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Pharmaceutical Calculations

FOR PHARMACY STUDENTS

santhipriyanagam
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Pharmaceutical Calculations

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  1. PHARMACEUTICAL CALCULATIONS

  2. Weights&Measures: • Therearetwosystemsofweightsandmeasures: • TheImperialSystem • TheMetricSystem

  3. THEIMPERIALSYSTEM • Itisanoldsystemofweightsandmeasures. • Measurementsofweightsinimperialsystem: • Weightisameasureofthegravitationalforceactingonabodyandis directlyproportionaltoitsmass. • Theimperialsystemsareoftwotypes: • Avoirdupoissystem • Apothecariessystem

  4. AVOIRDUPOISSYSTEM • Inthissystempound(lb)istakenasthestandardofweight (mass). • 1poundavoir(lb)=16ozavoirozispronouncedasounce. 1poundavoir(lb)=7000grains(gr)

  5. APOTHECARYORTROYSYSTEM • Inthissystemgrain(gr)istakenasthestandardof weight(mass). • 1poundapoth(lb)=12ounces • 1poundapoth(lb)=5760grains(gr) • 1ounce=8drachms • 1drachm=3scruples • 1scruple=20grains(gr)

  6. MEASUREMENTSOFVOLUMES • 1gallon(c)=4quart • 1quart=2pint(o) • 1pint(o)=20fluidounce • 1fluidounce=8fluiddrachm • 1fluiddrachm=3fluidscruple • 1fluidscruple=20minims

  7. THEMETRICSYSTEM • ‘Kilogram’istakenasthestandardweight(mass)

  8. MEASUREMENTSOFVOLUMES • ‘Litre’istakenasthestandardofvolume. • 1liter(L,lit)=1000ml • 1microliter(µl)=1/1000ml

  9. PERCENTAGESOLUTIONS • The concentration of a substance canbe expressedinthefollowingthreetypesof • percentages: • Weightinvolume (w/v):Requiredtoexpress concentrationofasolidinliquid. • Weightinweight(w/w):Requiredtoexpress concentrationofasolidinsolidmixture. • Volumeinvolume(v/v):Requiredtoexpress concentrationofaliquidinanotherliquid.

  10. PERCENTAGESOLUTIONS Weightinvolume (w/v) 1partbyweight 100partsbyvolume Solute: Solvent: • Inthiscasethegeneralformulafor1%(w/v)is: Solute: Solvent: 1g upto100ml

  11. PERCENTAGESOLUTIONS Weightinvolume (w/v) Exercise:Calculatethequantityof Sodiumchloriderequiredfor500ml of0.9%solution ANS:0.9%w/vsolutionofNaCl=0.9gNaCl/100ml So500mlsolutionwillcontain0.9gNaCl/100mlsolution*500ml =0.9*500/100 =4.5gNaCl

  12. PERCENTAGESOLUTIONS

  13. CONVERSIONTABLE

  14. WEIGHTMEASURECONVERSION • 1kg=2.2pounds(lb) • 1ounceapoth=30g • 1poundavoir=450g • 1grain=65mg

  15. CALCULATIONBYALLEGATION METHOD • Thistypesofcalculationinvolvesthemixingoftwo similar preparations, butof different strengths, to produceapreparationofintermediatestrength. • ThenameisderivedfromtheLatinalligatio, meaning the act of attaching and hence refers to the linesdrawnduringcalculationtobindquantities together.

  16. CALCULATIONBYALLEGATIONMETHOD • Therearetwoalligationmethods: • 1.AlligationMedial: • Involvescalculatingtheweightaveragepercentage strenght of a mixture of two or more substances of known quantityandconc. • Inotherwords,thismethodscalculatestheamountof activeingredientsineachsubstanceinthecompoundand then calculates the active ingredients per cent present in wholecompound. • Thequantitiesareexpressedinacommondenomiationof eitherweightorvolume

  17. CALCULATIONBYALLEGATIONMETHOD • Therearetwoalligationmethods: • 2.AlligationAlternate: • Thisrapidmethodinvolvesdeterminingthe proportions in which substances of different strengths aremixedtoyieldadesiredstrengthorconcentration. • Oncetheproportionisknown,theexactamountsof substancesrequiredcanbecalculated.

  18. CALCULATIONBYALLEGATIONMETHOD Therearetwoalligationmethods: 2.AlligationAlternate: Thestepsinvolved: Therequiredpercentageorconcentrationisplacedinthecentre Thepercentageofthesubstancewiththelowerstrengthisplaced onthelowerlefthandside Thepercentageofthesubstancewiththehigherstrengthisplaced ontheupperlefthandside Therequiredpercentageissubtractedfromthelowerpercentage, andtheobtaineddifferenceisplacedontheupperrighthandside Thehigherpercentageissubtractedfromthedesiredpercentage, andtheobtaineddifferenceisplacedonthelowerrighthandside

  19. CALCULATIONBYALLEGATION METHOD Required percentage–lower concentration Higher concentration Required percentage Lower concentration Higherconcentration- Requiredpercentage

