I. Aim of the experiment

Transcription

1 Task VIII TRAUBE S RULE I. Aim of the eperiment The purpose of this task is to verify the Traube s rule for a homologous series of apillary ative substane solutions (i.e. alohols or arboyli aids) on the basis of measured surfae tension results as a funtion of the onentration. II. Introdution 1. Definition of the surfae tension 2. The surfae tension of solutions: a) Capillary ative substanes (surfatants) b) Szyszkoski s equation ) Traube s rule 3. Measurement of surfae tension a) Capillary rise method b) Drop volume method (stalagmometri method) ) Ring method (tensiometri method) d) Maimum bubble pressure method (Rebinder method) 4. Variation of surfae tension ith temperature 5. Adsorption on the surfae of solution a) The Gibbs adsorption equation b) The Gibbs adsorption isotherm equation 6. The struture of the adsorption surfae layer 7. Effet of temperature on the surfae tension of solutions Bibliography: 1. J. Ośik, Adsorption, PWN Polish Sientifi Publishers Warszaa, 1982, pp A.W. Adamson, Physial Chemistry of Surfaes, Intersiene Publishers, Ltd., London 1960, pp D. J. Sha, Introdution to Colloid and Surfae Chemistry, Butterorth Co. Publishers, Ltd, London 1970, pp

2 Adsorption at the liquid/gas interfae III. Theory III. 1. Surfae tension Cohesive fores (van der Waals) beteen moleules are unbalaned at the interfae. For eample, in the ase of a liquid/gas interfae the resultant fore ating on the surfae moleules from the liquid side eeeds that from the gas side (Fig.1). Surfae moleules of the liquid are therefore dran into the liquid phase, hose surfae tends to redue. Due to interations among liquid moleules, the fore direted normal to the surfae into the liquid is aompanied by another fore direted tangentially to the surfae to prevent its area from inreasing. This tangential fore per unit length is a measure of surfae tension (denoted by or σ). Fig. 1. Surfae layer at the liquid/gas interfae (r is the radius of intermoleular interation). Figure 2 shos a sheme of surfae formation. Sine the liquid tends to diminish its surfae area, inrease of that area requires ork against the surfae tension. We shift the lid to unover a part of the liquid surfae of the length equal to d. In general: or W = l d (1a) 2

3 W = da (1b) here da = l d is the hange of surfae area. shift the lid d surfae of the liquid Fig. 2. Formation of a ne surfae of the liquid. For the quasi-stati proess at a onstant temperature and pressure, the ork ill be equal to the inrease of Gibbs free energy of formation of the ne area of surfae (G = f (T, p)): or dg s = da (2) G = (3) A T, p, n It follos that the unit of surfae tension is N/m (defined as a fore) or it is surfae free energy J/m 2 (defined as ork). Surfae free energy represents the ork neessary to form unit area of ne surfae or, equivalently, the inrease of Gibbs free energy orresponding to the formation of unit area of the surfae. 3

4 Adsorption at the liquid/gas interfae III. 2. Surfae tension of solutions In the ase of to liquids solutions having similar surfae tensions almost linear variation of the surfae tension ith the onentration is observed. In regular solution the surfae tension is given by the Prigogine and Defay s relation: = β (4) p 1 2 here: 1 and 2 are the surfae tension of the pure liquids, and 1 2 are their mole frations and β p is a semi-empirial onstant. If the surfae tension of both liquids differ signifiantly, the addition of a small amount of liquid of loer surfae tension usually diminishes the surfae tension of the solution as ompared to that of the solvent (Fig.3). Water- ethanol 25 o C, mn/m C 2 H 5 OH, eight % Fig. 3. Surfae tension of aqueous solutions of ethanol at 25 o C. Substanes hih, in small onentrations, ause derease in the surfae tension of a solution are referred to as apillary or surfae ative substanes. These inlude suh organi ompounds as alohols, fatty aids, esters, ethers, et. 4

5 In the ase of dilute aqueous solution of organi substanes, the Szyszkoski s equation desribes the relation beteen the surfae tension o of the solvent, the surfae tension of the solution, and its onentration : o = B ln 1 + o A (5a) or ( a ) o = b ln 1+ (5b) here: B and b are onstant speifi for a given homologous series and the speifi apillary ativity harateristi of a given ompound. a = 1/ A is The Traube s rule (1884) states that for a homologous series of various surfae ative substanes, the onentration in the dilute aqueous solution at hih a given loering of surfae tension is observed dereases 3.2 times for eah additional methyl group in the series. For equal loering of the surfae tension in a homologous series, e.g. by, it is suffiient to use a suessive member of the series ith a onentration 3.2 times loer. In the ase of equal, for to members of a homologous series, e an rite in aordane ith the Szyszkoski s equation that: + n = + n+ 1 b n ln 1 bn+ 1 ln 1 (6) An An+ 1 here: n is the number of the homologue in the series. Sine b n = b n+ 1, the Traube s rule gives: A A n an = a + 1 = n+ 1 n n+ 1 n =3,2 (7) 5

