Determination of the heat of formation of co, and co (Hess's law)

Relatecl conceptsFirst law of thermodynamics, thermochemistry calorlmetry,enthalpy of formation, enthalpy of reaction, Hess,s law.

PrincipleThe standard molar enthatpies of formation A'II are importantcompiled thermodynamic tabulation quantities for calculatingstandard enthalpies of reactjon for any arbilrary reaction. Theyare defined as the heat of reaction occurring in the direct forma-tion of one mole of the pertinent pure substance from the stablepure elements at constant oressure.For spontaneous and quantitative formation reactions, e.g. theconversion of carbon and oxygen to COr, standard enthalpies offormation can be measured directly using calorimetry.Alternatively, they can be calculated from known enthalpies ofreaction using Fless's law.

TasksDetermine the enthalpies of reaction for the combustion of1. carbon and2. carbon monoxidecalometrically.Use the experimentally determined enthalpies and Hess,s law tocalculate the enthalpies of formation of CO and CO.,.

H-base -PASS-Support rod, / = 250 mmBarrel base -PASS-Right angle clampUniversal clarnpMagnetic stirring ba / = 30 mmMagnet, d = 10 mm, / = 200 mmWeather monitor, 6 lines LCDLaboratory therrnometer -10... +SO.CMagnifying glass, 10 x, d = 23 mmFunnel, glass, d^ = 55 mmGraduated vess!,1 | , with handlePaper, ceramic fibre 1.0 x 500 x 2000 mmCommercial weight, 500 gStopcock, 3-way, T-shaped, glassTest tube Gl'.25/8, with hose connectorGlass tube, right-angledPinchcock, zo = 15 mmFunnel for gas generato[ S0 ml, GL18Flask, round, 1-neck, 100 ml, GL2S/12U-tube, 2 side tubes, GL2S/BTest tube,1B0 x 20 mm, PN19Rubber stopper, d = 22/17 mmRubber stopper, d = 38/31 mm, t hole 15 mmTest tube holder, d = 22 mmTeclu burner, natural gasSafety gas tubingHose clip, d = 12...20 mmLighter for natural / liquified gasesSteel cylinder oxygen, 2 l, filled

02615.0002615.0102613.0040461.0037694.00

02009.5502031.0002006.5537697.0037715.0046299.O20631 1.0087997.0138034.0064598.0034457.O036640.0038750.0144096.5036731.0036330.1 536701.5943631.1535854.'15s5841.1536959.1 536293.0039255.0039260.1 I38B23.0032171.0539281.1040995.0038874.0041778.00

1

1

71

1

1

z1

1

1

1

1

1

1

1

EquipmentGlass jacketCalorimeter insert for glass jacketCombustion lance for gasesGasomete 1000 mlRetod stand, = 750 mm

Fig. 1. Experimental set-up.

1

1

1

1

2

z1

1

PHYWE series of publications . Laboratory Experiments . Chemistry. @ PHWVE SYSTEN4E GMBH & Co. KG . D-37070 Gttingen P3021601

Determination of the heat of formation of CO, and GO (Hess's law)

Reducing valve for oxygenWrench for steel cylindersTble stand for 2 | steel cylindersHose clip, d = 8...12 mmPrecision balance, 620 gMortar with pestle,150 ml, porcelainScissors, straight, blunt, / = 140 mmTweezers, straight, blunt, / = 200 mmWater jet pumpRubber tubing, d, = 6 mmProtective glasses, green glassQuartz glass wool, 10 gCharcoal, small pieces, 300 gFormic acid 98-100%,250 mlSulphuric acid, 95-98%, 500 mlSodium hydroxide, flakes, 500 gGlycerol, 250 mlWater. distilled. 5 |

Set-up and procedureSet up the experiment as shown in Fig. 1.Fit the calorimeter insert into the glass jacket as described in theinstruction manual. Fill the graduated vessel with approximately500 g of water and determine the mass of it on the balance(= rzl). Carefully pour the water into the glass jacket through oneof the vertical tubular sleeves (using a funnel) and weigh the ves-sel again (= mz). Calculate the mass of the water (m(HrO) =m2- m)'Put a magnetic stirrer bar into the glass jacket. Prepare and con-nect the bubble counter as follows: Fill a little water into the testtube with hose connector, fit the right-angled tube on and con-nect it to the outlet of the calorimeter. Connect the hose con-nector to the water jet pump. Fill the gasometer with 300 to400 ml of some flammable gas (natural gas, hydrogen, propaneor a similar gas which is used to produce a very small pilot flame)and connect it to the combustion lance via a rubber tube. Alsoconnect the steel cylinder with oxygen to the combustion lanceand secure all hose connections with hose clios.

Fig. 2: Experimental setrup for preparing the carbon monoxide

1. Burning of carbonSince it is not possible to burn the pure forms of carbon, i.e.graphite and diamond, in a glass jacket calorimeter because ofthe high activation energy levels involved, very strongly heatedand completely degassed charcoal is to be prepared and used.The heat value of this charcoal is only negligibly different fromthat of graphite (32682 kJ/kg compared with 32738 kJ/kg). lt isprepared as follows: Use a mortar and pestle to slightly crush asolid piece of charcoal to give some pieces of between 0.4 and0.7 g in size. Place these pieces in a test tube and heat themstrongly with the Teclu burner until all humidity, all tar residuesand all residual gases have been driven off. Allow it to cool in aclosed vessel.Accurately weigh one of the pre-treated pieces of carbon andplace it in the combusiion chamber on a strip of ceramic paper.Note the initial temperature of the water as 2,. Turn on the waterjet pump and adjust it so that a moderate flow of air is drawnthrough the calorimeter (use the pinchcock on the tube betweenthe pump and the bubble counter for this). The cunent of airensures that all of the hot gas generated is drawn through thecalorimeter.Wear dark protective glasses during the subsequent combustionof carbon in a flow of oxygen to avoid being dazzled.Place a weight of approximately 500 g on the plunger of the gas-ometer to achieve a sufficient speed of the gas outflow. Openthe precision control valve of the combustion lance, ignite theoutflowing gas, and adjust the flame to a length of 1 to 2 cm.Supply oxygen, adjust the length to approximately 0.5 cm, andthen move the barrel base to quickly insert this pilot flame intothe glass jacket calorimeter so that the charcoal ignites. Closethe precision control valve on the gasometer.The charcoal burns in the flow of oxygen with an extremelybright flame to form carbon dioxide. Stir the water in thecalorimeter during combustion in order to achieve a maximumtransfer of the reaction heat to the liouid. When combustion iscomplete, shut off the air flow and the oxygen supply, but con-tinue mixing until thermal equilibrium has re-established. Recordthe temperature on the thermometers as Tr.

