚

𝑣!

𝑑𝑒𝑛𝑠𝑖𝑡𝑦!(𝑔/𝑚𝐿)=!

𝑚𝑎𝑠𝑠!(𝑔)

𝑣𝑜𝑙𝑢𝑚𝑒!(𝑚𝐿)!

𝑐=

𝑛

𝑣!

𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛!(𝑚𝑜𝑙 𝐿)!=

𝑚𝑜𝑙𝑒𝑠!(𝑚𝑜𝑙)

𝑣𝑜𝑙𝑢𝑚𝑒!(𝐿)!

𝑛=

𝑚

𝑀𝑀!

𝑛𝑜.𝑚𝑜𝑙𝑒𝑠 =!

𝑚𝑎𝑠𝑠!(𝑔)

𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟!𝑚𝑎𝑠𝑠!(𝑔𝑚𝑜𝑙)!

𝑐!𝑣!=𝑐!𝑣!!

𝑢𝑠𝑒!𝑓𝑜𝑟!𝑑𝑖𝑙𝑢𝑡𝑖𝑜𝑛𝑠!

" dL!=!decilitre!=!100mL!

" If!a!mixture!is!made!up!of!water!and!drug,!add!x!grams!of!drug,!and!then!(100!–!x)!mL!of!water!to!

make!the!mixture!a!total!amount!of!100mL!(or!100g)!

o I.e.!add!water!to!make!the!volume!up!to!100mL!!

" Dilution!≈!paediatric!sample!–!use!C1V1=C2V2!

" If!working!with!a!liquid!drug!or!solvent!other!than!water!(e.g.!ethanol)!–!density!formula!!

Liquids(and(Solutions(

Solution(

Mixture!of!two!or!more!components!that!form!a!single!phase!which!is!homogeneous!

down!to!the!molecular!level!

Phase(

Part!of!a!system!separated!by!one!or!more!boundaries/interfaces,!which!can!be!

separated!physically!(e.g.!filtration,!centrifuge)!

Dissolution(

Transfer!of!molecules!or!ions!from!the!solid!state!into!solution!

Miscibility(

Combination!of!two!solvents!that!mix!completely!to!form!a!homogenous!solution!

Solubility!

" Limit!to!which!a!solute!can!be!dissolved!in!a!solvent!under!a!particular!set!of!conditions!

" Determined!at!20°C!

" Based!on!amount!of!solvent!in!mL!or!grams!(“parts”),!required!to!dissolve!1g!of!drug/excipient!

o Soluble!–!10"30!parts!solvent!

o Insoluble!–!>10000!parts!solvent(!

" Water!solubility!–!depends!on!polarity!and!functional!groups!–!H"bonds!and!ion"dipole!bonds!!

o "NH,!"OH!or!C=O!functional!groups!will!H"bond!with!water!

o Ion"dipole!bonds!are!even!stronger!than!hydrogen!bonds!

Salt!form!of!drugs!

" Salt!form!of!drugs!are!more!water!soluble!than!neutral!form!

" They!form!more,!and!stronger,!hydrogen!bonds!with!water!

" However:!

o Samples!can!be!hygroscopic!(draw!in!moisture!from!air)!

o Can!change!pH!of!solution!(important!for!injection!and!oral!solutions)!

o Reactions!with!packaging!(glass!and!basic!solutions)!

o Different!salts!of!a!drug!can!work!differently!

o Salts!interact!with!each!other!and!precipitate!out!of!solution!!

" Most!common!salt!forms!of!drugs:!

o Acidic!drugs!–!Na+,!K+,!Ca2+,!Zn2+!

o Basic!drugs!–!Cl",!SO4

2",!PO4

3"!

Salting!out!

" Precipitation!of!peptides!and!proteins!from!solution!at!high!salt!concentrations!

" At!high![salt],!water!molecules!bind!to!the!salt!instead!of!the!protein!(not!enough!free!water!

available)!–!causes!precipitation!of!protein!molecules!(less!soluble!solute)!

" Some!drugs!based!on!proteins!and!peptides!–!must!ensure!drugs!do!not!precipitate!

(

Drug/mixture(

w/w!

grams/100g!

w/v!

grams/100mL!

v/v!

mL/100mL!

v/w!

mL/100g!

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PHAR1822 Notes Pharmaceutical calculations 𝑑 =

