Determination of the Partial Molar Volume of Methanol in a Methanol (1)/ Water (2) System Abagon, Ma. Vitoria Vitoria 1, !uen"ia, #eil Daniel 2, $araas, $orine %as&er ' De&artment of $hemial ngineering, $ollege of ngineering ni*ersity of the Phili&&ines + Diliman ue-on $ity, Phili&&ines 1 *iy.abagongmail.om *iy.abagongmail.om 0 2n"nbuen"iagmail.om 0 'orinearaasgmail.om
Abstract — To determine the partial molar volume properties of methan methanol ol in a methano methanoll (1) – water water (2) system, system, soluti solutions ons of different concentrations of methanol were prepared and weighed. The masses obtained were used to calculate for the actual mole fract fractio ions ns of meth methan anol ol and and wate waterr. ecor ecorde ded d weig weight htss and and recalculated recalculated mole fractions fractions were used to calculate calculate for partial partial molar volume values. The obtained infinite dilution values for methanol and water at 2! " are #$.%& m'mol and 1&.2 m'mol and deviated by 2.2&&* and 1.111* respectively.
he first first t:o relati relations ons are no:n no:n as the summab summabili ility ty relations an" the thir" is the
dM d x1 ´ = M − x dM M 2 1 d x1 ´ = M + x M 1 2
Keywords-partial molar volume, methanol, water, infinite dilution
.
#34D$4#
Part Partia iall mola molarr 5uan 5uanti titi ties es rela relate te han hange gess in e6te e6tens nsi* i*ee &ro&erties of the solution to hanges in onentration. onentration. 718 S&eifially, the &artial &ro&erty re&resents the hange in the total &ro&erty nM of a mi6ture ause" by the a""ition of an infinitesimal amount of s&eies i to a "efinite amount of solution at onstant tem&erature an" &ressure. he &artial molar ´ is gi*en by9 &ro&erty M i
[
´ = M i :here
∂ ( nM ) ∂ ni
]
(1)
P, P, T , n j≠ i
M is any thermo"ynami &ro&erty.
he molar &ro&erty of a substane in a &ure state at the same tem&erature an" &ressure as the mi6ture is "ifferent from the &arti &artial al molar molar &ro&er &ro&erty ty of the same same substa substane ne.. 728 he he "ifferene omes from the fat that the moleules in a &ure state only interat :ith its o:n s&eies :hile moleules in a solution ten" to interat :ith other s&eies :hih may lea" to "ifferent interation &otentials. 7'8 he &artial molar &ro&erty of a substane an be obtaine" from the molar &ro&erty of the solution an" *ie+*ersa. hese relations may be "eri*e" from (1) an" are gi*en as9
´ M =∑ x i M i i
´ nM =∑ ni M i i
´ =0 ∑ x d M i
i
i
(2) (') (;)
(>) (?)
he &artial molar *alue of &ure om&onent 1 at a solution om&ose" of &ure om&onent 2 is the infinite "ilution *alue, ´ ∞i . his is a &ro&erty of the om&onent at the mi6ture M shoul" shoul" an infini infinites tesima imall amoun amountt of the sai" sai" om&o om&onen nentt be &resent in the solution. 6&erimentally, the &artial molar *olume t:o s&eies in a binary solution may be obtaine" through the use of a &ynometer. &ynometer. :o :o s&eies are mi6e" at "ifferent onentrations. onentrations. he molar *olumes are then obtaine" an" from these "ata, the &artial molar molar *olume of methanol methanol an" :ater :ater an be alulate". alulate". n this e6&eriment, the &artial molar *olumes of :ater an" ethanol in a binary solution are "etermine" an" are om&are" :ith a*ailable literature *alues. .