33482.00 140322.OO 141774.OO 140996.01 448852.93 132604.00 164625.00 140955.00 1o2728.0O 139282.00 539317.00 131773.O3 130088.30 130021.25 130219.50 130157.50 130084.25 131246.81 1

^,,^*- ^l^^^vud L grd-

Sodium hydroxide flakes

1

P302160.1

,

PHYWE series of publcatons . Laboratory Experiments . Chemistry . O PHYWE SYSTEI\,4E GMBH & Co. KG . D.37070 Gttingen

Determination of the heat of formation of co, and co (Hess's law)

2. Burning of carbon monoxideThe experimental set-up is analogous to that of the first experi-ment.The carbon monoxide (Caution: toxic!) is prepared by dehydrat-ing formic acid with concentrated sulphuric acid. To do this, pre-pare the set-up shown in Fig. 2 under an e)dractor hood. Dropformic acid from the graduated funnel into the round flask con-taining sulphuric acid. Clean and dry the carbon monoxide thatevolves with sodium hydroxide flakes held in a U-tube betweentwo balls of quartz glass. Fill the gasometer with 1000 ml of car-bon monoxide and again connect it to the combustion lance,which is furthermore connected to the oxygen cylinder.Determine the initial temperature of the calorimeter and adiustthe airflow. Subsequently, adjust a weak flow of carbon monox-ide and ignite the gas at the tip of the combustion lance. Set theflame length to approximately 2 cm and add oxygen in order toguarantee complete combustion. Wait until the sinking piston ofthe gasometer touches a certain mark on the scale (e.g. 900 ml)and then move the lance to a position deep inside the combus-tion chamber of the calorimeter by moving the barrel barrel base.Continuously but gently stir the water in the catorimeter, com-bust exactly 500 ml of carbon monoxide, then turn off the airflow and the oxygen supply. Wait until thermal equilibrium hasestablished and record the final temperature as To. In addition,also measure the room temperature ? and the-atmosphericpressure p.

Theory and evaluationMolar enthalpies of reaction ARH characterise the heat balanceof substance transformations.'They are defined as the heat ofreaction Qo = Lh occurring per mole formula conversion A{ atconstant piessure p and constant temperature Z.

For spontaneous and quantitative conversions, the molar en-thalpies of reaction can be determined directly usng calorimetry.Otherwise, they can also be calculated using Hess's law of con-stant heat summation (the additivity of reaction enthalpies). Themolar formation enthalpy ArH corresponds to the molar en-thalpy of reaction in the direct formation of 1 mole of the respec-tive comoound from the elements in stable modification (forwhich the enthalpy of formation is zero by definition). The for-mation enthalpies of most substances at p = 1913 hPa and T =298 K are listed in Tables. Therefore, the standard enthalpy ofreaction ArHo of any arbitrary reaction is equal to the stoichio-metric sum of the standard enthalpies of formation ArHa of thepafticipating educts and products, whereby the original sub-stances are entered with negative stoichiometric values 2,.

AR/@= )2, ArI/,oWith regard to the reactions

-+ CO, AnH.,--) COz LaHz

The following is obtained from equation (2):

The enthalpy of formation of CO, is hence directly equal to theenthalpy of reaction A*11, arising from the complete combustionof 1 mole of carbon. The enthalpy of formation of CO is calcu-lated adding reactions 1 and 2:

C * Oz -+ CO, ^RI1CO, -

-+ CO'+ 1/zO, -L^fi,

(1)o-": (#)",

C + 1/2O, --+ CO AR13 = ABH(CO)= AnHr - LaHz

Fig. 3: Application of the Hess Law to determine the molarenthalpy of formation of CO from the enthalpies of com-bustion of carbon and carbon monoxide

A'pH." = ARH([0?)-l

i LaHz , AnH = ABH(IU) itw ru-vry

II

The molar enthalpies A*-1, and L^Hrcan be calculated fromthe experimental data using equation (1). The change in enthalpyof the reacting system Aft corresponds to the negative heat bal-ance Q"", of the calorimeter which can be derived from equa-tion (3):

-Lh=O^^,=\m,c.LT= (m(HrO).c(HrO) + C"u,) LT (3)

wherem(HrO) Mass of water in the calorimeterc(HrO) Specific heat capacity of water (4.1BOB J . 9-t . 1-tCcat Mean heat capacity of the glass jacket calorimeter

used(410J.K-r)LT 7., - Tz(temperature difference in gAs a result of the expression

Ln'= Y 61 g)the amount of formula conversions Af is equal to the convertedmaterial Az, of carbon (reaction 1) or carbon monoxide(reaction 2) which can be calculated using

m (C\^,,

(c) : ,ic; (5)

wherem(C) Mass of carbon usedM(C) Molar mass of carbon (12.01 g . mol-l)It can also be derived from the general equation of state for idealgases (ideal gas law) if the room temperature Z, the atmospher-ic pressure p and the volume of carbon monoxide combusted Vare Known.

ar(co) =# (6)R Universal gas constant (8.31441 Nm . K-1 ' mol-1)

Q)

C+OzCO + 1/2C.2

and

AnHr = ABII(CO2)

LRH2 = ABI(CO2) - AB/(CO)

(2.1)

(2.2)

PHYWE series of oublications . Laboraiorv Exoeriments . Chemistrv. O PHYWE SYSTEME GN/BH & Co. KG . D-37070 Gttinqen P3021601

Data and resultsThe combustion of 0.4627 g of carbon t(n = S8.5S mmol) in-creased the temperature of the 500 g water in the filled glassjacket calorimeter by Af = 0.6 K.The oxidation of 500 ml CO at ? = 298.05 K and p = 986 hpa(n

= 19.89 mmol) caused a temperature increase oi tf = Z.Z X.The molar enthalpies of reaction calculated from these valuesare:

^RH1 =

^BH(CO2) = -389.9 kJ'mol-1,

LRH2 = -276.8 kJ'mol-l andaR13 = ABI1(CO) = -1 13.1 kJ.mol-l.Lit. values:

^B1(CO2) = -393.5 kJ . mol-1,

^811(CO) = -110.5 kJ.mol-1.

J_.

P3021 60 1

,

PHYWE series of publicatons . Laboratory Experiments . Chemistry. @ pHyWE SYSTEME GMBH & Co. KG . D-37070 Gttinoen

Dilatometry

Related conceptsState variables, linear thermal expansion, volume expansion,heat capacity, lattice potential, equilibrium separation, intermol-ecular interactlon.

PrincipleThe linear expansion of solid bodies and the volume expanstonof water are functions of temperature. In order to investigateexpansion, tubes made of brass, steel, copper, aluminium andglass are clamped tight at one end, and water from a tempera-ture controlled bath is circulated through them. The change inlength at various temperatures is measured using a dilatometer.The measurement of the volume change of water is achievedusing a flat-bottomed flask with an upright graduated tube,which is located in a temperature controlled bath (pycnometer).Tasks1. Measure the linear expansion of brass, steel, copper, aru-

minium and Duran glass at five different temperatures n arange between 20"C and 70.C using a dilatometer. Calculatethe linear expansion coefficients.

