Asimpledilutionisoneinwhichaunitvolumeofaliquidmaterialofinterestiscombinedwithanappropriatevolumeofasolventliquidtoachievethedesiredconcentration.Thedilutionfactoristhetotalnumberofunitvolumesinwhichyourmaterialwillbedissolved.Thedilutedmaterialmustthenbethoroughlymixedtoachievethetruedilution.Forexample,a1:5dilution(verbalizeas"1to5"dilution)entailscombining1unitvolumeofdiluent(thematerialtobediluted)+4unitvolumesofthesolventmedium(hence,1+4=5=dilutionfactor).

Example:Frozenorangejuiceconcentrateisusuallydilutedin4additionalcansofcoldwater(thedilutionsolvent)givingadilutionfactorof5,i.e.,theorangeconcentraterepresentsoneunitvolumetowhichyouhaveadded4morecans(sameunitvolumes)ofwater.Sotheorangeconcentrateisnowdistributedthrough5unitvolumes.Thiswouldbecalleda1:5dilution,andtheOJisnow1/5asconcentratedasitwasoriginally.So,inasimpledilution,addonelessunitvolumeofsolventthanthedesireddilutionfactorvalue.

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2.SerialDilution

Aserialdilutionissimplyaseriesofsimpledilutionswhichamplifiesthedilutionfactorquicklybeginningwithasmallinitialquantityofmaterial(i.e.,bacterialculture,achemical,orangejuice,etc.).Thesourceofdilutionmaterialforeachstepcomesfromthedilutedmaterialoftheprevious.Inaserialdilutionthetotaldilutionfactoratanypointistheproductoftheindividualdilutionfactorsineachstepuptoit.

Finaldilutionfactor(DF)=DF1*DF2*DF3etc.

Example:InthemicroBIOLOGylabinBio201thestudentsperformathreestep1:100serialdilutionofabacterialculture(seefigurebelow).Theinitialstepcombines1unitvolumeculture(10ul)with99unitvolumesofbroth(990ul)=1:100dilution.Inthenextstep,oneunitvolumeofthe1:100dilutioniscombinedwith99unitvolumesofbrothnowyieldingatotaldilutionof1:100x100=1:10,000dilution.Repeatedagain(thethirdstep)thetotaldilutionwouldbe1:100x10,000=1:1,000,000totaldilution.Theconcentrationofbacteriaisnowonemilliontimeslessthanintheoriginalsample.

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3.Makingfixedvolumesofspecificconcentrationsfromliquidreagents:

V1C1=V2C2Method

Veryoftenyou’llneedtomakeaspecificvolumeofknownconcentrationduetolimitedavailABIlityofliquidmaterials(somechemicalsareveryexpensiveandareonlysoldandusedinsmallquantities,e.g.,micrograms)ortolimittheamountofwaste.Theformulabelowisaquickapproachtocalculatingsuchdilutionswhere:

V=volume,C=concentration;inwhateverunitsyouareworking.

(sourcesolutionattributes)V1C1=V2C2(newsolutionattributes)

Example1:Supposeyouhave3mlofastocksolutionof100mg/mlampicillin(=C1)andyouwanttomake200ul(=C2)ofsolutionhaving25mg/ml(=V2).Youneedtoknowwhatvolume(V1)ofthestocktouseaspartofthe200ultotalvolumeneeded.

V1=thevolumeofstockyou’llstartwith.Thisisyourunknown.C1=100mg/mlinthestocksolutionV2=totalvolumeneededatthenewconcentration=200ul=0.2mlC2=thenewconcentration=25mg/ml

Byalgebraicrearrangement:

V1=(V2xC2)/C1

V1=(0.2mlx25mg/ml)/100mg/ml

andcanceltheunits,

=0.05ml

=50ul

So,youwouldtake0.05ml=50ulofstocksolutionanddiluteitwith150ulofsolventtogetthe200ulof25mg/mlsolutionneeded(rememberthattheamountofsolventusedisbaseduponthefinalvolumeneeded,soyouhavetosubtractthestartingvolumeformthefinaltocalculateit.)

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4.Molarsolutions(unit=M=moles/L)

Sometimesitmaybemoreefficienttousemolaritywhencalculatingconcentrations.A1.0Molar(1.0M)solutionisequivalentto1formulaweight(FW)(g/mole)ofchemicaldissolvedin1liter(1.0L)ofsolvent(usuallywater).Formulaweightisalwaysgivenonthelabelofachemicalbottle(usemolecularweightifitisnotgiven).

Example1:Topreparealiterofasimplemolarsolutionfromadryreagent:

Multiplytheformulaweight(orMW)bythedesiredmolaritytodeterminehowmanygramsofreagenttouse:

ChemicalFW=194.3g/mole;tomake0.15Msolutionuse

194.3g/mole*0.15moles/L=29.145g/L

Example2:Toprepareaspecificvolumeofaspecificmolarsolutionfromadryreagent:

AchemicalhasaFWof180g/moleandyouneed25ml(0.025L)of0.15M(M=moles/L)solution.Howmanygramsofthechemicalmustbedissolvedin25mlwatertomakethissolution?

#grams/desiredvolume(L)=desiredmolarity(mole/L)*FW(g/mole)

byalgrebraicrearrangement,

#grams=desiredvolume(L)*desiredmolarity(mole/L)*FW(g/mole)

#grams=0.025L*0.15mole/L*180g/mole

aftercancellingtheunits,

#grams=0.675g

So,youneed0.675g/25ml

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5.PercentSolutions(=partsperhundred)

Manyreagentsaremixedaspercentconcentrations.Whenworkingwithadrychemicalitismixedasdrymass(g)pervolumewhere#g/100ml=percentconcentration.A10%solutionisequalto10gdissolvedin100mlofsolvent.

Example1:Ifyouwanttomake3%NaClyouwoulddissolve3.0gNaClin100mlwater(ortheequivalentforwhatevervolumeyouneeded).

Whenusingliquidreagentsthepercentconcentrationisbaseduponvolumepervolume,i.e.,#ml/100ml.

Example2:Ifyouwanttomake70%ethanolyouwouldmix70mlof100%ethanolwith30mlwater(ortheequivalentforwhatevervolumeyouneeded).

Toconvertfrom%solutiontomolarity,multiplythepercentsolutionvalueby10togetgrams/L,thendividebytheformulaweight.

Molarity=(%solution)*10xxxxxxxxxxFW

Example3:Converta6.5%solutionofachemicalwithFW=325.6tomolarity,

[(6.5g/100ml)*10]/325.6g/L=0.1996M

Toconvertfrommolaritytopercentsolution,multiplythemolaritybytheFWanddivideby10:

%solution=molarity*FWxxxxxxxxxx10

Example4:Converta0.0045MsolutionofachemicalhavingFW178.7topercentsolution:

[0.0045moles/L*178.7g/mole]/10=0.08%solution

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