UMR ChemLabs PCh8-99 - Diagram of a Binary : The Question of Fatty Acids Dimers in the Liquid Phase Gary L. Bertrand University of Missouri-Rolla

Overview Two components will be assigned for this experiment. One will be a carboxylic acid, and the other will be a relatively non-polar material. Pre-Lab: Access the Computer-Simulated Experiment FPWin.STA or FPMac, and observe the DEMO section of this simulation. If you have any questions about the performance of the actual experiment, go through several exercises with the simulation. Students will obtain the required physical properties of the assigned materials from handbooks or other sources: Molecular Weight, Point, and of Fusion. These will be used in spreadsheet calculations to prepare graphs representing the equilibrium - composition diagram for co-existence of ideal with these two pure solid components. One of these diagrams will assume that the carboxylic acid exists entirely as monomers in the melt, and the other will assume that it exists entirely as dimers. By analysis of these diagrams, students will select four mass fractions (in addition to the pure components) at which experimental measurements will give the most definitive differentiation between the two models, and provide a reasonable description of the real system. Laboratory: Starting with 5-6 grams of a pure component (A) and adding two increments of the other (B), three cooling curves will be obtained for one-half of the phase diagram. The other half of the phase diagram will be obtained by starting over with 5-6 grams of the other pure component (B) and adding two increments of A. It is likely that the experimental work will be divided between two groups. Cooling curves will be recorded with the Vernier data acquisition system on laboratory computers. It is important that this data be transferred to a floppy disk, along with a text file describing the composition for each recorded curve, before leaving the laboratory. The TA will insure that this data is made available to all students.

Thermodynamic Relationships The equilibrium of a component (A) between a pure solid (S) phase and a pure or mixed liquid (L) phase:

A(S,T,P) ® A(L,T,P,XA) ; XA = is described in terms of the Raoult’s Law activity (aA) as T ln(aA) = ln(XAgA) = ò (DfusHA°/RT2)dT (1) TA° This relationship is derived in most texts in the unit on Colligative Properties, though many only present an approximate . The utility of Eq (1) derives from the fact that the quantity on the right depends solely on the temperature and properties of the pure component. It is important to note that as the activity of the component decreases (the Raoult’s Law activity cannot be greater than unity), the equilibrium temperature must decrease, since the enthalpy of fusion (DfusHA°) is a positive quantity.

1 The application of Eq (1) to an ideal liquid solution (gA = gB = 1) neglecting the difference in the heat capacities of the solid and liquid phases gives ln(XA) = -(DfusHA°/R)(1/T - 1/TA°) (2a) and ln(XB) = -(DfusHB°/R)(1/T - 1/TB°) (2b) These equations may be improved by including terms for DfusCpA° and DfusCpB°, and with estimated values for activity coefficients. They are used to model the solid-liquid phase diagram for pure in equilibrium with an ideal liquid solution. Values of T are calculated from these equations for values of XA and XB ranging from 0 to 1.0, generating two lines - one from Eq. (2a) for pure solid A in equilibrium with the solution, and one from Eq (2b) for pure solid B in equilibrium with the solution. These are graphed as T vs XA(= 1 - XB). They cross at the temperature and composition known as the Eutectic Point.

Dimer

Monomer

This calculation is easily performed with a spreadsheet such as Microsoft Excel or Corel QuattroPro. Since experimental will be prepared by weighing the components, it is more convenient to base the calculations on mass fractions rather than mole fractions. Create a column (Column B) with values for mass fraction of A ranging from zero to 1 in increments of 0.05. In a column to the left of this(Column A), create a column which will convert mass fractions to mole fractions. In Columns C and D, calculate the equilibrium for components A and B. [Equation 3a shows an error for XA = 0, and Equation 3b shows an error for XA = 1.] The equilibrium temperature for solid A in equilibrium with the solution (the melt) is T = 1/ [1/TA° - (R/DfusHA°)ln(XA)] (3a) and for component B, T = 1/[1/TB° - (R/DfusHB°)ln(1 - XA)] (3b) By observing the differences between the temperatures calculated with Equations (3a) and (3b) for the same composition, the cross-over condition (the eutectic) may be easily identified. The spreadsheet may be expanded in this region for smaller increments of composition to obtain a better estimate of the eutectic temperature and composition. Equilibrium temperatures calculated below this temperature have no physical meaning, since one of the components will precipitate before such temperatures are reached. The spreadsheet can be used to construct a graph with a temperature scale ranging from slightly above the higher of a pure component to slightly below the