6 Adsorption at the liquid/gas interfae III. 3. Methods of measuring surfae tension The most frequently applied methods of measuring surfae tension are: - apillary rise method The end of a apillary is immersed into the solution. The height at hih the solution reahes inside the apillary is related to the surfae tension by belo equation [4]: here h is the height of liquid inside the apillary, l is the liquid surfae tension, ρ is the density of the liquid, r is the radius of the apillary, g is the aeleration due to gravity, 2 l osθ h = (8) ρgr θ is the angle of ontat liquid ith the apillary all. Fig.4 Sheme of apillary rise method. Contat angle less than 90 (red olour); ontat angle greater than 90 (blue olour) [4]. 6

7 If θ is greater than 90, the liquid ill be depressed rather than lifted. - drop volume method The drop volume (drop eight method) eights the mass of the liquid drop that falls off a dispense tip of knon diameter hen pumped very sloly. It is a very simple method but requires an empirial orretion (fudge fator) for the etted diameter of the dispense tip. Usually many drops (minimum three drops) are dispensed into a eighing boat and taken to a sensitive balane [5]. Knoing its density, the mass an be alulated. The drop volume method is useful hen it is diffiult to form a pendant drop ith suffiient stability. Beause the pendant drop detahment proess is irregular, it is best to average a number of measurements [5]. - ring (plate) method It is knon that the ring method as the first method to be developed. This is hy many of the values for interfaial and surfae tension given in the literature are the results of the ring method. In the ring method the liquid is raised until ontat ith the surfae is registered. Fig.5. Sheme of ring method [5] Similarly, in the plate method the liquid is raised until the ontat beteen the surfae (interfae) and the plate is registered. The maimum tension ats on the balane at this moment. 7

8 Adsorption at the liquid/gas interfae Fig.6. Sheme of plate method [5] - maimum bubble pressure method III. 4. Maimum bubble pressure method One of the useful methods to determine the dynami surfae tension is measuring the maimum bubble pressure or simply bubble pressure (Rebinder s method). Fig. 7. The gas bubble (dr is derease of radius) 8

9 The pressure in the Rebinder s devie produes air bubbles at onstant rate and blos them through a apillary hih is submerged in the sample liquid and its radius is already knon. The surfae free energy for bubble is equal to 4π r 2. The pressure inside the gas bubble ontinues to inrease and the maimum value is obtained hen the bubble has a ompletely hemispherial shape hose radius is orresponding to that of the apillary. A bubble appears on the end of the apillary. If the radius of a bubbles inreases from r to r+dr, then the inrease in surfae free energy ill be 8 π r dr. At the point of the maimum bubble pressure, the bubble has a omplete hemispherial shape hose radius r is idential to that of the apillary denoted by R ap. The surfae tension an be determined using the Young and Laplae equation in the redued form for the spherial bubble shape ithin the liquid: r P = (9) 2 here: r is the bubble radius idential to that of the apillary denoted by R ap. Bubble pressure in the apillary is measured by the Rebinder manometer filled ith liquid (for eample ater, density d). Then: P = h d g (10) here: h is the differene beteen height of liquid in the manometer arms h r g d = (11) 2 After ahieving the maimum pressure, the pressure in the bubble dereases and the radius of the bubble inreases until the bubble is detahed from the end of the apillary and a ne yle begins. Usually relative measurements are used for standard (ater, surfae tension, ) and tested liquids (surfae tension, ). Their surfae tensions are given from the relation: h = h (12) or 9

10 Adsorption at the liquid/gas interfae h = (13) h here / h is the onstant and it an be substituted by symbol k. Then the surfae tension of the tested liquid an be presented in the form: = k h (14) The bubble pressure method is ommonly used to measure the dynami surfae tension for the system ontaining surfatants or other impurities beause it does not require ontat angle measurement and has high auray even though the measurement is performed rapidly. Moreover this method is an appropriate tehnique to apply to biologial fluids like serum beause it does not require a large amount of liquid sample. 10