MA3A@S A#D M4DS
A. Preparation he bulb of an alohol thermometer :as :ra&&e" :ith a small &iee of otton seure" using a rubber ban". he otton :i :as "am&ene" :ith :ater an" then the thermometer :as s:un s:ung g in a ir irul ular ar moti motion on for for abou aboutt 2B seo seon" n"s. s. he he tem&erat tem&erature ure rea"ing rea"ing :as reor"e", reor"e", an" the &roe"ure &roe"ure :as on"ute" for three times. 3oom tem&erature an" &ressure :ere reor"e" &rior to &reå si6 methanol+:ater mi6tures. o meet the re5uire" mole fration methanol methanol x as in"iate" in 7>8, the amount of methan methanol ol in m@ V :as "etermine" using the *alue gi*en by a mo"ifie" *ersion of the e5uation belo:, roun"e" off off to the the near neares estt tent tenth. h. 3es&e 3es&et ti* i*ee mole mole fra fratio tions ns an" an"
amounts are &resente" in able 2. $om&onent &ro&erties are sho:n in able 1.
x =
V ρC H OH M W C H OH 3
V ρC H
3
m H O 2
(F)
ρ H O 2
3
M W C H OH +( 50 −V ) ρ H O M
OH 3
V pyc =
(C)
A!@ 1. V4@M 4= MA#4@ P3 MG3
2
+ethanol
he flas use" to &re&are the mi6tures :ere :eighe" three times9 (1) before the mi6ture :as a""e" (i.e. em&ty flas) (2) :hen the re5uire" amount of methanol is transferre" to the flas, an" (') :hen the re5uire" amount of :ater :as a""e" to om&lete the mi6ture. he mole fration of methanol in eah mi6ture :as realulate" to "etermine the atual amount of methanol &resent in the &re&are" mi6ture.
, g/m@ , g/mol
3 S@S A#D DS$SS4#
o illustrate the &artial molar *olume &ro&erty of the methanol (1) / :ater (2) mi6ture, a &lot of the &artial molar ´ , V ´ *olumes V an" total *olume V as funtions of 1 2 methanol mole fration x 1 is generate" through a series of alulations "isusse" belo:. A.
he res&eti*e masses of methanol &er mi6ture :ere taen from the "ifferene of the thir" an" seon" olumns of able '. @ie:ise, the masses of :ater :ere taen from the "ifferene of the fourth an" thir" olumns. sing the moleular :eights of eah om&onent, the number of moles of methanol an" :ater :ere "etermine" res&eti*ely. =rom these *alues, the mole frations sho:n in able ; :ere "eri*e". V o obtain the molar *olume (m@/mol) of eah mi6ture, the res&eti*e moleular :eights an" "ensities :ere obtaine".
ρ=
(
32.04
mol
g
)
the *olume of the &ynometer (F),
+ ( 1− x 2 )
( ) 18 g
mol
1E
olume, m' B 1E.B 'B.B 'E.? ;> >B
ρ :as gi*en by (1B).
mass of the mixt!e , g V pyc , m"
(1B)
he ratio of the moleular :eight an" the "ensity ga*e the total molar *olume of eah mi6ture. Values obtaine" :ere &lotte" against methanol mole frations, an" the best+fit seon"+"egree &olynomial "etermine" through Mirosoft 6el is sho:n belo:. 2
V = 4.3318 x 1 + 18.5305 x 1 + 18.3964
(11)
he "eri*ati*e of (11) :ith res&et to x 1 is taen, an" the &artial molar *olumes oul" then be alulate" using (>) an" (?). =igure 1 sho:s the &lot of the total molar *olume an" &artial molar *olumes against the mole fration of methanol in eah mi6ture, obtaine" using the "ata reor"e" un"er realulation. he molar *olumes of the mi6tures in the thir" &art of the e6&eriment :ere "etermine" similarly, ho:e*er inor&orating the mole frations &re*iously alulate". he &lot of the *alues obtaine" are sho:n in =ig. 2. A!@ '. M4@ =3A$4# 3 $A@$@A4# DAA
Moleular :eights :ere "etermine" using (E),
MW = x 1
'2.B;
an" the "ensity of eah mi6ture
Calculating the Molar Volume
Data sho:n in able ' :ere use" to obtain *alues neessary to generate the theoretial &artial molar *olume *ersus methanol mole fration &lot.
