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CH3511: PHYSICAL CHEMISTRY LAB I Lab 6: Colligative Properties: Freezing Point Depression PRELIMINARY REPORT November 15, 2004 Section 1, Group 1 R. B. Student ([email protected]) T. Y. Student (tystudent) M. G. Student ([email protected]) INTRODUCTION In this experiment, the molar heat of fusion and the freezing point depression constant of water will be calculated. The system being studied is an aqueous solution of varying salts. Multiple systems containing different concentrations (ranging from 0.0179 m to 0.8961 m) of the salts magnesium chloride hexahydrate and calcium chloride dihydrate will be observed. An Omega HH508 digital thermometer will be used to measure the freezing points of each solution. From these freezing points, the freezing point depression of each solution caused by colligative properties will be used to determine the degree of dissociation of the salts in conjunction with the provided sucrose data [1]. THEORY Whenever a pure substance undergoes a phase change at constant temperature (for instance from liquid to solid), equilibrium is reached between the two phases such that the chemical potentials of the two phases are equal, satisfying equation (1). µ A( s ) * = µ A( l ) * (1) Where µA(s)* is the chemical potential of pure substance A in the solid phase and µA(l)* is the chemical potential of pure substance A in the liquid phase. Since the chemical potentials of the two phases are only equal at one temperature (for a specified pressure), it can be concluded that chemical potential is a function of temperature. For equation (1) relating the liquid and solid phases, the specific temperature is called the freezing temperature, Tf. When a solute is added to the liquid phase, forming a solution with A as the solvent, the chemical potential of A in the solution is usually lower than the chemical potential of pure liquid A. This expression is displayed in expression (exp1). µ A( s ln) < µ A(l ) * (exp1) Where µA(sln) is the chemical potential of substance A in the solution. With the reduced * chemical potential of the non-solid phase, the temperature at which µ A( s ) = µ A( s ln) is reduced, exhibiting a freezing point depression in the solution. Equation (2) relates the chemical potential of substance A in solution to the chemical potential of pure substance A (as a liquid) for all solutions. µ A( s ln) = µ A(l ) * + R ⋅ T ⋅ ln (Α A ) (2) Where R is the gas constant, T is the absolute temperature, and ΑA is the activity of * substance A in solution. At the freezing temperature, µ A( s ) = µ A( s ln) , transforming equation (2) into equation (3). 2 µ A( s ) * = µ A(l ) * + R ⋅ T f ⋅ ln (Α A ) (3) Rearranging equation (3) produces equation (4). ln (Α A ) = µ A( s ) * − µ A( l ) * (4) R ⋅Tf Using the definition of chemical potentials, it can be observed that the chemical potential of a pure substance (a single phase) is equal to the molar Gibbs energy of that substance. This relation is described in equation (5). ∂G * = Gm, A ∂ n T ,P µ A* ≡ (5) Where G is Gibbs energy, n is moles, P is pressure, and Gm,A* is the molar Gibbs energy of pure substance A. Applying equation (5) to equation (4) twice produces equation (6). ln (Α A ) = * G m , A( s ) − G m , A( l ) * (6) R ⋅Tf Where Gm,A(s)* is the molar Gibbs energy of pure substance A in the solid phase and Gm,A(l)* is the molar Gibbs energy of pure substance A in the liquid phase. The molar change in Gibbs energy for fusion of substance A is then defined in equation (7). * ∆ fus Gm , A ≡ Gm , A(l ) − Gm , A( s ) * (7) Where ∆ fus Gm , A is the molar change in Gibbs energy for fusion of substance A. Applying equation (7) to equation (6) produces equation (8). ln (Α A ) = − ∆ fus Gm , A R ⋅Tf (8) The definition of activity is then presented in equation (9). Α A = γ A ⋅ xA (9) Where γA is the mole-fraction-adjusted activity coefficient of substance A and xA is the mole fraction of substance A in the solution. Applying this definition to equation (8) produces equation (10). 