11 IV. Eperimental A. Apparatus and materials 1. Apparatus: Rebinder s devie for measuring the surfae tension by the maimum bubble pressure method. 2. Glass equipment: alibrated flask (25 m 3 ) 4 p., plasti vessels (100 m 3 ) 21 p., alibrated pipettes (10 m 3, 25 m 3 ), beaker (400 m 3 ), ash bottle, thermometer, absorbent paper. 3. Reagents: aqueous solutions : alohols: methyl, ethyl and propyl (onentrations 2.5; 1.0; 1.0 M), aids: formi, aeti and propioni (onentrations 2.5; 1.0 ; 1.0 M), NaCl or KCl (2.0 M). B. Task sheme 1. Determination of surfae tension values for the homologous series of alohols or arboyli aids aqueous solutions and inorgani eletrolyte by the maimum bubble pressure method. 2. Verifiation of the Traube s rule. C. Apparatus servie Before measurements hek if ater from bottom vessel [6] has overflon to the upper vessel and if a ok [4] is losed. Then the measuring vessel [1] (after preise leaning) fill ith ater and set up apillary [2] (after preise leaning and drying) to touh a liquid surfae. Close the ok [3] and open the ok [5] in suh a ay that ater drips very, very sloly to the vessel [6]. After determining the ater flo from the upper to the bottom vessel during the hole measurement it must not be hanged. During measurements the pressure ontinues to inrease to suh a value thet bubbles appear on the end of the apillary and at this moment make a readout of the height of liquid in the Rebinder manometer. 11

12 Adsorption at the liquid/gas interfae Fig. 7. Sheme of the Rebinder s devie to measure the surfae tension by the maimum bubble pressure method In the net measurement open a ok [3], to balane a pressure in the apparatus ith the eternal pressure (same height of liquid in the manometer arms). Close the ok again [3], and inrease pressure to the value that a bubbles ill appear on the end of the apillary. Read the differenes in the liquid levels in the manometer for the maimal defletion. h and h (for ater and investigated solutions) are sum of liquid heights in the left and right arms of manometer (starting from zero level). 12

13 D. Program of ativity 1. Prepare 25 m 3 aqueous solution of alohols or aids (aording to the demonstrator s instrutions). To aomplish this, 2.5 m 3 of initial solution onentration: 2.5 M CH 3 OH (or HCOOH), 1.0 M C 2 H 5 OH (or CH 3 COOH), 1.0 M C 3 H 7 OH (or C 2 H 5 COOH), 2.0 M NaCl (or KCl). drop to the alibrated flask (apaity 25 m 3 ), then filled ith distilled ater to the sale mark. Transfer a prepared solution to a plasti vessel ith number 1. For the residual solutions there are the same readings but: 5, 10, 17.5 or 25 m 3 of stok solution. Calulate a final onentration of thus prepared solutions 2. Measure temperature of distilled ater used to prepare the solutions. 3. Measure a surfae tension of distilled ater and all prepared solutions in the Rebinder s devie onforming the instrutions of the apparatus. After measurements the distilled ater must be flon from the bottom to the upper vessels. E. Results and disussion 1. Read a surfae tension of distilled ater, from Table I at the measurement temperature. Table I. T [ o C] [mn/m] T [ o C] [mn/m]

14 Adsorption at the liquid/gas interfae 2. Calulate a onstant k for apillary in aordane ith: k = (15) h 3. Calulate the surfae tension of the solutions aording to equation: = k h (16) 4. Plot the relation of the surfae tension of the investigated homologous solutions as a funtion of their onentration, = f () (all urves start from the surfae tension of distilled ater, for the onentration = 0). On the same plot illustrate the relation, = f () for NaCl (or KCl). 5. Based on the obtained plot verify the Traube s rule. For the same value of surfae tension, alulate the ratio of onentrations for to members of a homologous series: CH3OH C2H 5OH and C2H 5OH C3H7OH (17) 6. Put the obtained results in Table II. Table II. Substane CH 3 OH Conentration [mol/dm 3 ] h [m] [mn/m] C 2 H 5 OH C 3 H 7 OH NaCl 14

15 or Substane HCOOH Conentration [mol/dm 3 ] h [m] [mn/m] CH 3 COOH C 2 H 5 COOH NaCl 6. Verify the Traube s rule on the ommon graph = f (). For eample: Butanoi aid Surfae tension, [mn/m] ,0 0,1 0,2 0,3 0,4 0,5 Conentration, [mol/dm 3 ] 15