Phase Diagram of Naphthalene-Biphenyl
Phase diagrams are of considerable practical utility. They lead to recovery of salts by crystallization, to methods of purification and testing of purity through mixed melting points. They are also of vital importance in metallurgy, geology and ceramic technologies. Even clearing streets of snow by "salting" is an example of the practical use of the freezing point depression effect.
A phase diagram is a diagram from which the physical state of a system may be deduced once the temperature, pressure and composition of the system have been defined. The theory is found on page 204 of Atkins. A one-component phase diagram is a plot of the temperature vs. pressure of the three equilibrium processes (Figure 1).
Figure 1. The one-component phase diagram for water.
These curves define the temperatures and pressure at which two phases can co-exist in equilibrium. The areas bounded by the curves represent temperature and pressure conditions for which only a single phase exists. Thus when the temperature and pressure of the one-component system is known, it is simple to deduce from the phase diagram the physical state of the system. For example, if for water, T = 25°C and vapour pressure p = 1 atm, then the point (25°C, 1 atm) is in the liquid region, so that water can only exist as the single-phase liquid. If T = 100°C and p = 1 atm the point (100°C, 1 atm) is on the liquid-vapour equilibrium line so that the two phases, liquid and vapour, can co-exist simultaneously.
A two-component phase diagram is more complex since the composition of the system must be specified, along with temperature and pressure, in order to define the state of the system (Figure 2). This means that the phase diagram should be 3 dimensional with T, p and composition axes. To simplify matters the pressure is fixed at some value and a 2 dimensional temperature vs composition diagram is used.
Figure 2. An example of a simple solid-liquid phase diagram of the two components A and B. TA and TB are melting points of A and B respectively, and XB is the mole fraction of component B. Usually the phase diagram is for the case when p = 1 atm since the data used to obtain the phase diagram are obtained under atmospheric conditions (i.e. done in the open).
The diagram consists of two curves and a horizontal line. Since this is a solid-liquid phase diagram the curves are solubility curves or freezing point of solution curves. The areas above these curves represent systems whose temperature and concentration are such that the system exists as a single-phase liquid solution of A and B. The area below the horizontal line represents systems whose composition and temperature are such that the system exists as a physical mixture (not a solution) of solid A and solid B. i.e. a mixture of two solid phases pure A and pure B. For example if a salt solution is cooled sufficiently the system will exist as a mixture of salt crystals and ice crystals. The areas between the curves and the horizontal line represent systems whose temperature and concentration are such that two phases, a liquid solution phase and a precipitated solid, can co-exist. This is simply a saturated solution along with some precipitate. There are two such areas since the precipitate may be A or B.
It is simple to deduce the physical state of a binary system once the temperature and composition of the system have been defined. For example, if the temperature and composition are such that they define the point X, then the system consists of a liquid solution of A and B saturated with respect to A, and solid precipitate A. The point Y represents a single-phase liquid solution of A and B.
Phase Rule
The phase rule gives the number of quantities (such as temperature, pressure, and composition) that can be varied without altering the physical state of the system. For example: in the one component system, H2O, ice and liquid water can co-exist indefinitely at a variety of temperatures and pressures, but if one of these variables is set then the other is automatically fixed. If the pressure is chosen as 1 atm, then ice and water can be in equilibrium only if T = 0°C. There is only one degree of freedom (i.e. only one of the variables can be set independently).
The Phase Rule F = C - P + 2 predicts this.
Where F = number of degrees of freedom C = number of components
P = number of phases in equilibrium
For 2 phases to be in equilibrium (co-exist indefinitely) for a one-component system, then C = 1, P = 2 and F = 1 - 2 + 2 = 1. The phase rule predicts that for two phases to co-exist in a one-component system only one of the two variables can be chosen independently. For 3 phases to co-exist, C = 1, P = 3 and F = 1 - 3 - 2 = 0. Here there is no degree of freedom. Thus ice, water and water vapour can only co-exist at one temperature and pressure, a point on the phase diagram known as the “triple point”.
When the number of components is increased the number of degrees of freedom increases. In a two component system C = 2 so that F = 2 – P +2 = 4 - P. Since the pressure is fixed in phase diagrams like the one above, only one degree of freedom is used up. For practical purpose F=3-P. Possible cases are:
(a) The system is a single phase (e.g. liquid solution) F = 3-1 = 2 This means that a liquid solution can exist over a variety of temperature and concentration conditions each of which can be chosen independently.
(b) The system consists of two phase (e.g. liquid solution plus one precipitate) F = 3-2 = 1 This means that a two-phase system can exist at a variety of temperature and concentration conditions but that only one of these variables can be chosen independently.
(c) The system consists of three phases (e.g. liquid solution plus two precipitates) F = 3-3 = 0 This means that neither the temperature nor the composition can change. The temperature and composition at which three phases co-exist are said to be at their “eutectic” values. Cooling Curves
Phase diagrams of simple binary systems can be established by examining: “cooling curves”, which are temperature vs. time graphs of solutions. Two compounds, A and B, are first mixed and then heated until a single-phase liquid solution is formed. As the solution cools, the temperature is measured as a function of time. This procedure is repeated for solutions of composition from pure A to pure B.
As a system cools any internal thermodynamic process that generates heat will change the rate of cooling and hence the shape of cooling curve. For example, a pure liquid open to the atmosphere so that the pressure is set, cools in a regular manner until it beings to freeze (Figure 3(a)). Then the heat of fusion is released which offsets the heat lost to the surroundings so that the cooling curve becomes horizontal (i.e. temperature remains constant until the freezing process is over).
This temperature halt is predicted by the phase rule since C = 1 component, P = 2 phases, liquid and solid, so that F = 1 - 2 + 2 = 1 degree of freedom.