2. Determine the volume of a defined mass of water with a pyc-nometer at five different temperatures in a range between20'C and 70'C.

EquipmentDilatometer with clock gaugeBrass tubelron tubeGlass tubeCopper tubeAluminium tubeRetort stand, ft = 750 mmRight angle clampUniversal clampPrecision balance, 6209Syringe 1 mlCannula 0.6 x 60 mmGlass beaker, 100 ml, tallFlask, flat bottom, 100 ml, IGJ'I9/26Measuring tube, I = 300 mm, lGJ19/26lmmerson thermostat,'1 00"CAccessory set for immersion thermostatBath for thermostat, 6 l, MakrolonRubber tubing, d, = 6 mmHose clip, d = 8...12 mmWash bole, 500 mlWater, distilled, 5 |

04233.0004231.0204231.0s04231 .0404231 .05042s1.0637694.0037697.0037715.0048852.9302593.0302599.0436002.003581 1.0103024.0008492.9308492.01oe487.0239282.0040996.013393.1.0031246.81

1

1

1

1

1'1

A

o

1

1

Fig. 1. Experimental set-up.

$|$iq$i

PHYWE series of publications . Laboratory Experments . Chemstry . O PHWVE SYSTEME GMBH & Co. KG . D-37020 cttinqen p3021801

Dilatometry

li i'l:.t) ti :i, il | : :iji.: :: r: ;r:

\i:iliilii;l

1,: - -j: I

t{: ;

ffi; *:ffir m'

Set-up and procedureSet up the experiment as shown in Fig.1 and Fig. 2.Fig.2:

1, Measurenrent of linear expansionClamp the first tube over its whole length (600 mm) in thedilatometer and connect it to the circulating pump of the ther-mostat via rubber tubing. Keep the tubing as far as possibleaway from the dilatometer in order not to heat uo the frame ofthe dilatometer. For the same reason, avoid long periods of read-justment of the temperature controlled bath and set the temoer-ature only with the accuracy of the thermostatic control. After theinitial temperature (approximately 20'C) has been reached, setthe meter'to '0', and then raise the temperature in four steps,each of 10'C to 15'C. Record the respective changes in lengthand the corresponding temperatures.Repeat this measurement seres with each of the remaininq fourmaterials.

2. Measurement of change in volumeFirst calibrate the pycnometer. To do this, determine the emptymass of the flat-bottomed flask with graduated tube, then fill theflask with water and refit the graduated tube. Use a syringe witha cannula to fillthe graduated tube up to approximately the ,100'mark. Now warm the filled pycnometer to BO.C in the tempera-ture controlled bath to remove any dissolved gases. After this,subject it to temperature equilibriation at 25"C, and meticulous-ly remove all gas bubbles (Caution: knocking on the graduatedtube can easily cause it to break!). Now read off the fluid level inthe graduated tube, carefully dry its outer sudace, and againaccurately weigh the pycnometer. Use the injection syringe toadd 1 ml water to the upright graduated tube and temperatureequilibrate the new volume at the same temperature. Again readoff the level and weigh the apparatus. Repeat this process forvarious fill levels. From these values and the density of water(0.997 g/cm3 at 25'C) calculate the volume corresponding toone graduation. This value should be about 0.01 ml. With theempty mass of the pycnometer, the absolute vatue can bederived.After calibration, measure the water volume at five different tem-peratures between 20'C and 70.C.

Theory and evaluationAn increase in the temperature of a solid body intensifies oscil-lation of the atoms in the lattice. This causes the average dis-tance between the atoms to be increased, and with this, anincrease in the volume V at constant pressure p.

7 is the cubic coefficient of expansion. lf only one dimension isconsidered (e.9. length), one obtains the linear coefficient ofexoansion a.

wnere/ Total length of the bodyln a fluid, a temperature increase intensifies the thermal move-ment of the particles and hence increases the volume. (Anexception is the anomalous behaviour of water between 0'C and4'C).

vo.LT

Ll* lo-LT

Vo Initial volume prior to temperature changeIo Corresponding initial lengthTo evaluate the experiment, prepare plots of the changes in thelength of the tubes and the volume change of water versus thetemperature (Figs. 3 to 8). Calculate the coefficients of expan-sion from the slopes using equations (3) and (4). In the case ofmaterials with temperature-dependent coefficients of expan-sion, the plot does not give a straight line; the coefficient ofexpansion can only be calculated for temperature intervals orexpressed as approximate polynomials.

Data and resultsIn the cases of all of the five materials tested, the length is a lin-ear function of temperature in the temperature range selected,

Linear coefficient of expansion:

'(depends upon type)

The cubic coefficient of expansion of water is temperaturedependent (Fig. B). ln the temperature range between 20'C and30"C, it is calculated to be 2.75 . 10-4 K-1. For the temoeraturerange considered in this experiment, it can be formulated asV = Vo + 14.36 - 0.114 T. + 2.215 Tr.

1 /6y\v:-.1-l' v \67/p (1)

(2)1 /6/\a:7'\ar/,

(3)

(4)

LV

P3021 801

Experiment ReferenceBrass 1.847.10-5 K-1 1.8 . 10-5 K-lCopper 1.603.10-5 K-1 1.5.10-5 K-1Aluminium 2.212 . 10'5 K-l 2.3 . 10-5 K-1Steel 1.170.10-5 K-1 1.2'10-5 K-1Duran glass 2.933 . 10-5 K-1 .3.6 ' 10-5 K-1

PHYWE series of publications . Laboratory Experiments . Chemistry o @ pHWVE SYSTEME G|\4BH & Co. KG . D-37070 Gttinqen

A/r"""mm

Fig: 3: Length change (A/) of the brass pipe as function of tem-peralure

^ 0.7

't'I| 0.6

0.5

0.1

0.1

0.2

0.1

0.0

-0.1

290 100 110

Fig. 5: Length change (44 of the aluminium pipe as function oftemperature

Fig, 4: Length change (A4 of the copper pipe as function of tem_perature

^olcopper IImm | 0q

0.4

0.1

0.2

0.1

0.0

Fig. 6: Length change (^4 of the steel pipe as function of tem-perature

AI| 0.15I

0.30

0.2s

0.20

u, t)

0.10

0.05

0.00

290 100 310 320

310 320 ll0 i40 _150-=--->-K

120 ll0 110 150-f*

K

A/atumnium 4mm lot A/steelmm

0.