3 ln (γ A ⋅ x A ) = − ∆ fus Gm, A (10) R ⋅Tf For dilute solutions under ideal conditions, γA is equal to 1 and equation (10) simplifies to equation (11). ln ( x A ) = − ∆ fus Gm, A (11) R ⋅Tf Differentiating equation (11) with respect to Tf produces equation (12). − ∆ fus Gm , A d R ⋅T d (ln( x A )) f = dT f dT f (12) Using an applied form of the results from the discussion on pages 182-183 of Levine [2], equation (13) can be produced. − ∆ fus Gm , A d R ⋅T ∆ H f = fus m , A 2 dT f R ⋅Tf (13) Where ∆ fus H m, A is the molar heat of fusion of substance A. Substituting equation (13) into equation (12) produces equation (14). d (ln ( x A )) = ∆ fus H m , A R ⋅Tf 2 ⋅ dT f (14) Using mathematical formulas for differentiation, equation (14) can become equation (15). d (ln ( x A )) = − ∆ fus H m , A R 1 ⋅ d T f (15) By equation (15), the slope of ln(xA) with respect to (1/Tf) is directly proportional to the molar heat of fusion of substance A, allowing the molar heat of fusion of substance A to be directly calculated from the slope of the plot. The integration of equation (14) from a state of pure substance A (xA = 1 and Tf = Tnfp, the normal freezing point) to another state (0 < xA < 1) produces equation (16). For this 4 integration, it was assumed that the molar heat of fusion of substance A was constant with respect to temperature/freezing temperature. xA Tf 1 Tnfp ∫ d (ln(xˆ A )) = ∫ ln ( x A ) − ln(1) = ln ( x A ) = ∆ fus H m , A ⋅ dTˆ f ⇒ 2 R ⋅ Tˆ f ∆ fus H m, A 1 1 ⋅ − ⇒ T R nfp T f ∆ fus H m , A T f − Tnfp ⋅ T ⋅T R f nfp (16) Where x̂ A and Tˆ f are dummy variables for integration. It should be noted that Tfpd is the same as the freezing point of pure substance A, Tf*. The change in freezing temperature caused by the addition of solute, ∆Tfpd, can be defined by equation (17). ∆T fpd ≡ T f − Tnfp (17) If it is assumed that ∆Tfpd is small, that is, Tf ≈ Tnfp, equation (16) can be simplified to equation (18). This simplification also applies equation (17). ln ( x A ) = ∆ fus H m , A ∆T fpd ⋅ T 2 R nfp (18) In the derivation of equation (18), it was assumed that the solution was ideal in order to simplify the activity expression. If it is further assumed that the solution is dilute, equation (19) will hold. ln ( x A ) = − x B (19) Where xB is the mole fraction of the solute (substance B) in the solution. The definition of mole fraction is then displayed in equation (20). xB = nB n A + nB (20) Where nB is the number of moles of substance B in solution and nA is the number of moles of substance A in solution. In a dilute solution where substance A is the solvent, equation (20) can be simplified to equation (21). xB = nB nA (21) 5 The definition of molality is displayed as equation (22). m= nB mA (22) Where m is the concentration of the solution (molality) and mA is the mass of substance A (solvent) in the solution. Recognizing that mA = nA * MWA (where MWA is the molecular weight of substance A), equation (22) can be reduced to equation (23). m= nB x = B n A ⋅ MW A MW A (23) Substituting equation (23) into equation (19) and then into equation (18) produces equation (24). − m ⋅ MW A = ∆ fus H m , A ∆T fpd ⋅ T 2 R nfp (24) Solving equation (24) for ∆Tfpd produces equation (25). ∆T fpd = − MW A ⋅ R ⋅ Tnfp 2 ∆ fus H m , A ⋅m (25) In the derivation of equation (25), several assumptions about the solution were made. It was assumed that the solution is at constant pressure, the molar heat of fusion of substance A is constant with respect to temperature, the solution