Transcript
(Data Reporter) (Leader)
(Safety Inspector) Expt 4: Liquid Vapour Equilibrium
Section 031, Group 1
Oct 13, 2008
Objectives of Experiment:
An Othmer equilibrium still with a methanol/water solution shall be utilized for this experiment consisting a simple boiler and a reflux condenser for three methanol concentrations. The first objective is to experimentally calculate the mole fraction of methanol in vapour phase using a known liquid phase concentration. The second objective is to compare the experimental value to two theoretical values using Rault’s law for ideal solution and modified Raoult’s law (using Van Laar’s constants for non-ideal solution. Thus it shall be determined if this solution behaves as an ideal or non-ideal solution by utilizing a plot based upon mole fraction. The final objective is to prove the consistency of obtained results by calculating the area under the curve of ln(1/2) versus mole fraction of methanol in the liquid. If the net area found is close to zero (-0.10 and 0.125), it can be concluded that our results are thermodynamically consistent.
Design Basis:
For this experiment an Othmer’s Equilibrium Still apparatus shall be utilised, which is comprised of a simple reflux distillation unit. In the Othmer’s still, the methanol-water solution vaporizes, and the condensate is recycled back into the boiling flask, until the system reaches equilibrium after four equalizations. Once the temperature stops increasing, it shall be recorded and used later in Antoine’s equation for the calculation of vapor pressures of methanol and water. for each of the three different concentrated solutions to be the densities of the distillate, residue and the initial solution shall be measured using a pycnometer.
Lastly, Raoult’s equation for ideal solutions was used to calculate the liquid and vapour compositions (x and y) and Van Laar’s constants were calculated and used with the modified Raoult’s equation for non-ideal solutions. Finally, all results obtained were plotted in one graph called a xy-diagram showing how well the theoretical design equations mentioned above hold for this experimental study of phase equilibrium.
The Othmer’s Still apparatus is not frequently used in industrial application, but it is mainly used for informational purposes. It is used to determine the vapour-liquid equilibrium relationship. This relationship is extremely useful for many industrial applications, such as petroleum refining and alcohol brewing.
In petroleum refining, distillation is utilized in the petroleum industry to separate different types of hydrocarbons. The lighter fractions travel to the top while the heavier ones go to the bottom
Introduction and Theoretical Background
Methanol has a higher vapour pressure than water, which means that in a mixture of methanol and water, methanol has a greater tendency to vaporize than water when distilled. When equilibrium is reached between vapour-liquid phases the concentration gradients between the two phases and the rate of diffusion between them fall to zero. At equilibrium the concentrations of the two phases are not equivalent but that the chemical potential of the methanol in the two phases is the same. A theoretical plot consisting the mole fraction of methanol in vapour and liquid phases at equilibrium is called a Vapour-Liquid Equilibrium curve.
Figure 1: Equilibrium Curve for Methanol
The fundamental relation that is utilized in ideal vapour-liquid equilibrium systems with one condensable component is Raoult’s law.[2]
(1)
Where:
pA = partial pressure of component A,
yA = mole fraction of component A in the vapour phase
P = total pressure
xA = mole fraction of A in the liquid phase
pA*(T) = vapour pressure of component A at the equilibrium temperature T
This equation is employed when both the vapour and liquid phases are ideal [6]. In equation (1),
Antoine equation is used to determine the vapour pressure of a component at a specific temperature and shall be used in equation 1. [2].
(2)
Where:
p* = vapour pressure of a component
T = temperature
A= 7.87863, B= 1473.11, and C =230 [2].
For the systems in which the liquid phase behave non-ideally, a modified form of Raoult’s law is utilized [6].
(3)
Where:
yA = mole fraction of component A in the vapour phase
P = total pressure
?A = activity coefficient of component A in the solution
xA = mole fraction of A in the liquid phase
pA*(T) = vapour pressure of component A at the equilibrium temperature T.
Van Laar’s equations shall be used to calculate the activity coefficient in equation (3)
(4)
(5)
Where:
x1 and x2 = mole fractions of components methanol and water respectively
A12 =0.8041 and A21 = 0.5619 (Van Laar coefficient). [1]
Thermodynamic Consistency can be obtained when the predicted and the experimental values match within an acceptable experimental uncertainty [3].
The integral test can be utilised to check the thermodynamic consistency of the obtained results. The integral test if derived from Gibbs-Duhem thermodynamic consistency test.
(6)
(7)
A plot shall be constructed between against x1 to determine the thermodynamic consistency. If the net area found is close to zero (-0.10 and 0.125), it can be concluded that our results are thermodynamically consistent.
Duty Distribution:
Varun Tomar (Leader) will be responsible to monitor the temperature of the system and make sure adequate heat is provided using Bunsen burner. Also prepare three desired concentration of the solution
Marwa Alhaji (Safety Inspector) will be responsible for the safety aspect of the experiment; and making sure all members are wearing proper laboratory attire (i.e. hardhat, lab coat, safety glasses) to avoid contact with skin, eyes, and continuously wash hands to avoid any methanol residue. She will make sure that while using pycnometer fume hoods is used to avoid breathing vapours.
Ziyad Shaath (Data Reporter) will be responsible for the recording all relevant data: density of initial solution, distillate and residue. Also record the equilibrium temperature.
Reference:
It utilized an Othmer’s Equilibrium Still apparatus, which is comprised of a simple reflux distillation unit. The methanol-water solution vaporized, condensed, and recycled back into the boiling flask. A sample of the distillate and residue was taken, where the density was determined with a pycnometer. The density was correlated to determine the mole fraction of methanol and water, which was used to determine if the system was ideal or non-ideal. It was determined that the methanol-water solution behaved as a non-ideal solution, based on the modified form of Raoult’s law. Also, the experiment was thermodynamically consistent as the integral test held valid. One of the limitations was the lack of data points. Different concentrations of methanol-water solutions could be used to increase the range of the results. Overall, the experiment was successful at determining if methanol-water solution behaves ideally or non-ideally and the thermodynamic consistency of the system.
