Raoults Law And Binary Liquid Vapour Phase Diagram

Abstract

This experiment will look into and study the Raoult’s law behaviour of a binary solution of acetone and toluene to see if the mixture solution follows Raoult’s law of ideal solution. This experiment is conducted by introducing the vapour-phase of mixture solution into the cuvette using cotton wool with solution and a Ultra-Violet Visible Light (UV-VIS) spectrum is obtained to find out the absorbance of the acetone and toluene individually using the correction of the spectra. The absorbance of acetone and toluene will use to calculate the partial pressure of each solution. These partial pressures will be compared to the pure partial pressure obtained from literature by constructing a Raoult’s law plot graph and Phase Diagram (liquid-vapour diagram). The experiment result has shown that acetone-toluene solution is not an ideal solution and did not follow Raoult’s law entirely with a positive deviation from the theoretical Raoult’s law plot was observed. The positive deviation shows that the acetone-acetone and toluene-toluene interaction is stronger than the acetone-toluene interaction. Possible errors will discuss in later part of report.

Introduction

The aim of this experiment is to study the Raoult’s law behaviour of a binary solution of acetone-toluene.

Raoult’s law stated that the partial pressure of any component will equal the vapour pressure of that component in the pure state multiplied by its mole fraction in the liquid mixture of an ideal solution.

Raoult’s law only obeyed when the solution is ideal and the intermolecular interaction is equal to those of the pure components. It is also satisfied only for mixture with component of very similar molecular size, shape and chemical properties. In an ideal solution containing component A and B, the A-B interaction are assumed to be equivalent to A-A and A-B interaction. Raoult’s law of ideal solution can be shown as:

—————————————- (1)

—————————————– (2)

——————————– (3)

PA and PB are the vapour pressure of A and B over a solution while XA and XB is the respective mole fraction. and are the vapour pressure of the component A and B in pure forms and P total is the total vapour pressure of the solution.

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It is uncommon for solution to obey Raoult’s law exactly and real solution used in experiment deviate from Raoult’s law by positive deviation or negative deviation that are caused by the A-B interaction to be less or more than the A-A and B-B interactions in which resulting in the solution containing higher or lower pressure than predicted.

In this experiment, a series of different concentration of acetone-toluene will be prepared and will be evaporated in the cuvette which will be used to be measure for the respective absorbance. The amount of evaporation is assumed to be and the partial vapour pressure of acetone or toluene component using:

i = A, B ——- (4)

Pi is the partial pressure for i , Absi is the measured absorbance of i in the vapour phase at its wavelength of maximum absorption (λmax) corrected for any spectral overlap between component A and B, is the vapour pressure of pure i at the temperature of measurement and is the measured absorbance of pure i in the vapour phase at its λmax.

Experimental Procedure

A series of acetone-toluene solutions were prepared by pipetting the solvent into four 5ml volumetric flasks according to the Table 1 below:

Table 1: Composition of acetone-toluene solution

Solution

1

2

3

4

Acetone(mL)

4.00

3.00

2.00

1.00

Toluene (mL)

1.00

2.00

3.00

4.00

Then, a small cotton ball was wet with appropriate amount of pure acetone and was inserts into top of one of the two empty 1cm quartz cuvette that were used to conduct the baseline scan with the UV-VIS spectrometer over the wavelength 225 to 350nm. There is precaution to make sure no introducing liquid into the cuvette or wall of cuvette. The cap of the cuvette was covered immediately to minimize evaporation loss into the atmosphere and after three minutes to reach equilibrium, the absorption spectrum of the vapours was obtained. Final absorption spectrum was obtained with no further change observed. Lastly, air was flushed into the cuvette to remove vapour of acetone. It is then repeated for pure toluene and Solution 1 to 4.

Data Treatment and Analysis

Table 2: Table of literature values [1]

Literature Value

Vapour pressure of pure acetone is 30.8 kPa at 25oC

Density of acetone is 0.7845 g/ml at 25oC

Molecular mass of acetone is 58.079 g/mol

The following data was collected from the absorption spectrum using the UV-VIS spectrophotometer (SHIMADZU UV2450):

Table 3: Raw data collected from Experiment

Solution

Wavelength (nm)

Absorbance (Å)

Pure Acetone

276.1

0.194

Pure Toluene

266.80

0.554

Solution 1

266.8

0.324 (Total absorbance of acetone and toluene)

276.1

0.170 (Absorbance of acetone)

276.1 + ( 276.1-266.8) = 285.40

0.137 ( Absorbance equivalent to absorbance at 266.8nm)

Toluene at 266.80

0.554 – 0.137= 0.187 (Absorbance of toluene)

Solution 2

266.8

0.430 (Total absorbance of acetone and toluene at 266.8nm)

276.1

0.150 (Absorbance of acetone)

276.1 + ( 276.1-266.8) = 285.40

0.123 ( Absorbance equivalent to absorbance at 266.8nm)

Toluene at 266.80

0.430 – 0.123= 0.307 (Absorbance of toluene)

Solution 3

266.8

0.523 (Total absorbance of acetone and toluene at 266.8nm)

276.1

0.115 (Absorbance of acetone)

276.1 + ( 276.1-266.8) = 285.40

0.101 ( Absorbance equivalent to absorbance at 266.8nm)

Toluene at 266.80

0.523 – 0.101= 0.422 (Absorbance of toluene)

Solution 4

266.8

0.544 (Total absorbance of acetone and toluene at 266.80nm)

276.1

0.072 (Absorbance of acetone)

276.1 + ( 276.1-266.8) = 285.40

0.061 ( Absorbance equivalent to absorbance at 266.8nm)

Toluene at 266.80

0.544 – 0.061= 0.483 (Absorbance of toluene)

The following data was calculated using the collected experimental data and Equation (4):

Table 4: Tabulated data calculated using Equation (3) & (4) and experimental data collected.