is ideal, the solution is dilute, and that ∆Tfpd is sufficiently small. The molal freezing-point depression constant, Kf, is then defined by equation (26). Kf = MW A ⋅ R ⋅ Tnfp 2 ∆ fus H m , A (26) Substituting equation (26) into equation (25) produces equation (27). ∆T fpd = − K f ⋅ m (27) Colligative properties have been shown in previous experiments to be dependent on the number of species in the solution, not solely on the concentration of the solute in the solution [1]. However, for a solution with a non-electrolytic solute, equation (27) still 6 holds. For this reason, the van’t Hoff factor, i, is used to account for the increased colligative properties of electrolytes. The van’t Hoff is defined in equation (28). i= ∆T fpd (∆T ) (28) fpd 0 Where ∆Tfpd is the freezing point depression of a solution with electrolytes and (∆Tfpd)0 is the freezing point depression of a solution with a non-electrolytic solute at the same concentration. As the concentration (molality) of the solution decreases, the van’t Hoff factor approaches the number of species in solution (1 for non-electrolytes like sucrose, 2 for 2-species electrolytes like sodium chloride, 3 for 3-species electrolytes like magnesium chloride, etc.). Since the colligative properties of a non-electrolytic solute can be described by equation (27), equation (29) must hold. (∆T ) fpd 0 = −K f ⋅ m (29) Substituting equation (29) into equation (28) and rearranging produces equation (30). ∆T fpd = −i ⋅ K f ⋅ m (30) Equation (30) then accounts for the freezing point depression of solutions of both electrolytes and non-electrolytes. The laboratory information sheet provided on the CH3511 website [1] and the textbook Physical Chemistry by Ira Levine [2] were used heavily in the preparation of this analysis. PRE-LABORATORY EXERCISES 1. The requested information was included in the theory section of the report. 2. Using the CRC Handbook of Chemistry & Physics, 1996-1997 edition [3], the literature values for the Kf of water and the molar heat of fusion of water. The Kf value was found to be 1.86 K-kg/mol and the molar heat of fusion was found to be 6.01 kJ/mol at the normal freezing point of water (Tnfp = 0.00°C). 3. The requested information was included in the procedure section of the report. 4. The normal freezing point of ethanol was obtained from the CRC Handbook of Chemistry & Physics [3] and found to be -114.1°C at 0.1 MPa (roughly atmospheric pressure). The freezing point depression of the solution of methanol in ethanol was then calculated using this normal freezing point of ethanol and equation (17). 7 ∆T fpd ≡ T f − Tnfp = -115.3°C – (-114.1°C) = -1.2°C This freezing point depression represents the (∆Tfpd)0 since methanol is not an electrolyte. Using equation (17), the freezing point depression of the KCl in ethanol solution was also calculated to be -2.0°C. This freezing point depression represents a ∆Tfpd since KCl is an electrolyte. Lastly, the van’t Hoff factor for KCl in ethanol was calculated using the freezing point depressions of the two solutions and equation (28). Equation (28) was only able to be used since the two solutions had the same concentration (1 molal). i= ∆T fpd (∆T ) fpd 0 = -2.0°C / -1.2°C = 1.67 The calculated van’t Hoff factor for KCl in ethanol is not the expected value. Since two dissociated species are produced when KCl is dissolved in solution, the expected van’t Hoff factor for KCl would be 2. According to the laboratory protocol [2], the van’t Hoff factor is only equal to the “expected” value for decreasingly lower concentrations (small molalities), as described in equation (1e). lim i = iexp ected m →0 (1e) At higher concentrations, the van’t Hoff factor is lower than the expected value, as observed with the data for this question—1 molal solutions are sufficiently concentrated for the van’t Hoff factor to differ from the expected value. EXPERIMENTAL PROCEDURE I. II. Equipment Setup A. Place 25mL of distilled water into a test tube. B. Place the thermometer probe with the metal stirrer around it into the test tube. 1. Make sure that the thermometer probe is attached to an Omega HH508 digital thermometer. C. Fill the Dewar with liquid nitrogen. D. Layer a large beaker with equal amounts of non-reagent-grade salt and ice. Calibration A. Attach the test tube to a ring stand with a clamp. 