0.5

0.1

U.J

0.2

0.1

0.0

290 100 i10 320 ll0 140--T-

K

ll0 110--r-

K

PHYWE series of publications . Laboratory Experiments . Chemistry . @ PHYWE SYSTEME GMBH & Co. KG . D-37070 Gttingen P3O21SO1

LEC02.18 Dilatometry

Fig. 7: Length change (A/) of the Duran glass pipe as function of Fig. 8: Volume of water as function of temperaturelamarr+r rra

a/nru." (Duran@) t'.nm I o.oa

0.06

0.04

0.02

0.00

70.t,

70.2

70.0

9.8

290 100 110 ]20 310 140 150-f-

K

loo llo l2o jlo rg_.IgT

P3021 801

,

Vrater AI n4 t*l I rl.+ilil |

I

71.2

71.0

. 70.8

/u.o

PHWVE series of publications . Laboratory Experiments . Chemistry. O PHYWE SYSTEME GMBH & Co. KG . D-37070 Gttingen

Evaporative equilibrium

Related conceptsEnthalpy of vaporization, vapour pressure, entropy of vaporiza_tion, Clapeyron-Clausius equation, Trouton-pictet rule, taws ofthermodynamics.

PrincipleFor each temperature, a specific pressure of the gas phase ofthe liquid establishes itself above the liquid

- the vapour pres-

sure. lf the external pressure is lowered by drawing off the gasphase, the equilibrium re-establishes itself through evaporarronof pad of the liquid phase

TaskDetermine the enthalpy of vaporization of acetone by measurrngthe vapour pressure at different temperatures.

Silicone hose, d, = 7 mmSilicone hose, d, = 2 mmRetort stand, h = 7SO mntRight angle clampUniversal clampRound flask, .100 ml, 'l x GL 2518, Z xGL25/12Jointing for connecting caps, GL 25lBGlass tube, straght, / = B0 mmOne-way stopcock, straightSecurity bole with manometerWater jet pumpRubber tubing, vacuum, d = 6 mmHose clip, d = 12...20 mmGraduated cylinder, S0 mlFunnel, glass, d" = 55 mmGlass rod, r/ = B mm, / = B mmGraduated vessel with handle, 1 |Pasteur pipettesRubber bulbsAcetone, 250 mlGlycerin,250 mlSodium chloride, chem. pure, 500 g

Water

EquipmentCalorimeter, transDarentTemperature meter, digital, 4-2Temperature probe, Pt1 00Protective sleeve for immersion probeBarometer / Manometer, hand-heldPressure sensorTubing adapter, 3-5 / 6-10 mm

04402.O013617.9311759.0111762.0507136.0007'1s6.0147517.O1

39296.00 139298.00 137694.00 237697.00 337715.00 335677.15 141242.03 13670'1 .65 136705.00 134'170.88 102728.00 139286.00 340995.00 236632.00 134457.00 140485.06 136640.00 136590.00 139275.03 130004.25 130084.25 .130155.50 1

1

1

2

Fig. 1. Experimental set-up.

PHYWE series of publications . Laboraiory Experments . Chemistry . O PI'IYWE SYSTEN/E Gl\4Bt-l & Co. KG . D-37020 cttnqen p3030101

Evaporative equilibrium

Set-up and procedureSet up the experiment as shown in Fig. 'l .Equip the three-neck round flask with a one-way stopcock, ashort straight glass tube and a protective sleeve for temperatureprobes as follows: Replace the two GL 25/12 gaskets with twoGL25/8 gaskets. Fix the short glass tube in the middle neck ofthe flask, connect it to an adapter with a short piece of siliconehose (d' = 7 mm) and connect the other end of the adapter to themeasuring probe of the digital manometer with a piece of thinhose (d' = 2 mm). Use a piece of rubber vacuum tubing to con-nect the one-way stopcock attached to the second neck to thesafety bottle, and connect this to the water jet pump. Put a fewdroos of acetone into the orotective sleeve in the third neck toimprove heat transfer, then insed the temperature immersionDrobe.Fill the calorimeter with a mture of ice and table salt, and mon-itor the temperature of the mixture with a second temperatureimmersion probe. Fill the round flask with 50 ml of acetone, butdo not yet immerse it in the freezing mixture. Set the water jetpump in operation and evacuate the flask until the acetonebegins to boil. When this occurs, close the straight stopcock onthe round flask and lower the flask into the freezing mixture. Assoon as the temperature has sunk below

-5 "C, reopen thestraight stopcock for residual air to be removed from the flask.When the pressure is approximately 50 hPa, close the straightstopcock and carefully open the three-way stopcock on thesafety bottle to let air slowly flow in. Turn off the pump and readthe pressure in the round flask as shown by the digital manome-ter. In the course of 10 minutes, it should rise maximally by twohPa (otherwise check the connections for gas-tightness).

Fig. 2'. Plot of the logarithm of the vapour pressure against thereciprocal temperature

Increase the temperature in the round flask in steps of 2 to 3 "Cby adding water to the freezing mixture (stir the mixture well).After each temperature increase, wait until evaporative equilibri-um has re-established, then record both the temperature of theacetone in the flask and the corresponding pressure. Continuethe experiment until a temperature of 20 'C has been reached.Carefully let air into the flask by gradually opening the stopcock.

Theory and evaluationA vapour is formed above a liquid until the two phases are inequilibrium. The vapour formed is richer in energy than the liq-uid, and occcupies a larger volume. The enthalpy of vaporizationAII is required to increase the internal energy and to performvolume work. The temperature dependence of the vapour pres-sure is described by the Clapeyron-Clausius equation:

dp * LuHdr rvs-u)

wnerep Yapour pressure in PaLuH Molar enthalpy of vaporizationVo,Vt Molar volumes of the gaseous and liquid phases in- equilibrium

T Temoerature in KAs neither All nor AV are independent of temperature, we musrwork with approximations. At a sufficient distance from the crit-ical point (at which both AV and All are equal to zero), AV forthe vaporizing process is practically equal to the volume of thegaseous phase, as the volume of the liquid phase can beneglected. When we limit ourselves to a relatively narrow tem-perature range, then we can also assume that AH is tempera-ture independent within this range. We can also assume that thevapour acts as an ideal gas. We then have:

withd Inpdr

we obtain

Subsequent to indefinite integration, a linear form is obtained:

C Integration constantTo determine AuH, plot Inp against 1lT (Fig.2). The slope of thestraight compensation lines is -dufl/R. Multiplication by the neg-ative gas constant provides the desired enthalpy of vaporization.

Data and results

^vI = 35.93 kJ . moli (Lit.: AuH (25 "C) = 30.99 kJ . mol-1);

^,r' (56 "C, boiling point) = 29.10 kJ .mol-l

(1)

1 dp AuHp dT: R7'

!.dp =pdr

d\tnr | 10.2

I

10.0

d lnp LuHdT : Rr,

nn:ff+c

(2)

(3)

(4)9.8

QA

9.1+

9.2

9.0

8.8

8.6

(5)

3.603./.0 r.s51.50 1.65 3.70 3.75;------>f .r

Determination of the mixing enthatpy of binary ftuid mixtures LEC02.06

Related conceptsDifferential molar mixing enthalpy, real and ideal behaviour, inte_gral molar mixing enthalpy, fundamental principles of thermody_namics, calorimetry.