  20. CALCULATIONBYALLEGATION METHOD Problem1:Calculatethevolumeof95%alcoholrequiredtoprepare600ml of70%alcohol 70-0= Given: 95 70 • Volumerequired=600ml • Percentageofalcoholrequired70% • Percentageofalcoholtobeused=95% 70 95-70= 25 0 Ans:70partsof95%alcoholand 25partsofwaterwillproduce70% Qty of 95%alcohol required =600*70 / 95=442.10 ml Qtyofwaterrequired=600*25/95=157.90ml

  21. CALCULATIONBYALLEGATION METHOD Problem2:Calculatetheamountof70%,60%,40%and30%alcoholthat shouldbemixedtoget50%alcohol Solution:When20partsof70%alcohol, 10partsof60%alcohol, 10partsof40%alcohol 20partsof30%alcoholaremixedtogether Theresultingsolutionwillproduce50%alc. 50-30= 20 50-40= 10 60-50= 10 70-50= 20 70 60 50 40 30 =(20X70)+(10X60)+(10X40)+(20X30) =1400+600+400+600=3000

  22. PROOFSPIRIT • Forexcise(tax)purpose, thestrengthofalcoholinindicatedbydegrees proof.ThatisAlcoholstrengthiscalculatedintermsofproofspirit • TheUSSystem:Proofspiritis50%alcoholbyvolume(or42.49%by weight). • TheBritish/Indiansystem: Proofspiritis57.1%ethanolbyvolume(or 48.24%byweight). • Definition:Proofspiritisthatmixtureofalcoholandwater,whichat51ºF weighs12/13thofanequalvolumeofwater. • [N.B.Densityofproofspirit=12/13ofdensityofwaterat51ºF=0.923 g/ml] • Thestrengthvalueaboveproof strengthisexpressedasOVERPROOF (O/P) • ThestrengthvalueaboveproofstrengthisexpressedasUNDERPROOF (U/P)

  23. PROOFSPIRIT

  24. PROOFSPIRIT Problem1:Convert90%v/valcoholintoproofspirit Solution:As57.1%alcoholcorrespondsto100volumesofproofspirit, 1volumeof57.1%v/valcohol=100/57.1=1.753volumesofproofspirit 90volumesofethylalcohol=90X1.753=157.77volumesofproofspirit i.e. 100L(orml)of90%alcoholareequal to157.77L(or ml)ofproof spirit Theproofstrengthof90%^alcohol=157.77–100=57.77

  25. ISOTONICSOLUTION • Osmosis: If a solution is placed in contact with a semipermeable membranethemovementofthesolventmoleculesthroughthe • membraneiscalledosmosis. • Anideal semipermeablemembraneonlylets the solvent moleculesto passthroughitbutnotthesolutemolecules. • Thebiologicalmembranesarenotidealsemipermeablemembranes. • Theyareselectivelypermeable;theygivepassagetosomesolutes while stopthepassageofothers.Incaseofbiologicalmembranes anotherterm tonicityisused. • Isotonicity: Asolution is isotonic withaliving cell if there is nonetgain orlossofwaterbythecell,whenitisincontactwiththissolution

  26. ISOTONICSOLUTION • If aliving cell is keptin contactwithasolutionandthereis nolossor gainof waterbythecell thenthe solutionis said to beisotonic with thecell. • It is foundthat the osmoticpressureof 0.9%w/vNaClsolutionis same asbloodplasma.So0.9%w/vNaClsolutionisisotonicwithplasma. • Tonicity: • Isotonic:Whenasolutionhassameosmoticpressureasthatof 0.9%w/vNaClsolution. • Paratonic:Notisotonic • Hypotonic:Theosmoticpressureofthesolutionishigherthan 0.9%w/vNaClsolution • Hypertonic:Theosmoticpressureofthesolutionislowerthan 0.9%w/vNaClsolution

  27. ISOTONICSOLUTION • Aredbloodcorpuscleis placedinasolutionandaftersometimeit is viewedundermicroscope.

  28. IMPORTANCEOFADJUSTMENTOFTONICITYIN PHARMACEUTICALDOSAGEFORMS • Solutionforintravenousinjection:Theinjectionmustbe isotonic with plasma, otherwise the red blood corpuscle maybe haemolysed. • Solution for subcutaneous injection: Isotonicity is required but not essential, because the solution is coming in contact with fatty tissueandnotincontactwithblood. • Solutionforintramuscularinjection:Theaqueoussolution maybeslightlyhypertonic.Thiswilldrawwaterfromthe adjoiningtissueandincreasetheabsorptionofthedrug. • Solution for intracutaneous injection: Diagnostic preparations mustbeisotonic,becauseaparatonicsolutionmaycausea falsereaction.