1
+ole -raction, +ethanol B B.2 B.; B.? B.E 1
A ta& :ater bath :as &re&are" an" the tem&erature of bath an" the room :as taen. he &re&are" mi6tures :ere &lae" in the :ater bath for aroun" ten minutes so that the sam&les oul" be :eighe" at the same tem&erature.
.
B.CF2
A!@ 2. V4@M 4= MA#4@ P3 MG3
B. Experiment Proper
he &ynometer :as fille" :ith a mi6ture from the flas an" then &lae" to the :ater bath for aroun" ten minutes before :eighing. hree trials :ere &re&are" for eah mi6ture an" the orres&on"ing :eights :ere reor"e" aor"ingly.
at
(E)
V pyc :as obtaine" using
+i/ture
+ass of 0mpty olumetric -las
+ass of olumetric -las with +ethanol
A ! $ D =
'>.>CEF '>.>;?1 'E.B12F '>.E;2> '>.2'EF '>.?FC'
'>.>CEF ;>.>;;> ?'.>FEB ?>.CF>1 CB.2'BB C;.>?>'
+ass of olumetric -las with +ethanol ater E;.C'B1 E2.>E1; E2.?'2F CE.>?C' C>.FCEE C;.>?>'
the methanol+:ater solution, as obser*e" from the realulate" mole frations of methanol in eah mi6ture alone. A!@ ;. M4@ =3A$4#S +i/ture
mol fraction, +et34 B B.1'1?EF;;2 B.;'B2'E?F> B.>?E;FF>1C B.CC'C2F1?C 1
A ! $ D =
mol fraction, ater
1 B.E?E'1B>>E B.>?FC?1'B> B.;'1>BB;E' B.22?2CBE'' B
Partial Volume Pro&erties of methan ol (1) / :ater (2) sys tem >B ;B
f(6) H ;.''6I2 J 1E.>'6 J 1E.; 3K H 1
'B
Molar Volume, m@/mo l
2B 1B B B .1 B .2 B .' B .; B .> B .? B .C B .E B .F 1 mol fration, methanol
Mola r Volume Polynomial (Molar Volume) Vbar1 Vbar2 =igure 1. Molar *olumes obtaine" from realulation "ata &lotte" against mole fration of Methanol
Partial Volume Pro&erties o f meth anol (1) / :ater (2) sys tem >B ;B Molar Volume, m@/mo l
'B
f(6) H ?.B>6I2 J 1>.1E6 J 1E.CF 3K H 1
2B 1B B B .1 B . 2 B .' B . ; B .> B . ? B .C B . E B .F 1 mol fration, methanol
Molar Volume Polynomial (Molar Volume)
As the mole fration of methanol in the solution inreases, the &artial molar *olume of methanol in the mi6ture also inreases an" the &artial molar *olume of :ater in the mi6ture "ereases, :hih oul" be notie" in both gra&hs. his illustrates that the total *olume of the mi6ture is also "e&en"ent to the onentration of its om&onents. he e6&erimental *alues obtaine" from the thir" &art of the e6&eriment :ere om&are" to the molar *olumes obtaine" using realulation "ata. A*erage "e*iations bet:een these *alues are &resente" in able >. At x 1=0 , or at the &ure :ater solution, a *alue for the &artial molar *olume of methanol :as obtaine". @ie:ise, at x 1=1 , or at the &ure :ater solution, a &artial molar *olume *alue :as obtaine" for :ater. hese are the &artial molar *olume *alues of the res&eti*e om&onents at infinite "ilution
´i V
∞
, :hih in"iates the limiting *alues of the
&artial &ro&erties that may be e6hibite" by the om&onents in that &artiular mi6ture. nfinite "ilution *alues obtaine" from realulation "ata :ere om&are" to literature "ata of the &artial molar *olume at infinite "ilution of the methanol+:ater system at 2C L$. 3es&eti*e *alues an" the "e*iation of these *alues are sho:n in able ?. o:e*er, all the &artial &ro&erty *alues obtaine" are uni5ue for the system un"er obser*ation in this e6&eriment. Methanol an" :ater may beha*e "ifferently shoul" they be mi6e" :ith other om&oun"s in other solutions. he "ifferene bet:een the alulate" &ro&erties oul" be attribute" to the inonsistent rea"ing gi*en by the analytial balane. Also, the effets of minute mistaes in solution &re&aration, suh as material loss from the transfer of flui"s from the *olumetri flas to the &ynometer, :ere not taen into aount an" may ha*e ause" the "ifferenes of the molar *olumes alulate". Differential hanges in tem&erature throughout the "uration of the e6&eriment oul" also ha*e affete" the "ensity of the mi6tures.