2 eutectic temperature. Two separate lines are graphed with the solutions to Equations (3a) and (3b), crossing with a discontinuity in slope at the eutectic point. Dimer Model: Carboxylic acids are known to have a tendency to form hydrogen - bonded dimers in the solid state and when dissolved in non-polar . There are then two different ways to model the “” leading to Equations (2a,b) and (3a,b). These will obviously differ in the molecular weight assigned to the carboxylic acid, since a dimer weighs twice as much as a monomer. The enthalpy of fusion is an experimental quantity which is determined with the primary units of energy/mass. The molar enthalpy of fusion is reported for one gram-molecular-weight of the monomer, and the molar enthalpy of fusion for the dimer model is then twice the molar enthalpy of fusion of the monomer. On the spreadsheet discussed above, calculate the mole fraction (Column G) from the weight fraction (Column B) for the Dimer Model, by dividing the weight fraction of the acid by twice its normal molecular weight. These mole fractions are used to calculate the equilibrium temperatures in Columns E and F with the same equations that were used in Columns C and D, except that the enthalpy of fusion for the acid is doubled. Select the data block in columns B through G to create two phase diagrams on a single graph. These graphs based on the ideal solution models will be compared to experimental data to gain insight regarding the actual state of the carboxyllic acid molecules in solution. It is interesting to consider the effect of the model on the point depresssion constant (Kf), which can be calculated from Eq (1). Kf = (MARTA°2)/(1000 DfusHA°) . The effect of the model on the molecular weight is cancelled by the effect on the molar enthalpy of fusion, so the experimental evaluation of the freezing point depression constant gives no information regarding the model.

Cooling Curves Experimental solid - liquid phase diagrams are constructed from observations of the cooling curves (temperature vs time) of molten mixtures through the point of solidification. When a pure liquid is cooled, the temperature may drop below the melting point without the formation of - a phenomenon known as “supercooling”. As soon as the first crystals form, however, the temperature rises quickly to the melting point and remains constant. The heat (enthalpy) released by the solidification process (the negative of the enthalpy of fusion) exactly compensates the heat transfer to the surroundings, maintaining the equilibrium temperature as long as both liquid and solid phases are present. When solidification is complete the temperature again decreases with time. A similar process occurs if an impurity is present in the liquid, but after supercooling, the temperature returns to a slightly lower value since the activity of the is less than unity. In this case, however, the formation of a pure solid phase lowers the (and the activity) of that component in the liquid phase and thus lowers the equilibrium temperature. The heat of solidification compensates for the heat transfer to the surroundings, at a slowly but steadily deceasing temperature. If supercooling is minimal, the cooling curve shows a sharp discontinuity in slope at the temperature at which the pure solid is in equilibrium with a solution of the original composition of the melt. This temperature must be estimated if supercooling distorts the discontinuity. As solid is removed from the solution, the concentration of that component decreases, leading to further lowering of the equilibrium temperature. The composition of the remaining liquid phase may eventually reach a point such that both materials begin to solidify - the eutectic point. The liquid composition and the temperature then remain

3 constant until all of the material has solidified. This region of the cooling curve is often not observed, and may be obscured by the appearance of new solid phases. When these complexities are not present, this region of constant temperature will be observable if the initial composition of the liquid is close to the eutectic composition. If there are no new solid phases, this horizontal region of the cooling curve will occur at the same temperature, irrespective of the initial composition of the mixture. If the initial composition of the mixture is exactly that of the eutectic, the cooling curve will flatten at the eutectic temperature in the same manner as a pure component. The phase diagram is constructed by plotting the temperature of the discontinuity for each cooling curve vs the corresponding composition of the melt.

Experiment: In the laboratory, observe the actual cooling curves for the calculated compositions, based on the ideal solution graphs. If the expected temperature is above 40°C, the “bath” can be the air in the room. For lower temperatures, a beaker of cold may be required. If the break point is expected above 40°C and the eutectic is expected at a lower temperature, observe the break (and the appearance of crystals) in air then take a few more readings before transferring to a water bath. Try to observe the eutectic halt for at least one composition near the eutectic composition.

Report: Show the observed cooling curves, indicating the point at which crystals were first observed on each. Note any eutectic points that were observed. Plot the experimental points on the graphs constructed from the spreadsheets. Comment on similarities and differences between the experimental and model phase diagrams.

References: 1 Atkins, Peter Physical Chemistry, 6th Ed., Freeman, NY, 1998, p. 204-5 2. Halpern, A. M. Experimental Physical Chemistry, 2nd Ed., Prentice-Hall, Upper Saddle River, NJ 1997, p. 233.

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