PrincipleWtren two miscible liquids are mixed, a positive or negative heateffect occurs, which ls caused by the interactions between themolecules. This heat effect is dependent on the mixing ratio. Theintegral mixing enthalpy and the dlfferential molar mixinoenthalpy can be determined by calorimetric measurements o-fthe heat of reaction.

Tasks1. Measure the integral mixing enthalpy of 7 differenr warer_

acetone minures.2. Plot the molar integral mixing enthalpy versus the quantity of

substance (mole fraction) and determine the molar mixinoenthalpy.

3. Discuss the results on the basis of the interactions in themxture.

Calorimeter, transparentHeating coil with socketsWork and power meterUniversal power supplyConnectin cable, / = 500 mm, blackAccessory set for immerson thermostatlmmersion thermostat, 100 .CBath for thermostat, 6 l, MakrolonRubber tubing, d, = 6 mmHose clips, d = 8...12 mmMagnetc heating stirrerMagnetic stirrer bar, / = 30 mm, ovalSeparator for magnetic barsSupport rod, / = 500 mm, M1O threadRight angle clampUniversal clampRetort stand, /. = 500 mmLaboratory balance

with data output, B0O/1600/3200 qStop watch, digital, 1/100 sErlenmeyer fiask, 250 ml, narrow neck, pN 29Erlenmeyer flask, 100 ml, narrow neck. pN 19Funnel, d^ = B0 mmPowder fnnel, /^ = 65 mmPasteur pipettes,2 out ofRubber bulbs, '1 out ofWash bottle, 500 ml, plasticAcetone, chem. pure, 250 mlWater, distilled, 5 |PC, Windows@ 95 or higher

04402.0O04450.001371 5.9313500.9307361 .0508492.0108492.93oB4B7.O239282.0040996.0135720.9335680.0435680.0302022.2037697.0037715.0037692.00

48803.9303071.0136424.O036418.0034459.0034472.0036590.0039275.0333931.0030004.2531246.81

1

1

1

/,

1

1

1

EquipmentCobra3 Basic-UnitPower supply 12V/2 AData cable, RS232Temperature measuring module ft 100Software Cobra3 TemperatureTemperature probe Pt 100

12150.001 21 51 .9914602.0012102.O014503.611 l759.0 i

o1

ir"l{;.

PHYWE series of publications . Laboratory Experments . Chemistry. O PHWVE SYSTEME GMBH & Co. KG . D-37070 Gttingen p30206.11

Determination of the mixing enthalpy of binary fluid mixtures

Set-up and procedureSet up the experiment as shown in Fig.1 but for the time beingdo not connect the heating coil with the work and power meter.Weigh out the individual components of these mixtures with anaccuracy of 0.1 g in accordance with the values given in Table 1.

Connect one of the temperature probes to T.1 of the measuringmodule, the other to T2. Call up the 'Measure' programme inWindows and enter as measuring instrument.Set the measuring parameters as shown in Fig. 2. Under choose Temperature TOa as channel, under Temperature TOb. Under selectTemperature T0a, the appropriate range for the temperature andthe X bounds and 'auto range'. Now calibrate the sensors under each by entering the temperature value measuredwith a thermometer and pressing . After havingmade these settings, press to reach the field for therecording of measured values. Arrange the displays as you wantthem.

For the first measurement, fill 432 g water into the calorimeter.Insert the oval magnetic stirrer bar in the calorimeter and switchthe magnetic stirrer on (Caution: Do not switch on the heatngunit by mistake!). Insert the heating coil and the temperatureprobe into the lid of the calorimeter and fix them in position.Weigh '154 g of acetone in a 250 ml Erlenmeyer flask. Cut a rub-ber stopper with hole lengthwise, put the second temperatureprobe through the hole and close the Erlenmeyer flask beforehanging t into the temperature-controlled bath. Adjust theimmersion thermostat to the temperature of the water in thecalorimeter and wait until the temperature difference betweenthe acetone in the bath and the calorimeter does not exceed0.02 K.Start the measurement with . Wait a fewminutes, then pour the acetone into the water in the calorimeter.After a new temperature equilibrium has been reached, performelectrical calibration for the determination of the total heatcapacity of the calorimeter. To do this, supply '10 V AC to thework and power meter for the electric heating. Push the button and then put the free ends of the heating coil connectioncables into the output jacks. The system is now continuouslyheated and the supplied quantity of energy is measured. Whenthe temperature increase in the calorimeter induced by the elec-trical heater is approximately equal in size to the temperaturechange resulting from mixing the two liquids, switch off the heat-ing and read the exact quantity of electrical energy supplied.Continue to measure for another three minutes, then stop tem-perature recording by .Fig. 3 shows the graph as it is presented by the programmewhen the measurement is stopped. lf you use from thetoolbar you can read the temperature difference data.In a second experiment, add an additional portion of acetone(194 g) to the mixture in the calorimeter (see Table 1). Performthe experiment completely analogously to the first measurementand pay attention that the temperature of the mixture in thecalorimeter and of the acetone is the same.In a fuher series of experiments, successively add the 5 por-tions of water listed in Table 1 to the 464 g ol acetone in thecalorimeter. Carry out this series in the same manner as in thefirst set of measurements, after carefully cleaning and drying thecalorimeter. lt is important that the calorimeter is recalibratedafter each addition, as the heat capacity of the system is differ-ent after each temperature change.

Fig.2: Measurementparameters

P302061 1

Table 1: Preparation of the seven test mixtures

Substance quantity Calorimeter Erlenmeyer flask Mixture numberX=0.1 432 g Water 154 g Acetone 1X=0.2 Mixture'1 194 g AcetoneY-O 464 g Acetone 16 g Water 7X=0.9 Mixture 7 20 g Water 6X=0.6 Mixture 6 60 g Water

Mixture 5 49 g WaterX=0.4 Mixture 4 72 g\Naer

PHYWE series of publications . Laboratory Experiments . Chemistry . O PHYWE SYSTEN4E GMBH & Co. KG . D-37070 Gttingen

Determination of the mixing enthalpy of binary ftuid mixtures

Theory and evaluationThe change in enthalpy observed when two liquids are mixed isthe sum of the changes in enthalpy which occur during the mix-ing process. The mixing enthalpy

^Ml is influenced by the inter-

actions of the molecules involved, which in turn are a function ofthe mixing ratio. The mixing enthalpy is zero if there are no inter-actions between the molecules (so-called ideal mixtures). Theinteractions between two liquids can cause endothermic effects(decreasing supramolecular assemblies) or exothermic effects(formation of supramolecular assemblies of different molecules).The quantity of heat exchanged by mixing no moles of the com-ponent A with n, moles of component B is iermed the integral

mixing enthalpy Ar11l. lf a substance is successively added toanother one until a certan mixing ratio is reached, the integralmixing enthalpy is obtained by adding the individual enthalpyVAIUES:

LMht: )"i (1)with

^"i: Q*r: e"nffi: %,ff e)T

oc

Fig. 3 Temperature-time curve of the mixing enthalpy of mixture 1

X1: ?23 s X2: 275s AX: 51 sY1: 25,43 "C Y2: 31,80 'C aY: 6,38 'C

100 20 300 400 500 600 700 800 900 1000 1100 't200 130

Fig. 4 Integral molar mixing enthalpy as a function of the molar fractionarH'

"/.mot-1

-400

-600

-800 xacetone

PHYWE series of publications . Laboratory Experiments . Chemistry . @ PHWVE SYSTEME GMBH & Co. KG . D-37070 cttingen

400

0,90.80,70,60,50,4n20,20,1

LEC02.06

P302061 1

r-rf-iLECli _

I O|OO ]1 Oetermination of the mixing enthalpy of binary fluid mixtureslilThe nrolar integral rrixirr.cl enthalpy (referred io 1 nrol of the mix-ture) rs calcuiated rs follows;:

a|,rllr == -4u'il (3)t1A + t1B

The mixing ralio is norrnally characterised by tlre molecularabrrndance (rrrole f racti,:n).

11 a.

n/.i nA

-tB ::

^

1.

tr\ nB

(4.1)

(4 2\

(4.3)

with/ {^,ftr ) \Arl/i: (,_u,,;

,/, r, (7)

Avffj Dilferential molar mixing enthalpy of the conrponent jIntegration at co)stant composition results in:

Lrht : L[Itzo * AHsrxs (B)

Division of (5) by (no+ n) results in:AMHI = Ar-loxo + Ar/1r-r, (9)

Fig. 4 shows the graph of A*111 versus the rnixing ratioexpressed as the molecular abundance of aoetone xacetone.Using the equations (10) and (1 1),

for binary mixtures.

The dependence of the integral mixing enthalpy on the numberof rnoles of the two conlponents at constant pressure and con-stant temperature is defined by:

/(6^\,/rr) \ / (DAM/II)\d(AMr)-{t"" -}drro+l " -l tlne (5)\ d/n ,/ t, \ ns / no

or

d(AM/r) -= Avl/ndnn t ,\lfgd (6)

--)/--

avF/n: (t!t#).:rs * aNaH,aNHe: (ry3)xa*a11r

(10)

(1 1)

the differential molar mixing enthalpy of water anci acetone forthe different compositions of the solutions can be calculated.You can enter the results each for water and acetone into a datatable and then put them togelher in one diagranr with under as shown in Fiq. 5.

Fig. 5 Differential nrcllar mixing enthalpies of water and acetone as a function of the composition

0

-20tl

-40

-60

-Ett00,8 ,9 1racetone

P302061 1 PI{YWE series of publications . Laboraiory Experiments . Chemistry . O PHYWE SYSTEME GMBH & Co. KG . D-37070 cttngen

Partial molar volumes

Related conceptsPrinciples of thermodynamics, ideal and non_ideal behaviour ofgases and liquids, volume contraction, molar and partial molarquantities.

PrincipleDue to intermolecular interactions, the total volume measuredwhen two real liquids (e.g. ethanol and water) are mixed deviatesfrom the total volume calculated from the individual volumes ofthe two liquids (volume contraction). To describe this non_idealbehaviour in the mixing phase, one defines partial molar quanti-ties which are dependent on the composition of the system. Thevalues of these can be expermentally determined.

TasksMeasure the densities of different ethanol-water mixtures ofspecified composition at 20.C with pycnometers. Calculate thereal volumes and the mean molar mixing volumes of the investi_gated ethanol-water mxtures and also the partial molar volumesof each liquid for selected compositions. Compare them with themolar volumes of the pure substances at 20.C.

Set up the experiment as shown in Fiq. 1.Prepare the ethanol-water mixtures i the narrow neck bottleson the laboratory balance in the approximate mass compositorspecified in Table 1, weighing ethanol into the predetermnedmass of water (weighing accuracy 0.001 g). Close the botflesimmediately when the desired mass has been reached. Fill drypycnometers of known empty mass completely with the mix_tures. Cover them with aluminium foil and position them in thetemperature-controlled bath for about 30 min at 20.C for tem_perature equilibration. Subsequently, remove the pycnomerersand weigh them after meticulous drvinq.

Support rod, 1= 500 mmRight angle c;lampUniversal clampPycnometer, calibrated, 25 mlBottle, narrow neck, 100 mlFunnel, glass, d^ = 55 mmGlass beake6 5 ml, tallPasteur pipettesRubber bulbsRubber tubing, d, = 6 mmHose clip, d = 8...12 mmWash bottle, 500 mlEthyl alcohol, absolute, 500 mlWater, distilled 5 |

Set-up and procedure

02032.00 237697.00 537715.00 403023.00 I41101 .0'1 934457.00 I36001.00 236s90.00 139275.03 '139282.00 340996.01 433931.00 130008.50 131246.81 1

EquipmentPrecision balance, 620 glmmersion thermostat, 1 00.CBath for thermostat, 6 l, Makrolon-oase -PAS:i-

Fig. 1. Experimental set-up.t, I l: i :;:a ) :: i:.. :, ::: : a;:t : ).:;!t) ;:::;:t1l:,:; :: t: irii ;:J !

48852.93 108492.93 108487.02 102009.55 1

::i:.1,.: j:' :!:n ! :.. ;1

::

" "'l_:;

',::

l;:l;: llitttil,i;

'"!.Cj!

it:

PHYWE series of publications . Laboratory Experiments . Chemistry . @ PHYWE SYSTEME G4BH & Co. KG . D-g2070 Gttingen P3020501

Partial molar volumes

Calculate the masses of 25 ml of the respective mixtures as thedifference of the two weights.

m (CrHuOH) / g m (HrO) / g,JU. O 1.35

29.35 2.8527.90 4.7026.20 6.8524.15 9.4521.60 12.6518.35 16.75

14 t5 22.108.35 29.40

Table 1: Ethanol-water mixtures to be investiqated

Theory and evaluationThe volume o,o and the mean molar volume V

,o o't an ideal mix-ture of the components A and B can be calculated if the quanti-tative comoosition is known.

under consideration of the Gibbs-Duhem equation.Analogous correlations can be formulated for r, due to the factthatxo=1-xr.After substituting (6) in (5), the following relationships areobtained:

The dependence of it on the composition is described byrelationship

d (AMY) -

dV, -

dVo -

r. _ - _ (v. , t/ \dro d"o dxo - \'e 'BI vA /B)

d (A.y)Vs= L\V - -i;;rxr + Vn

_ d (A^"y)V: LV - -frxa + Ve

the

(6)

(7.1',)

n1'+ nB

.rA, -rB mole fraction of the components A and B, respectivelynA, nB amounts of A and B respectively

r/ -

/id -

: V,x * Vsxs (2)nA+ nB

However, the assumed additivity in equation (2) loses its validityin cases of real mixtures (e.9. ethanol / water). The real volumesu, and V, deviate more or less strongly from the ideal volumesdue to volume contraction but can still be calculated if the molarvolumes of the pure components A and B are replaced by thepartial molar volumes Vo and V, which are independent of thecomoosition.