  29. IMPORTANCEOFADJUSTMENTOFTONICITYIN PHARMACEUTICALDOSAGEFORMS • Solutionsfor intrathecal injection:Intrathecal injectionsare introduced in the cavities of brain and spinal chord. It mixes with the cerebrospinal fluid (CSF). Thevolume of CSFis only 60to 80ml. • Solutionsfornasaldrops:Aqueoussolutionsappliedwithin the nostril may produce irritation if it is paratonic. So nasal drops mustbeisotonicwithplasma. • Solutionsforophthalmicuse:Onlyoneortwodropsof ophthalmic solutions are generally used. So it is not essential for eyedropstobeisotonic.Slightparatonicitywillnotproducegreat irritation because the eyedrops will be diluted with the lachrymal fluid

  30. TONICITYADJUSTMENT • Tonicityofisotonicsolutionsisadjustedbyemploying osmoticpressureasthesesolutionsareusuallyiso-osmotic • Pharmacistdoesnotusuallyreceivedaprescriptionfor paratonicsolution • Tonicitycanbeadjustedbyintroducinganinertmaterial into thesolution, providedthis materialis compatiblewith thedrug • Themethodsbywhichisotonicitycanbecalculatedare: • Freezingpointmethod • MolecularWeightmethod

  31. TONICITYADJUSTMENT • 1.Freezingpointmethod • Inlacrymalfluid,anumberofsoluteswhichfreezeat • -0.52ºCarepresent,henceallthesolutionswith freezingpoint of -0.52ºCwillbeisotonicwith lachrymalfluid • Similarly,humanbloodplasmaalsoexhibitsthe same freezing point, thus, the solutions freezing at - 0.52ºCwillbeisotonicwith it

  32. TONICITYADJUSTMENT • 1.Freezingpointmethod • Tonicity adjustment can be eased if the freezing point of the drug and the inert salt is known for various strenght of their solutions. • Tablesprovidingthisinformationaremaintainedbythe pharmacists and the same information can also be obtained fromthestandardtexts. • Freezingpointsin this caseareexpressedin termsof1% solutions and the quantity can be determined by multiplying thefreezingpointswiththefactor.

  33. TONICITYADJUSTMENT 1.Freezingpointmethod ………..Eq(1)

  34. TONICITYADJUSTMENT 1.Freezingpointmethod Example:200mlofaneyewashcontaining1%ofboricacidistobe dispensed.(F.P.of1%boricacid=-0.29ºCandF.P.of1%solutionofNaCl= -0.58ºC) Onapplyingtheequation01: -0.52=-0.29+(-X) X=0.52-0.29=0.23i.e.NaClsufficienttoproduceafreezingpointlowering of0.23ºCisrequired Itisgiventhat1%NaCllowersthefreezingpointby0.58ºC,thus,NaCL requiredtoproduceloweringof0.23ºCwillbe: 1X0.23/0.58=0.39g/100mlor0.39% Thus,theworkingformulafor200mloftheeyewashwillbe:

  35. TONICITYADJUSTMENT Contd… BoricAcid(1%,for200ml)=1X2=2gm SodiumChloride(0.39%for200ml)=0.39X2=0.78g Purifiedwatersufficienttoproduce200ml However,ifpharamcisthasbeenaskedtodispense200mlofeyewashof boricacid,thecalculationwillbefollows: Loweringof0.29ºCinF.P.isproducedby1gmofboricacid Therefore,loweringof0.52ºCinF.P.isproducedby1X0.52/0.29=1.8kg Hence,1.8gof boricacidisrequiredformaking100mlofaneyewashand workingformulawillbe: BoricAcid(1.8%for200ml)=1.8*2=3.6g Purifiedwatersufficienttoproduce200ml

  36. TONICITYADJUSTMENT • 2.MolecularWeightMethod • Asolution'sfreezingpointinverselydependsonthe concentration ofthe solutesdissolvedinit. Thus,greater soluteconcentrationlowers thefreezingpointofthe solution. • Thisindicatesthatfreezingpointisafunctionofthe concentrationofgrammoesofthesolute. • Itcanalsobesaidthatfreezingpointdependsontheno.od ions,thedrugweightanditsmolecularweight. • :

  37. TONICITYADJUSTMENT • 2.MolecularWeightMethod • Fora0.9%solutionofsodiumchloridetheconcentration canbeexpressedas: {No.ofgramsofNaCLXNo.of effectiveions} Isotonicfactoror Isotonicity = MolecularWeightofNaCl • Inotherwords:gXn/m=IsotonicFactorOR 0.9X2/58.5=0.03(IsotonicfactorforNaCl)

  38. TONICITYADJUSTMENT • 2.MolecularWeightMethod • Isotonicityof0.9%NaCl(normalsaline)issimilartothoseof body fluids. Thus, 0.03 will be the isotonicity or tonicity factor for tearsecretionandbloodserum. • Thequantitiesformakingeyesolutioncancalculatedby equatingthe 0.03 value with the tonicity factor of the drugand additive(S) • Theequztionforcalculatingtheadditivequantity: gxng1xn1g2xn2 = = m m1 m2 0.03 =

  39. TONICITYADJUSTMENT • 2.MolecularWeightMethod • Where,g=Weightingram • n=Effectiveionconcentration • m=molecularweightofthemedicament

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