Binary Solid-Liquid Phase Diagram – Benavides
The purpose of this experiment is to study heterogenous equilibrium between solid and liquid phases of a two-component binary mixture consisting of naphthalene and diphenylamine. The solid-liquid phase diagram will be constructed by measuring the cooling curves of the mixture at different overall compositions. The eutectic temperature and composition will be determined from the phase diagram.
A solid-liquid phase diagram shows the phase relationships in mixtures of two or more components as a function of composition and temperature, at constant pressure. These diagrams are very helpful in understanding the behavior of mixtures for applications such as metallurgy. Our system, naphthalene and diphenylamine produces a solid-liquid phase diagram that consists of four regions: (1) all liquid, (2) mixed liquid plus solid A, (2) mixed liquid plus solid B, (4) all solid (see figure 1a). When this mixture is cooled, one component preferentially solidifies out (phase separation). As the temperature is lowered, the remaining solution reaches a unique composition and temperature, referred to as the eutectic composition and eutectic temperature, at which both components solidify simultaneously.
Figure 1. (a) Solid-liquid phase diagram. (b) Cooling curves at various overall compositions.
Unlike gaseous phase, the pressure dependence in solid and liquid phases is negligible. If the liquid solution behaves ideally, the solubility of each component in the liquid as a function of temperature is given by:
Where XA and XB correspond to the mole fractions of components A and B, respectively; HA and HB are the heats of fusion of components A and B, respectively; and TA and TB are the freezing points of components A and B.
The binary system is represented in Figure 1(a). The eutectic composition (XE) and eutectic temperature (TE) are given by the intersection of two liquid curves. The curves in figure 1(b) are plots of temperature versus time obtained from cooling curves when liquid solutions of various compositions are cooled.
Liquid-solid phase transitions are determined by thermal analysis, which is an important technique for constructing phase diagrams. Liquid →solid transitions can be detected from cooling curves where heat is extracted at a constant rate and the temperature and time are monitored. Temperatures at which sample cooling momentarily stops (“thermal arrest”) indicate changes in composition with temperature such as phase separation or changes in heat capacity such as a phase transition (liquid to solid). An abrupt change in slope occurs when a solid begins to form (“break”). When the composition of the solution reaches XE, solid A and solid B form simultaneously and separate from the solution at the temperature TE until no liquid remains and arrests occurs (see Figure 1(b)).
In this experiment you will use thermal arrest and break temperatures for several overall compositions to construct the phase diagram of a binary mixture consisting of naphthalene and diphenylamine.
This experiment is primarily based on experiment # 15,”Binary Solid Phase Diagram” of Shoemaker et al . The temperature measurements will be conducted with a thermocouple.
Equipment required: an inner test tube, thermocouple, wire stirrer, a larger test tube that serves as an outer jacket, a large one-hole rubber stopper to support the inner test tube, a cold water or iced water bath, and a hot water bath.
1. Prepare mixtures according to Table 1. Notice that in most cases the mixture is prepared by adding A or B to the previous mixture in order to minimize the quantities of materials required.
2. In order to obtain a cooling curve, you must first heat the mixture in a beaker of hot water until it is completely liquefied. Wipe the test tube dry, place it in the outer tube and place the assembly in the cold water bath.
3. Stir continuously and record the temperatures at 15- or 20-seconds intervals. If possible, continue recording until the temperature is below 30 ⁰C.
4. Plot each temperature reading as a function of time as soon as it is obtained.
5. After each run determine each break and/or arrest temperatures and plot them as a function of mass % B.
6. From the results of the runs 1 through 8, draw the liquidus curves and extrapolate them to an intersection at a point on the eutectic line.
7. At the end of the experiment dispose the mixtures in the appropriate waste containers.
Table 1. Composition of samples (A = diphenylamine, B = naphthalene)
Run # Mass % B Add to tube Add to sample used in run #
1 100 5.00 g B
2 83.3 1.00 g A 1
3 66.7 1.50 g A 2
4 50.0 2.50 g A 3
5 33.3 5.00 g A 4
6 0 5.00 g A
7 16.7 1.00 g B 6
8 25.0 0.67 g B 7
1. Convert the mass % to mole fractions. Determine the mole fraction XNaphthalene for all mixtures. Determine the mole fraction XDiphenylamine for runs 6 through 8.
2. Plot the break and arrest temperatures against the overall composition XNaphthalene. Draw the eutectic line and the liquidus curves. Label all fields to show the phases present.
3. Determine the eutectic composition and eutectic temperature from the phase diagram.
4. Using equations (1) and (2), plot ln XNaphthalene against 1/T for runs 1-3 and plot ln XDiphenylamine against 1/T for runs 6-8.
The plots should be linear with:
Slope = – Hi/R
-slope/intercept = Ti (the melting temperature of the pure component)
5. Calculate the enthalpy of fusion and the melting point for each component, assuming that an ideal liquid solution is formed. Compare to literature values by calculating the percent error for fusH and temperature.
1. Shoemaker, D.P., Garland, C.W., Bibbler, J.W., “Experiments in Physical Chemistry”, 7th Ed. , McGraw-Hill, New York, 1996.
2. Meyer, E.F., Meyer, J.A., “A binary solid-liquid phase diagram experiment including determination of purity, enthalpy of fusion and true melting point”, J. Chem. Ed., 57(8), 1980, 831-831.
3. Ellison, R., “Binary solid-liquid phase equilibria”, J. Chem. Ed., 55(6),1978, 406-407.