8 III. B. Slowly lower the test tube into the Dewar until the water in the test tube is submerged in the liquid nitrogen. C. Use the metal stirrer to stir the water. D. Remove the test tube when the water is close to freezing and place it in the ice/salt/water bath until it freezes in order to slow the freezing process and obtain a more accurate reading. 1. Continue stirring while the test tube is in the ice/salt/water bath. E. When solid ice is present and the temperature remains constant, record the temperature from the digital thermometer. 1. This temperature is the freezing point. 2. Do not use the lower temperature produced by super cooling. F. After the water is significantly slushy, place the test tube in a beaker of warm water until all the slush is melted. G. Cool the water again using the same procedure to obtain more freezing temperatures. 1. Repeat this process enough times to determine the freezing point of water. Collection of Freezing Point Depression Data A. Prepare 12 solutions of roughly 35mL of MgCl2·6H2O and CaCl2·2H2O 1. Prepare the solutions using the mass of water to obtain concentration in molalities. 2. The freezing point depressions should range from 0.1 to 1K, ~2.5K, and ~5K (in absolute value). Solubility may limit the freezing point depressions to less than 5 degrees. A sample calculation using equation (30) is given for a freezing point depression of 0.1 K in an aqueous solution of magnesium chloride hexahydrate (i = 3, ideally). The literature value of 1.86 Kkg/mol was used for the Kf of water. By definition, ∆Tfpd is negative, so the value -0.1 K is used. ∆T fpd = −i ⋅ K f ⋅ m ⇒ m= − ∆T fpd i⋅Kf = – -0.1 K / (3 * 1.86 K-kg/mol) = 0.0179 m Using the definition of molality, the amount of solute can be calculated using equation (1p) as described in the next sample calculation (for magnesium chloride hexahydrate). For this calculation, it is assumed that the mass of the solution is 35 g and that the entire mass of the solution comes from the water solvent (for dilute solutions, the mass of solute is negligible). 9 m= n solute mass solute = ⇒ mass solvent MWsokute ⋅ mass solvent (1p) mass solute = m ⋅ MWsolute ⋅ mass solvent = 0.0179 m * 203.29 g/mol * 35 g = 0.128 g In a similar fashion, the mass of calcium chloride dihydrate can be calculated using the formula weight of calcium chloride dihydrate instead of the formula weight of magnesium chloride hexahydrate. Table I displays the desired freezing point depression (in absolute value), the corresponding solution concentration (in molality), and the amounts of magnesium chloride hexahydrate and calcium chloride dihydrate needed to make the solutions. Table I: Masses of MgCl2·6H2O and CaCl2·2H2O Needed for the Desired Solutions ∆Tf (K) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.5 5.0 m (molal) mass MgCl2·6 H20 (g) mass CaCl2·2 H20 (g) 0.0179 0.128 0.092 0.0358 0.255 0.184 0.0538 0.383 0.277 0.0717 0.510 0.369 0.0896 0.638 0.461 0.1075 0.765 0.553 0.1254 0.893 0.645 0.1434 1.020 0.738 0.1613 1.148 0.830 0.1792 1.275 0.922 0.4480 3.188 2.305 0.8961 6.376 4.611 B. Determine the freezing point of each solution using the procedure described above for determining the freezing point of