𝑣 𝑑𝑒𝑛𝑠𝑖𝑡𝑦^ (𝑔/𝑚𝐿)^ =^

𝑣 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛^ (𝑚𝑜𝑙^ 𝐿)^ =^

𝑀𝑀 𝑛𝑜.^ 𝑚𝑜𝑙𝑒𝑠^ =^

-‐ dL = decilitre = 100mL -‐ If a mixture is made up of water and drug, add x grams of drug, and then (100 – x) mL of water to make the mixture a total amount of 100mL (or 100g) o I.e. add water to make the volume up to 100mL -‐ Dilution ≈ paediatric sample – use C 1 V 1 =C 2 V 2 -‐ If working with a liquid drug or solvent other than water (e.g. ethanol) – density formula Liquids and Solutions Solution Mixture of two or more components that form a single phase which is homogeneous down to the molecular level Phase Part of a system separated by one or more boundaries/interfaces, which can be separated physically (e.g. filtration, centrifuge) Dissolution Transfer of molecules or ions from the solid state into solution Miscibility Combination of two solvents that mix completely to form a homogenous solution Solubility -‐ Limit to which a solute can be dissolved in a solvent under a particular set of conditions -‐ Determined at 20 °C -‐ Based on amount of solvent in mL or grams (“parts”), required to dissolve 1g of drug/excipient o Soluble – 10 -‐30 parts solvent o Insoluble – >10000 parts solvent -‐ Water solubility – depends on polarity and functional groups – H-‐bonds and ion-‐dipole bonds o -‐NH, -‐OH or C=O functional groups will H-‐bond with water o Ion-‐dipole bonds are even stronger than hydrogen bonds Salt form of drugs -‐ Salt form of drugs are more water soluble than neutral form -‐ They form more, and stronger, hydrogen bonds with water -‐ However: o Samples can be hygroscopic (draw in moisture from air) o Can change pH of solution (important for injection and oral solutions) o Reactions with packaging (glass and basic solutions) o Different salts of a drug can work differently o Salts interact with each other and precipitate out of solution -‐ Most common salt forms of drugs: o Acidic drugs – Na+, K+, Ca2+, Zn2+ o Basic drugs – Cl-‐, SO 42 -‐, PO 43 -‐ Salting out -‐ Precipitation of peptides and proteins from solution at high salt concentrations -‐ At high [salt], water molecules bind to the salt instead of the protein (not enough free water available) – causes precipitation of protein molecules (less soluble solute) -‐ Some drugs based on proteins and peptides – must ensure drugs do not precipitate Drug/mixture w/w grams/100g w/v grams/100mL v/v mL/100mL v/w mL/100g

-‐ Van der Waals radius – imaginary radius of an atom or molecule o Physical space the drug/particle takes up -‐ Hydrodynamic radius – imaginary radius of drug/particle and any bound subparticles (e.g. water) that travel through the solution with the drug particle -‐ Brownian motion – random movement of particles suspended in a liquid or gas o Caused by collisions with molecules of the surrounding medium o Rate of drug/particle movement through solution is directly related to size Stokes – Einstein equation -‐ Rate at which drug diffuses through solution is largely dependent on hydrodynamic radius and solvent viscosity -‐ 𝐷 = !" !!"# o D = diffusion coefficient (m^2 s-‐^1 ) o K = Boltzmann constant (1.3810-‐^23 JK-‐^1 ) o T = temperature (K) o η = solvent viscosity (water: 1.23210-‐^3 Pa S) o r = hydrodynamic radius (metres) Vapour pressure -‐ Pressure of vapour above liquid when liquid and vapour are at equilibrium -‐ Amount of vapour about liquid depends on intermolecular forces o More bonding between molecules – less vapour formed – lower vapour pressure -‐ Lower vapour pressure – boils at higher temperature -‐ Higher vapour pressure – boils at lower temperature -‐ 50/50 mixture of ethanol and water o Does NOT mean mixture of vapour is also 50/ o More ethanol molecules in air than water since ethanol has a higher vapour pressure -‐ 𝑃!"!#$ = 𝑋!𝑃! + 𝑋!𝑃! o Ptotal = total pressure from all molecules in the gas/vapour phase o XA = mole fraction of gas A § Total of mole fractions (XA + XB) must equal 1 o PA = vapour pressure of gas A o Raoult’s Law 2 polar molecules 1 polar 1 non-‐polar 2 non-‐polar H-‐bonding – keeps in liquid phase Repulsion – more molecules in gas/vapour phase Ideal conditions Hydrophobic forces very weak; no repulsion Lower vapour pressure for both Higher BP Higher VP Lower BP No effect on partial pressures of the gases/vapours Freezing point depression -‐ Dissolution of polar solute into a solvent results in drop in the freezing point of the solvent o Salt + water – lowers freezing point, so water doesn’t freeze as easily o Blood contains many polar molecules (proteins, salts) – lowers freezing point of blood -‐ Size of FPD depends on solvent and amount of solute (no. molecules, not no. moles) -‐ Any solution injected into vein, or eye drops – must have FDP of 0.52°C Change Rate of drug diffusion Increase temperature Faster Change form water to oil Slower Change from neutral drug to salt form Slower Make a nanoparticle formulation of the drug Slower

Pharmaceutical calculations GPAt, Study notes of Pharmacy

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𝑣 𝑑𝑒𝑛𝑠𝑖𝑡𝑦^ (𝑔/𝑚𝐿)^ =^

𝑣 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛^ (𝑚𝑜𝑙^ 𝐿)^ =^

𝑀𝑀 𝑛𝑜.^ 𝑚𝑜𝑙𝑒𝑠^ =^