-

/d?1.\Ye:(:-l\dn / r,p,",

-

/d?,.\Ys=[;-l\ rltlB / r.p.no

t/ - nA+ nB iox + Vuxu

The difference between the mean molar volumes definedaccording to equations (2) and (4) is designated as the meanmolar mixing volume Ar/ and is an intensive measure of thedeviation of the mixture from ideal behaviour.

LuV:V-V

- [(7o - ir) - (vo - vu)]rn + qi, - vu

and

(7.2)

According to this, the partial molar volumes of the componentsA and B for the specific compositions (xo, xr) can be determinedif the molar volumes of the pure substances (V n, Vd and theirdifferential quotients d (AM n / dxoare known. These can beobtained as the tangent to the graphical plot of AMy versus -rA(Fig.2). This is, however, better calculated by deriving the func-tonal correlation Ady = f(xn) for selected values of xo.The following procedure is recommended for this: First, calcu-late the exact mole fractional compositions from the weighed-out masses of ethanol (A) and water (B) using equation (1 .1) or(1.2). With the pycnometer data (rn = mass of the liquid in thepycnometer; u = 25 ml = pycnometer volume), the densities(p = m/u) of the mixtures and the volumes vr corresponding tothe total masses (mo+ m) can be determined. These values canbe converted into the mean molar volume vr using equation (4)and then into the mean molar mixing volume ArV in accordancewith equations (2) and (5).The molar volumes of the pure liquids required for these conver-sions are V e = 58.z7z ml / mol (ethanol) and V, = 1 8.073 ml /mol (water) at T = 293.15 K.Plot the dependence of the mean molar mixing volume

^My on

the composition xo analogous to Fig.2, and determine the differ-ential quotients d(ArV) / dro from the slope of the tangents forselected mole fractions;ro and the corresponding estimated val-ues for A"V from the curve itself.[Note: The correlation between the variables can also be approx-imated by a polynomial of the second or higher degree using acomputer-assisted method. By substituting arbitrary mole frac-tions xo in the polynomial or its first derivative, the correspond-ing estimated value for AMy and the differential quotients d(AMy)/ dxo can be calculated.lThe partial molar volumes of both components are now acces-sible via equations (7.1) and (7.2).Finally, calculate the mean molai volume V, tor a selected mix-ture which corresponds well to the experimental conditions fromthe partial molar volumes determined according to equation (4)and compare it with your experimental results.

11

?)i

nA+ nBllg

(1 .1)

(1.2)

(3.1)

(3.2)

(4)

(5)

P3020501 PHYWE series of publcatons . Laboratory Experiments Chemistry . O PHWVE SYSTE,4E GMBH & Co. KG . D-37070 Gttingen

Partial molar volumes

Data and resultsFig. 2 illustrates the volume contraction that occurs on mxino ofethanol and water. From the corresponding polynomial and"itsfirst derivate, e.g. for rA = rB = 0.5, one oOts t'he partial mokrvolumes yn

= 56.64 ml / mol (ethanol) and Vo = 16.82 ml / mol(water) by substitution in equations (7.1) and (7.2. These valuesare definitely less than the molar volumes of the pure substances11?ry.j: K (l/A = 58.277 ml / mot, v" = l.ozs mt / mot).Substituting these values in eqn. (4), one"obtains a mean motarvolume ot Vt = 36.73 ml / mol. The perfect agreement with theexperimentally determined value (I/, = 36.73 ml / mot confirmsthe,validity of the additivity shown i eqn. (a) and thus the utilityof the partial molar volumes for the calculation of the volume ofmixed phases of known composition.

anv trurr1 j -o.t

-0.8

-0.6

-1.0

'1.00.80.0./*0.20.0)lA

Fig. 2: Dependence of the mean molar mixing vblumes a"Von the composition of different ethanol_water mitu?sdescribed by the mole fraction xo of ethanol (Z

=293.25 K)

PHYWE series of publications . Laboratory Experiments . Chemistry. @ pHyWE SYSTEME GMBH & Co. KG . D-37070 Gttingen P302050 1

Determination of the melting enthalpy of a pure substance LEC02.09

Related conceptsHeat capacity, melting point, latent het, calorimetry Gibbs,phase rule, enthalpy of sublirnation, enthalpy of vaporization.PrincipleWhen a solicl melts, energy is required for the destrLiction of thecrystal lattice. A substance whose melting point lies slightlyoetow room ternperature is first cooled until it solidifies and thenmelted n a calorimeter. The melting enthalpy is ialculated fromthe decrease n temperature due to the meltig process which ismeasured in the calorimeter.

Tasks1. Take a temperature-time-diagram for the melting process of

dioxan2- Calculate the melting enthalpy and entropy of 1,4_clioxan.

Magnetic heating stirrerMagnetic stirrer bar, / = 30 mm, ovalSeparator for magnetic barsSupport rod, / = S00 mm, M10 threadRight angle clampUniversal clampLaboratory balance_

with data output, 800/1600/3200 gTest tube, 30/200 mm, Duran, FN 29Rubber stopper 26132Dewar vessel, 500 rnlPasteur pipettesRubber bulbsWash bottle, 500 ml1,4-Dioxan, 1000 mlWater, distilled, 5 |PC, Windows@ 95 or higher

Set-up and procedure

35720.9335680.0435680.0302022.2037697.0037715.O0

48803.9336294.0039258.0033006.0036590.0039275.0333931.0031266.7031246.81

1.l

1

1

2

1

22

EquipmentCobra3 Basic-UnitPower supply 12 V/2 AData cable, RS232Temperature measuring module pt 100Software Cobra 3 TemperatureTemperature probe pt 100Calorimeter, transparentHeating coil with socketsWo'li and power meterUniversal power supplyConnection cable, / = 500 mm, black

Set up the experiment as shown in Fig. .1 but for the time beingdo not connect the heating coll with the work and'power meterConnect the temperature probe to T1 of the measuring module.Call up the 'Measure' programme in Windows ano enrer as measuring instrr-rment_ Set the measurinoparameters as shown in Fig. 2. Under seleclTemperature T0a, the appropriate range for the iemperature andthe X bounds and ,auto range,. Aftei having made these set-tings, press to reach the field fr the recordjnq ofmeasured values. Arrange the displays as you want them.