Since the pressure has already been set at 1 atmosphere, there is no degree of freedom for the temperature and it must remain constant until the number of phases is again reduced to 1 (i.e. when freezing is finished and there is no liquid left). The temperature then falls again in a regular manner although with a different slope than for the case of the liquid. The width of the temperature halt depends on the amount of substance. Note that there may be a dip in the curve if supercooling occurs.
Figure 3. Cooling curves for (a) a single-component system and (b) a two-component system When a two-component liquid solution is cooled it again cools initially in a regular manner (Figure 3(B)). As the temperature is lowered the solution will reach a saturation point with respect to one component, say “b”. Then “b” will begin to precipitate out of the solution i.e. freeze out of the solution. This process will release the heat of fusion of “b” and change the cooling rate but no plateau will be observed in this case since all of “b” does not freeze out immediately. As the solution continues to cool and more “b” freezes out, the solution approaches saturation also with respect to component “a”. At the eutectic temperature, the solution is saturated with respect to both components so that both “a” and “b” start to precipitate. Application of the phase rule shows that the temperature of the system must remain constant while both “a” and “b” are precipitating:
C = 2 components, P = 3 phases, solid “a”, solid “b”, and liquid solution so that F = 2 - 3 + 2 = 1 degree of freedom
But since the cooling is occurring in the open, the pressure is already set at 1 atm and there is no degree of freedom with respect to temperature. The temperature where this halt occurs is the eutectic temperature. It is a well-defined quantity for a simple binary system and is given in International Critical Tables Vol. IV (for the case when pressure = 1 atm). The length of the temperature halt depends on the amount of liquid solution left when the eutectic temperature is reached. This will vary depending on the amount of “b” which has already precipitated. This in turn will depend on the temperature at which “b” started to precipitate and hence on the initial
composition of the solution. When all of the liquid solution has disappeared, the number of phases is reduced to 2 and the temperature can again decrease.
Cooling curves can therefore be used to identify freezing points of pure compounds, freezing points of solutions of known composition, and eutectic temperatures (Figure 4). These data are all that are necessary to establish a simple binary phase diagram which in effect is a plot of the freezing point of a solution (i.e. temperature at which one component begins to precipitate) as a function of solution composition plus a eutectic temperature line.
Figure 4. The relation of cooling curves at different concentrations to the phase diagram. Often, it turns out that there is supercooling and the temperature at which one component first precipitates out is uncertain. In this case extrapolate back as shown in Figure 5.
Figure 5. Extrapolating back to the temperature of initial precipitation when supercooling occurs. Thermocouples
digital voltmeter or potentiometer
chromel
chromel alumel
The voltage generated in a thermocouple depends on the temperature difference between hot and cold junctions. One junction is used for reference, set in an ice water bath. When both junctions are set in an ice water mixture, the voltage should be zero. Imperfections in thermocouple junctions may result in non zero values. Due to these imperfections, thermocouples should be calibrated by measuring the voltage with the measuring thermocouple set in some constants temperature bath (e.g. boiling water). In the range from 0 to 100°C the thermocouple voltage should be linear with
temperature. With this assumption, the mV output can be converted to °C. Look up their emf values in HCP to check the thermocouples.
The objectives of this experiment are: 1. To calibrate the thermocouples.
2. To construct cooling curves for a two-phase naphthalene/biphenyl system. 3. To construct a phase diagram for the naphthalene/biphenyl system.
Procedure
Calibrate the 4 chromel-alumel thermocouples.
1. With the reference junctions in an ice bath, put the other junction in a glass tube in the rubber stopper in a tall beaker.
2. Almost fill this with distilled water and raise it to the boiling point.
3. Record in turn the readings (in millivolts) registered for each thermocouple on the digital volt meter.
Do not proceed with the experiment if you do not get readings of 4.1 ± 0.1 mV for all four thermocouples.
Eight tubes of designated “weight percent” of naphthalene are provided.
4. Place the four with the highest value naphthalene in a beaker of hot water until all contents are at least 90°C.
Do not raise the temperature any higher; otherwise the bottom of the tubes may break. 5. Clamp the tubes and allow them to cool in air and start recording thermocouple voltages. 6. Also at this time, place the remaining tubes in the beaker of hot water to melt the contents. 7. Take a reading every 15 seconds so that the temperature of each tube is recorded every
minute.
8. Continue readings until the temperature falls a few degrees below the eutectic temperature. 9. Repeat steps 5 – 8 with the remaining tubes.
The eutectic temperature is given in the International Critical Tables Vol. 4 (available in the reading room).
Interview Report
The TA will post the time for the interviews and when the following should be submitted: 1. Organize the data and produce the relevant plots.
2. Submit cooling curves on two graphs (four per graph) moving the time scale to the right for each curve to get good separation between curves.
3. Submit the phase diagram obtained from the cooling curves.
4. Be prepared to explain the phase diagram with respect to the number of phases, degrees of freedom and the equilibrium that exists in each area.
5. You should know why and how the length of the eutectic halt changes with the system composition.
Safety Notes
Ensure that the beaker containing the reference thermocouple is packed with ice at all times. The temperature can easily rise by a few degrees when the beaker is only half filled with ice.
As the tubes cool you should try to pick out temperature halts, super cooling and the formation of the first precipitate.
You should especially detect the eutectic halt.
In some cases, because of super cooling, the temperature will drop a few degrees below the eutectic temperature. Do not stop taking readings at this point since the temperature should rise again. i.e. ensure that you have observed the eutectic temperature halt before you stop taking readings.
In plotting cooling curves don't convert thermocouple output to temperature but rather plot thermocouple output vs. time. Then you can pick out the relevant thermocouple values form your plots and convert these to temperatures.
