Vapor-liquid Equilibrium

1. Priming the system

1. Vent the VLE system using the vent/control 3-way valve mounted on the frame of the apparatus, and (if necessary) by draining liquid out of the system into a waste flask.
2. Remove the sample tubes and replace with clean tubes (if necessary). The liquid will not completely drain out of the system.
3. For the first run of experiments, refill through the input valve with a mixture of roughly (vol %) 50% methanol, 30% isopropanol and 20% water. For the second week, refill with roughly 25% methanol, 45% isopropanol and 30% water. For the third week, refill with whatever liquid you need to repeat. The total liquid capacity is approximately 130 cm³.
4. Fill with liquid to just below the spot where the Cottrell pump intersects with the vacuum jacket. Too little liquid will cause the system to require very high boiling rates to get enough liquid to "spit" (when liquid pops while boiling intensely).
5. Use a beaker and pour the liquid into the addition port at the top of the equilibrium chamber. Close the port.
6. Check the barometric pressure with the mercury manometer on the wall. Adjust the "zero" on the digital pressure gauge to match (if necessary).
7. Switch the three-way vent valve to "control" and start up the vacuum pump and pressure controller.
8. Open the throttle valve on the pressure controller several turns and observe the pressure rapidly drop. Watch the pressure on the digital pressure gauge.
9. Set the control pressure set-point on the pressure controller to obtain ~ 700 mm Hg. Listen for clicking of the control valve. Once the control point is reached, the noise from the vacuum pump will be audibly different.
10. At this point, with the throttle valve opened several turns, every time the control valve opens, too much air is dumped to the vacuum pump and the pressure dips below 700 mm before slowly recovering. Close the throttle valve completely, then open it about ½ turn.
11. Wait for the control valve to begin clicking again, then close the throttle valve in small increments until the pressure fluctuates only ~0.5 mmHg or less when the valve is open. Make minor adjustments to the control point or the leak valve as necessary to maintain very near 700 mmHg.
12. Once the mixture is within ±10 mmHg of 700 mmHg, turn on the heater power, heating mantle power, condenser water and magnetic stirrer. Try 25-30 % heater power and 1.5-2 turns mantle power to start. The apparatus will require 20 min or less to approach equilibrium. Keep adjusting the pressure during this time.

2. Running the experiment

1. Upon boiling, the Cottrell pump will begin to spit liquid and liquid can be seen dripping back into the boiling chamber. Condensed vapor will require longer to appear. When equilibrium is reached, experimenters should see steady drips of condensed vapor (2 - 3 drops/s) and returned liquid (2 - 3 drops/s). The temperature should be stable to ± 0.03 ºC and the pressure should be stable at 700.0 ± 0.5 mmHg. When these conditions have been established for at least 2 min (or so), equilibrium is attained.
2. Open the magnetic valves (marked "1" and "2" on the controller) 4 or 5 times each for long enough to collect about 0.5 cm³ of liquid in each sample tube, and close the tubes. If a valve does not respond to its button, try flipping the power switch for the controller off then on. This first sample will be used to wash the tubes and delivery system and will be discarded. Washing replaces any remaining chemical on the sides of the tubes with the same chemical that is being sampled, so it will not affect the composition of the test.
3. Momentarily turn off the power to the heater, wait 30 s for the boiling to subside, then vent the system with the vent/control 3-way valve. Remove the sample tubes, swirl a few times, then dump them into the waste pot.
4. Refit the sample tubes on the system, turn the vent valve back to "control", turn the power back on to the heater, and wait for equilibrium to be reestablished. This will only take a few min if the apparatus does not cool. A slight difference in temperature may be observed when equilibrium is re-established. This can be due to a slight disturbance of the overall composition due to sampling.
5. Once equilibrium is re-established, take two new samples. Have two labeled vials with new septa ready.
6. After taking ~0.5 cm³ samples in each tube again, turn off the heater, vent the system, remove the sample tubes and pour them into the vials. Cap the vials and replace the sample tubes with clean tubes if necessary.
7. While analyzing the samples, prepare a new sample. Drain ~15 cm³ of liquid into a beaker or flask. Add ~20 cm³ of pure methanol or 50/50 methanol/isopropanol through the sample port. This will give a new overall composition.
8. Be sure the sample tubes are completely empty, then close the system off, switch the vent valve to "control", and turn the heater back on. If working quickly, equilibrium will be re-established rapidly. Note that there should be a temperature difference from the previous sample.
9. Repeat the equilibration and sampling procedure as before, remembering to take one sample to wash, and then take the final sample. Continue the experiments by adding component(s). Twelve data points are sufficient to determine the activity coefficients and (roughly) the binary interaction coefficients.

3. Shutting down the system

1. Turn the heaters off. When the apparatus begins to cool, shut off the stirrer and condenser water.
2. Return the system to atmospheric pressure; set the controller >1020 mbar, close the throttle valve, set the three-way valve to vent and open the valve on the tank.
3. Once atmospheric pressure has been reached, shut off the pump. Drain the liquid from the reservoir until it reaches the level of the valve, but leave the rest of the liquid in the reservoir. Close the 3-way valve.

4. Analysis

1. Using nonlinear regression and a standard sum of squared residuals objective function, use the activity coefficients computed from the raw data to regress the 6 constants for the ternary Wilson equation (below), for this system. Assess the quality of the fit by graphical methods and computing the average percent relative deviations (APRD), which are average fit errors x 100.
   
2. Converge on the true optimal values from several different directions in response parameter space by using a factorial method for the initial guesses. Compute the precision of the GC measurements by sufficiently replicating one GC sample to determine relative precisions according to the t-statistic, and use the precisions to determine whether to accept / reject a particular GC measurement by appropriate hypothesis test.
3. Compare the relative precisions of the GC measurement to the APRDs, and discuss. Also report the absolute precisions of the pressure and temperature gauges - determine these once per day.