121 50.00 112151.99 114602.00 112102.00 114503.61 11 1759.01 104402.00 104450.00 11371 5.93 113500.93 .107361 .05 4

PHYWE series of publications . Laboratory Experiments . Chemistry . O PHWVE SYSTEME GMtsH & Co. KG . D-37070 Gttingen p3020S11

Determination of the melting enthalpy of a pure substance

Weigh out 44.05 g (0.5 mol) of 1,4-dioxan in a test tube (weigh-ing accuracy 0.01 g) and close it with a stopper. Fill the Dewarvessel with 300 g of ice and 100 ml of cold water. Place the testtube in this water-ice mixture for about t hour until the dioxan isfrozen. In the meantime, fill the calorimeter with 850 g of distilledwater (weighing accuracy 0.1 g). Place it on the magnetic stirrer,put in the oval magnetic stirrer bar and switch on the stirrer(Caution: Do not switch on the heating unit by mistake!). Insertthe heating coil and the temperature probe into the lid of thecalorimeter and fix them in position.

When temperature equilibrium has been reached (after approxi-mately 10 min) start the measurement by pushing . Wait 3 to 4 minutes, then take the test tube out ofthe Dewar vessel, qulckly dry it, and inserl it through the hole inthe lid into the water. The water level in the calorimeter should beabout '1 cm higher than the level of the dioxan in the test tube.When the dioxan has completely melted and a thermal equilibri-um has been established, continue to measure the temperaturefor about another 5 minutes. Subsequently perform electricalcalibration to determine the total heat capacity of the calorime-ter. Supply '10 V AC to the work and power meter for the electricheating. Push the button and then put the free ends ofthe heating coil connection cables into the output jacks. Thesystem is now continuously heated and the supplied quantity ofenergy is measured. As soon as the temperature in the calorime-ter has reached the initial temperature, switch off the heating andread the exact quantity of electrical energy supplied. After a fur-ther three minutes, stop recording the temperature.Fig. 3 shows the graph as it is presented by the programmewhen the measurement is stopped. lf you use from thetoolbar you can read the temperature difference data.Perform an analogous experiment with an empty test tube inorder to determine the heat capacitv of the test tube.

Ps02091 1

Theory and evaluationPhase changes of substances are linked with energy changes.The phase transition from the solid into the liquid state is termedmelting. Under isobaric conditions the phase transition of a puresubstance occurs at constant temperature. The phase transi-tions temperatures (melting point, boiling point) can therefore beused as substance constants for characterising substances.lf energy is applied to solid (frozen) dioxan, its temperature risesuntil the phase transition temperature (melting temperature) isreached. During the melting process, solid and liquid dioxancoexist. However, as lng as both phases are present, addingheat does not result in a further temperature increase (latentheat), as this energy is required for phase transformation. Onlywhen the melting process is completed does the temperature ofthe system again increase.The melting process normally occurs under isobaric conditions.The heat of fusion O, is equal to the melting enthalpy ArH in thiscase.

Qr=LrH p=const. (1)

Referred to the amount of substance 2. this results in

This is the amount of energy which is required to overcome thelattice forces. The same quantity of energy which must be addedduring the melting process is released as heat of solidificationduring the freezing process (liquid-solid phase transformation).

AU_AUoFI -

-acryStr

LrhA-H -:

n(1a)

(2)

Fig.2'. Temperature-time diagram for the meltingdioxan

process of

x1 38s X2:1429s X1011s23,87 'C Y2t 21,88 'C Yr 1,9S 'C

Fig.2: Measurementparameters

PHYWE series of publications . Laboratory Experiments . Chemistry . @ PHYWE SYSTEIME GIVBH & Co. KG . D-37070 cttingen

Analogous energy changes occur during the vaporization orcondensation processes. According to Hess,s law, the subllma-tion enthalpy Arro,fl must be additively composed of the melt-ing enthalpy AFII and the enthalpy of vaporization AuI1.

AsrorH = LrH + LrH (3)The pressure dependency of the phase transition temperature isdescribed by the Clapeyron-Clausius equation.

dr _r{v" - U)

dp LrHYs Volume of solid substanceVt Volume of liquid substanceFor reversible processes, the phase transition entropy is calcu-lated according to the second law of thermodynamics. The fol-lowing relation results for the melting entropy AFS:

r.s = Y (s)tFlf n moles of a substance at a temperature Tl, which is below themelting point of the substance, is heated to a temperature Th,which is above the melting point, the following amount of heat isrequred under isobaric conditions:

Q = Lh = nCo1.f7-fr) * nL,rH + nCrr(76-T) (6)Cp(s) Molar heat capacity of the solid substanceCp(tl Molar heat capacity of the liquidTF Melting pointTt Arbitrary temperature below the melting pontTh Abitrary temperature above the melting pointn Quantity of dloxan

Using these variables, the enthalpy of fusion is:

otrH :1- Cor"r(I, - I) - Coru(Tn - G) )

When the enthalpy of fusion is determined in the mannerdescribed in this experiment, the temperature-dependent termsin equation (7) can be neglected, as the temperature changesare relatively small and the calibraiion of the system is performedunder identical conditions as those under which the measure-ment is performed. As a consequence, the following is obtainedfor the enthalpy of fusion:

Determination of the meltng enthalpy of a pure substance LEC02.09

Q can be determined from the experimentally measured valuesas follows:

9 = Qexo-Qempy

Qu*p= CK.LTexpW"t = C< .LT" = Q1

An""Qerp: W"1 ' ;l-:al cal

wnere

AT""o Temperature difference during the melting of dioxanAT""r Temperature difference during calibrationCK Heat capacity of the calorimeterWet Electrical work during calibrationO"rpty is the quantity of heat which must be applied to heat theempty test tube under the same experimental conUitions:

O".pty : W"t, empty : Ws1A4"p, u.p,ya4a,

".pty

where

^7"*p, "*pty Temperature difference during heatlng the emptytest tube^Tcat, empty

Temperature difference during calibration with the'

empty test tubeWut,

".pty Electrical work during calibration with the emptytest tube

Data and resultsValues from tlre literature:Co,", (dioxan) = 147.6 J .mol-1 . K-1Coi,(dioxan) = 152.7 J.mol-1 .K-1M(dioxan) = 88.11 9J.mol-rZ, (dioxan) = 11.8 'C = 284.9 KA.H (dioxan) = 12.8 kJ .mol-1AoS(dioxan) = 45.1 J.mol-l .K-lThe following values were determined experimentally:ArH (dioxan) = 13.6 kJ . mol-1A.S (dioxan) = 47.7 J.mol-r .K-l

(B)

(8.1)

(8.2)

(8.3)(4)

(e)

LrH (7.1):9n

PHYWE series of publcations . Laboratory Experiments . Chemistry . O PHYWE SYSTEME GN/BH & Co. KG . D-37070 Gttingen P302091 1