DETERMINATION OF MOLAR MASS FROM FREEZING POINT DEPRESSION

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1 Exercse 1 DETERINTION OF OLR SS FRO FREEZING POINT DEPRESSION Collgatve propertes The propertes we now consder are the lowerng of vapour pressure, the elevaton of bolng pont, the depresson of freezng pont, and the osmotc pressure arsng from the presence of a solute. In dlute solutons these propertes depend only on the number of solute partcles present, not ther dentty. For ths reason, they are called collgatve propertes. We assume that the solute s not volatle, so t does not contrbute to the vapour. We also assume that the solute does not dssolve n the sold solvent: that s, the pure sold separates when soluton s frozen. ll collgatve propertes stem from the reducton of the chemcal potental of lqud solvent as a result of the presence of solute. For an deal-dlute soluton, the reducton s from 0 for the pure solvent to 0 + RT ln x, when a solute s present (ln x s negatve because x <1). x s molar fracton of solvent wth solute. There s no drect nfluence of the solute on the chemcal potental of the solvent vapour and the sold solvent because the solute appears n nether the vapour nor the sold. s can be seen from Fgure 1, the reducton n chemcal potental of the solvent mples that the lqud-vapour equlbrum occurs at a hgher temperature (the bolng pont rased) and the sold-lqud equlbrum occurs at a lower temperature (the freezng pont s lowered). Fgure 1 The chemcal potental of a solvent n the presence of a solute The elevaton of bolng pont ebulloscopy When a nonvolatle solute s dssolved n a solvent, the vapor pressure of the latter s decrease

2 p p 0 p [Pa] (1) where: p 0 s the vapor pressure of the pure solvent at a partcular temperature p s the vapor pressure of the solvent over the soluton at the same temperature (Fgure 2) Fgure 2 The elevaton of the bolng pont of a solvent The extent of the elevaton ΔT=T b -T b depends upon the concentraton of the solute, and for dlute, deal soluton t may be shown that: T K b e [K] (2) where: K e s a constant characterstc of the solvent, called bolng pont constant (molal ebuloscopc constant) expressed n unts [K kg mol -1 ] b s molal concentraton (molalty) of the soluton olng pont constant K e : K e 2 RT0 H mv [K kg mol -1 ] (3) where: R s unversal gas constant T s thermodynamc temperature ΔH mv s molar heat of vaporzaton s molar mass of the solvent For water, K e = 0.51 K kg mol -1 olalty (b) t s the number of moles of solute () dssolved n solvent (): m b [mol kg m -1 ] (4) where: m s mass of solute () unt kg

3 s molar mass of solute unt kg mol -1 m s mass of solvent unt kg Freezng pont depresson Note, when the partal vapor pressure of the solvent s lowered, the temperature of freezng s also lowered because the vapor-pressure curve of the solvent n the soluton ntersects the sublmaton curve of the sold at a lower temperature (Fgure 3). The sold phase, whch s assumed to be pure solvent, separates when the temperature s lowered to a pont where the partal vapor pressure of the solvent s just nfntesmally greater than the sublmaton pressure of the sold. Fgure 3 The depresson of the freezng pont of a solvent Note, the extent of the freezng pont depresson s defned as: ΔT=T f T where T f s freezng pont of a solvent T s freezng pont of the soluton (ΔT >0) Smlarly to above, the extent of the freezng pont depresson depends on the molal concentraton T K b c [K] (5) where K c s the molal depresson constant [K kg mol -1 ] b s molal concentraton accordng Equaton 4 It s also called the cryoscopc constant of a gven solvent. The depresson of the freezng pont s thus proportonal to the molalty of the solute n soluton. Cryoscopc constant: K C RT H 2 0 [K kg mol -1 ] (6) mf

4 where: ΔH mf s molar heat of vaporzaton depends only on the propertes of the solvent For water K C = 1.86 K kg mol -1. For justfcaton for K e and K C (Equatons 3 and 6) see [1, 2]. The lowerng of the freezng pont consttutes one of the smplest and most accurate means of determnng the apparent molecular weght of a solute. It s of practcal value and s mportant n theoretcal studes of soluton behavor. Task Cryoscopc determnaton of molar mass of unknown non dssocatng substance (nonelectrolyte), n aqueous soluton. Equpments pparatus for cryoscopc measurements as t s shown n Fgure 4: eckman's thermometer (, Fgure 5), test tube wth thck walls (S), mxer (), vessel contanng coolng mxture (K); magnfyng glass, 3 peces of weghng bottle, 20cm 3 ppette, beaker, laboratory thermometer, stopwatch Fgure 4 pparatus for cryoscopc measurements Chemcals Coolng mxture (soluton of 5 deals of ce brash and 1 deal of NaCl swped water) sample of the unknown substance Fgure 5 eckman's thermometer Procedure Step I Preparaton of cryoscopc test tube - Usng analytcal balances wegh 3 portons of unknown substance n a clean and dry weghng bottles, each sample wth 0.5 grams of approxmate weght wrte the mass of bottle+sample nto Table 1.