Vbar1 Vbar2
A!@ >. AV3A< DVA4#S !W# GP3M#A@ DAA 5roperty
=igure 2. Molar *olumes obtaine" fr om e6&erimental "ata &lotte" against mole frations of Methanol
V
B. Analysis of Data he "ata obtaine" sho:s that methanol an" :ater moleules interat :ith eah other in the solution, e6&resse" as &artial &ro&erties. herefore, the in"i*i"ual *olumes of methanol an" :ater "o not neessarily a"" u& to the *olume of
6verage * 7eviation 1.C
´ V 1
;.F
´2 V
1.C
A!@ ?. #=# D@4# VA@S 728 5roperty
-rom ecalculation 7ata
-rom 'iterature 7ata 8/9
* 7eviation
´ V 1
∞
'?.E; m@/mol
'C.?EC m@/mol
2.2;;
´ V 2
1;.B2 m@/mol
1;.1EB m@/mol
1.111
∞
3 =3#$S V.
$4#$@S4# A#D 3 $4MM#DA4#S
=rom the obtaine" masses of methanol+:ater mi6tures of "ifferent onentrations, the &artial molar *olume of methanol in the solution :as obtaine". Also, as sho:n in the reor"e" *alues an" alulations, the molar *olumes of methanol an" :ater are not a""iti*e. hus, &artial molar &ro&erties of a om&onent in a solution oul" also be "e&en"ent on the other om&oun"s foun" in the system. he infinite "ilution *alues for methanol obtaine" from the e6&eriment "e*iate" 2.2;; from literature *alue. he *alue obtaine" for :ater "iffere" by 1.111 t is reommen"e" the &re&are" solutions are enough for three trials. Partial molar *olumes of other om&oun"s oul" be "etermine" through the same &roess in"iate" in this e6&eriment, so ombinations of other om&oun"s oul" be use" for further stu"ies.
718 $hen, =. (n.".). Bartender's Conundrum: Partial Molar Volume in ater! Ethanol Mixtures. 3etrie*e" Marh 2>, 2B1?, from htt&9//:::2.stetson.e"u/N:grubbs/"ata"ri*en/fhen/barten"er/&artialmol ar*olumehen.html 728 !ombay. (2B1', %anuary 1E). Chemical Engineering "hermodynamics #e$%. 3etrie*e" Marh 2>, 2B1?, from #P@ Website9 htt&9//n&tel.a.in/ourses/1B'1B1BB;/'E 7'8 DeVoe, . (n.".). &. Partial Molar (uantities. 3etrie*e" Marh 2>, 2B1?, from $DAVS $MWii9 htt&9//hem:ii.u"a*is.e"u/e6tbooOMa&s/PhysialO$hemistryOe6tbo oOMa&s/DeVoesO22hermo"ynamisOan"O$hemistry 22/BF'AOMi6tures/F.2OPartialOMolarOuantities 7;8 Smith, %., Van #ess, ., Q Abbott, M. (2BB>). )ntroduction to Chemical Engineering "hermodynamics (Cth e".). #e: Ror9 M8 $h 12; $hemial ngineering hermo"ynamis @aboratory Manual,T ue-on $ity, 2B1', &&. ;2+;>.