water. C. Calculate the freezing point depression of each solution using equation (17). ∆T fpd ≡ T f − Tnfp = -1.5°C – 0.0°C = -1.5 K IV. For an aqueous solution with a freezing point of -1.5°C. Data Analysis A. Correct molality concentrations so that the mass of solvent includes the water from the hydrated salts. This can be accomplished using equation (2p). mass water ,corrected = mass water + mass solute ⋅ hydrate ⋅ MWwater MWsolute (2p) 10 = 35.0000 g + 0.6579 g / (203.29 g/mol) * 6 * 18.01 g/mol = 35.3497 g Where masswater,corrected is the corrected mass of water in the solution hydrate is the number of water molecules associated with each formula unit of the salt (6 for magnesium chloride hexahydrate). MWwater is the molecular weight of water B. Construct a plot of ∆Tfpd versus m to determine the molal freezing point depression constant for water, which can be calculated from the slope of the plot using the differential of equation (30) with respect to m and the ideal van’t Hoff factor for the solute. This relationship is described in equation (3p). ∆T fpd = −i ⋅ K f ⋅ m ⇒ d (∆T fpd ) dm = −i ⋅ K f ⇒ (3p) d (∆T fpd ) dm Kf = −i = -4.76 K-kg/mol / -3 = 1.59 k-kg/mol C. Calculate the van’t Hoff factor for the two electrolytes using the measured data the sucrose data provided from the CH3511 website [1], and equation (28). i= ∆T fpd (∆T ) fpd 0 = -1.50 K / -0.51 K = 2.94 D. Construct a plot of ln(xA) vs. 1/Tf to determine the molar heat of fusion for water. xA is the mole fraction of water in each solution. The molar heat of fusion of water can be calculated from a rearranged form of equation (15). d (ln ( x A )) = − ∆ fus H m , A ∆ fus H m , A = − R ⋅ R 1 ⋅ d T f d (ln ( x A )) d (1 T f ) ⇒ = - 8.3145 J/(mol-K) * -7195 K = 59.8 kJ/mol 11 The slopes of the plots used in the calculations of steps B and D can be obtained from the linear regression of the appropriate data sets. SAFETY Information concerning the safety of all reagents used in a laboratory is crucial in the event of unforeseen problems. For this reason, safety guidelines for all used reagents were compiled in Tables II, III, IV, V, VI, and VII. General laboratory safety procedures like wearing eye protection and gloves (when needed) were followed in addition to the safety guidelines outlined in these tables. Table II: Safety Guidelines for Sucrose [4] Description Physical Constants Acute Chemical Hazards Disposal First Aid Fire Extinguishing Spills white or colorless solid MW 342.29 gram/mole BP N/A MP 185.0˚C eye irritation, skin irritation, respiratory tract irritation, gastrointestinal tract irritation, and digestive tract irritation dispose of in a designated disposal container skin: flush with plenty of water for 15 min. eyes: flush with plenty of water for 15 min. inhalation: remove to uncontaminated area, seek medical attention ingestion: if alert and conscious, give 2-4 cupfuls of milk water spray, dry chemical, carbon dioxide, or appropriate foam sweep up or vacuum material, place in a disposal container Table III: Safety Guidelines for Sodium Chloride [5] Description Physical Constants Acute Chemical Hazards Disposal First Aid Fire Extinguishing Spills white or colorless solid MW 58.43 gram/mole BP 1412.6˚C MP 801.0˚C eye irritation, skin irritation, respiratory tract irritation, nausea, vomiting, gastrointestinal tract irritation, rigidity, and convulsions dispose of in a designated disposal container skin: flush with plenty of water for 15 min. eyes: flush with plenty of water for 15 min. inhalation: remove to uncontaminated area, seek medical attention ingestion: if alert and conscious, give 2-4 cupfuls of milk water spray, dry chemical, carbon dioxide, or chemical foam sweep up or vacuum material, place in a disposal container 12 Note: non-reagent-grade sodium chloride is used in this experiment. The safety guidelines outlined above should still be followed. Table IV: Safety Guidelines for Magnesium Chloride Hexahydrate [6] Description Physical Constants Acute Chemical Hazards Disposal First Aid Fire Extinguishing Spills white to gray-white solid MW 203.2914 gram/mole BP 1412˚C MP 118˚C eye irritation, skin irritation, digestive tract irritation, respiratory tract irritation, nausea, vomiting, diarrhea, and metal fume fever (metallic taste, fever, chills, cough, weakness, chest pain, muscle pain, and increased white blood cell count) dispose of in a clean, dry disposal container skin: flush with plenty of water for 15 min. eyes: flush with plenty of water for 15 min. inhalation: remove to uncontaminated area, seek medical attention, do not attempt mouth to mouth resuscitation material will not burn sweep up of absorb material, place in a clean, dry disposal container Table V: Safety Guidelines for Calcium Chloride Dihydrate [7] Description Physical Constants Acute Chemical Hazards Disposal First Aid Fire Extinguishing Spills white, odorless solid MW 147.0128 gram/mole BP 1599.8˚C MP 259.9˚C eye irritation, skin irritation, gastrointestinal tract irritation, respiratory tract irritation, nausea, vomiting, seizures, rapid respiration, slow heartbeat, cardiac disturbances, and burns dispose of in a clean, dry disposal container skin: flush with plenty of water for 15 min. eyes: flush with plenty of water for 15 min. ingestion: if alert and conscious, give 2-4 cupfuls of milk inhalation: remove to uncontaminated area, seek medical attention, do not attempt mouth to mouth resuscitation material will not burn sweep up or vacuum material, place in clean, dry disposal container Table VI: Safety Guidelines for Liquid Nitrogen [8] Description Physical Constants colorless, odorless, cryogenic liquid MW 28.01 gram/mole BP -195.8˚C 13 Acute Chemical Hazards Disposal First Aid Fire Extinguishing Spills MP -209.9˚C dizziness, drowsiness, nausea, vomiting, excess salivation, diminished mental alertness, loss of consciousness, tissue freezing, severe burns, blisters do not attempt to dispose of unused product, return excess and container to supplier skin: warm frostbit area with warm water, seek medical attention eyes: warm frostbit area with warm water, seek medical attention inhalation: remove to uncontaminated area nonflammable evacuate area immediately and monitor oxygen level Table VII: Safety Guidelines for Water [9] Description Physical Constants Acute Chemical Hazards Disposal First Aid Fire Extinguishing Spills colorless, odorless liquid MW 18.0134 gram/mole BP 100°C non-hazardous Sink skin: no treatment eyes: no treatment ingestion: no treatment inhalation: no treatment liquid will no burn absorb with inert material and put in container REFERENCES 1. Smith, Kelley, “Physical Chemistry Lab”. <http://www.chemistry.mtu.edu/~kmsmith/PChem>. 14 Sep. 2004. 2. Levine, Ira N. Physical Chemistry, Fifth Edition, McGraw-Hill, New York, 2002, pp. 342-346. 3. Lide, David R. (ed.), et al. Handbook of Chemistry and Physics. The Chemical Rubber Company, Cleveland, OH, 1997, pp. 6-10, 6-53, 6-128, 6-131, 15-21. 4. “MSDS: Sucrose”. <https://fscimage.fishersci.com/msds/96540.htm>. 14 Nov. 2004. 5. “MSDS: Sodium Chloride” <https://fscimage.fishersci.com/msds/21105.htm>. 14 Nov. 2004. 6. “MSDS: Magnesium Chloride Hexahydrate”. <https://fscimage.fishersci.com/msds/13365.htm>. 14 Nov. 2004. 7. “MSDS: Calcium Chloride Dihydrate”. <https://fscimage.fishersci.com/msds/03901.htm>. 14 Nov. 2004. 14 8. “MSDS: Liquid Nitrogen”. <http://www.medicine.uiowa.edu/biochemstores/Pages/ln2msds.htm>. 14 Nov. 2004. 9. “MSDS: Water”. <http://www.chemistry.mtu.edu/~djchesne/classes/ch2212/>. 31 Aug. 2004. 15