5 - Clean the cryoscopc test tube usng dstlled water and dry t wth flter paper. - Usng a ppette or automatc burette add 20 cm 3 of dstlled water wth known temperature t (record measured temperature nto the Table 2). - fter nserton of the mxer, place the adjusted eckman's thermometer () so, that t s whole reservor, contanng mercury s mmersed to the soluton and t s not touchng nner walls of the test tube. - Insert the prepared cryoscopc test tube nto the coolng mxture. The surface of the coolng bath should be set 2-3 cm above the solvent s level. Step II easurements wth pure solvent - Record the ntal temperature of the lqud nsde the cryoscopc test tube when t drops to 5 degrees. - Start the stop watch and record the temperature every 5 seconds. ecause the ekman s thermometer dsplays relatve temperature and the thermometer's scale s gven n degrees (whch numercally equals to 1 Kelvn), the temperature depresson wll be gven n Kelvns. - The temperature wll decrease untl the sold phase starts to precptate from the soluton whch s ndcated wth sharply ncreasng temperature. - Curve of undercoolng looks as t s shown n Fgure 4. s a freezng pont (T 0 ) wll be regarded that temperature, whch represents the hghest value on flat part on the mentoned curve (pont n Fgure 6). Record ths temperature to the Table 2. Take out the cryoscopc test tube from the coolng bath nto a baker whch s flled wth warmsh water and mx the content untl the freezed solvent becomes fully melted. Determnaton of freezng pont the pure solvent, descrbed n step II, should be repeated 3 tmes. It s assumed that the determned values of freezng ponts wll be close. Fgure 4 Cryoscopc curves (dependence temperature vs tme) for pure lgud (curve a) and aqueous soluton (b) Step III easurements wth aqueous soluton of unknown sample - fter the last repetton of the measurement wth pure solvent heat up the test tube agan, so the eckman's thermometer could be gently removed from the lqud. - dd the frst porton of weghed sample nto the solvent and mx t. fter the sample dssoluton

6 the eckman's thermometer should be restored back to ts orgnal place n the test tube and the prevous procedure should be repeated as t was descrbed for pure solvent (see agan step II). - The maxmum temperature, measured after undercoolng, wll be consdered agan as the freezng pont of the soluton (T ). - Repeat the measurement for 3 dfferent concentratons gven wth gradually added portons of weghed unknown sample. - Record the determned freezng ponts of these solutons to the Table 3. - The total mass of added sample s gven as sum of the masses of all prevous addtons. Each temperature determnaton for the gven concentraton must be repeated 2 tmes and the results should be averaged. Step IV Completon the measurements - When the measurements are fnshed dscharge the soluton from the apparatus. - The kryoscopc test tube, thermometer and mxer should be carefully cleaned and dred up. - Fnally weght the masses of empty weghng bottles and record the results to the Table 1. Table 1 Weghng the samples Sample No: weghng bottle+sample (g) empty weghng bottle (g) mass of the sample (g) Table 2 Solvent data t =... C Solvent K K K kg mol -1 water m g T 0 average freezng pont ( o k) T o C T 01 o k T 02 o k T 03 o k Processng the results 1 Usng Table 2 calculate the average temperature ( T 0 ) from the columns T 01, T 02, T Usng Table 3 calculate step by step T and T as dfference between the average freezng pont of pure solvent T0 and the solutons T accordng to Equaton 7: T = T0 - T (7)

7 Table 3 Soluton data Run No. ass of the sample m (g) Freezng ponts of samples ( o k) T ( o k) T (K) (g mol -1 ) Rato m /T ndvdual total T 1 T 2 3 Calculate the molar mass of unknown substance as follows 3 Drect calculaton from a formula: K Km T m =... where: m s the total mass of the unknown sample n grams m s the mass of the solvent n grams calculated from volume densty data (Table 4) Calculate the average value of molar mass ( ), Equaton 9: N 1 N (9) where: N s the number of measurements Calculate the approprate standard devaton (s) usng Equaton 10: (8) s N 1 N 1 Table 2 (10) Table 4 Densty of water at varous temperatures Temperature ( o C) Densty (kg m -3 ) Temperature ( o C) Densty (kg m -3 ) Calculaton of the lmt value In case of solutons whch dffer from the deal t s necessary to make an extrapolaton to zero weght. The unknown molar mass should be calculated from Equaton 11 (below). Process the dependence [y=f(x)]:

8 m T K f ( m ) usng the least square method (S Excell). The ntercept of the lnear functon represents the requested lmt value n Equaton 11: lm m0 m T K Fnally, the molar mass s than determned usng the Equaton 11: K m K m lm m0 (11) TK In ths treatment, we wll express the expermental error of the molar mass n %, so called relatve error, where the table value of molar mass represents the reference (100%) data: Table (%) 100% (12) Table where: s value of molar mass calculated from Equaton 11 Table s molar mass of substance from Chemcal Table Report Include n your report the followng ponts: Theoretcal prncples of the molar mass determnaton usng cryoscopy. ref descrpton of the used devce and procedure. Tables of measured data. Calculatons of molar mass (procedures and ), standard devaton, relatve error. Dagrams: Tmes dependence of temperature for measurement of pure solvent and soluton of unknown substance (frst soluton) m Dependence f ( m) T Dscusson and conclusons. for determnaton of m 0 Lterature: 1 TKINS, P. W., de PUL, J.: Physcal Chemstry, Oxford Unversty, Great rtan (2006). 2 KOPECKÝ, F., et al. Laboratory anual for Physcal Chemstry (1996). anual edted by: RNDr. lexander úcs, PhD., Ing. Jarmla Oremusová, CSc. and doc. RNDr. Danela Uhríková, CSc.

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