Solution

Absorbance of Acetone ()(Å)

Pure vapour pressure of Acetone

() (kPa)

Pure Acetone abs () (Å)

Partial vapour pressure of Acetone

() (kPa)

Absorbance of Toluene

() (Å)

Pure vapour pressure of Toluene

()

Pure Toluene abs

() (Å) (kPa)

Partial vapour pressure of Toluene

() (kPa)

Total partial Pressure (kPa)

1

0.17

30.8

0.194

26.990

0.187

3.79

0.554

1.279

28.269

2

0.15

30.8

0.194

23.814

0.307

3.79

0.554

2.100

25.915

3

0.115

30.8

0.194

18.258

0.422

3.79

0.554

2.887

21.145

4

0.072

30.8

0.194

11.431

0.483

3.79

0.554

3.304

14.735

Table 5: Tabulated data calculated using Raoult’s Law Equation (1) & (2) and standard literature data:

Solution

Mole fraction of Aacetone (Xacetone)

Pure vapour pressure of Acetone

() (kPa)

Partial vapour pressure of Acetone

(Pacetone)() (kPa)

Mole fraction of Toluene

(Xtoluene)

Pure vapour pressure of Toluene

()

Partial vapour pressure of Toluene

(Ptoluene) () (kPa)

Total partial Pressure

(kPa)

1

0.852

30.8

26.237

0.148

3.79

0.561

26.798

2

0.683

30.8

21.041

0.317

3.79

1.201

22.242

3

0.489

30.8

15.072

0.511

3.79

1.935

17.007

4

0.264

30.8

8.142

0.736

3.79

2.788

10.930

Figure 1: Plots of partial pressures of acetone and toluene of Raoult’s law & experimental result and total pressure against mole fraction of toluene (XToluene)

Figure 2: Liquid-vapour binary phase diagram of total pressure against vapour-phase mole fraction (Y Toluene) and liquid-phase mole fraction of toluene (X Toluene)

Results and Discussion

Analysis of spectra

The spectrum gotten from the experiment which shows absorbance peaks of pure acetone, pure toluene and solution 1 to solution 4 can be found in Appendix 2.

The spectrum has shown a decreasing trend of acetone absorbance clearly from solution 1 to solution 2. This agrees with prediction of the spectrum as according to the composition of acetone for each solution.

At the maximum absorbance wavelength (λmax) of acetone, the absorbance is equivalent to the partial pressure of the acetone using the equation 4. At the maximum absorbance wavelength (λmax) of toluene, the absorbance is equivalent to the partial pressure of the toluene using the equation 4.

For the solution of mixture, it will be difficult to find out the absorbance of each individual absorbance of acetone and toluene. Fortunately, the spectra of the mixture of solution are addictive in accordance to Beer-lambert’s law which is proven when the spectra of solution 1 to 4 show combination peaks of pure acetone and toluene with only different in absorbance value from the pure acetone and toluene. Therefore, in order to find the absorbance of acetone and toluene individually in the mixture, there is a need to correct the overlap of the spectra. Firstly, it is assumed that the spectrum for pure acetone is symmetrical. At any point of the spectrum of pure acetone with a particular wavelength, there will be a corresponding point on the spectrum with the same absorbance at the exact same amount of wavelength away from the lambda max (λmax). So, at 266.8nm wavelength, it is the lambda max (λmax) of pure toluene and at 276.1nm is the lambda max (λmax) of pure acetone. At the lambda max of the spectra for solution 1 to 4, the wavelength is to be subtracted from the λmax of pure acetone of 276.1nm and added to the λmax of pure acetone 276.1nm to get the wavelength of the reflected side of the symmetric curve of pure acetone. Hence, from the absorbance gotten, the absorbance will be equivalent to the absorbance of acetone at the λmax of mixture. Hence, taking the total absorbance of acetone and toluene in the mixture to subtract the absorbance of acetone in the mixture at 266.8nm (lambda max of mixture spectra) to get the absorbance of toluene in the mixture.

Hence, from the individual absorbance of acetone and toluene, it can then be calculated for the partial pressure of acetone and toluene in the mixture of solution.

The reason for using the lambda max as proportionate to the partial pressure of acetone and toluene as it is to reduce the margin of error where if taken at less intense wavelengths, the partial pressure will fluctuate dramatically for a small percentage of error such as shifting of baseline.

Raoult’s law plot

It can be observed in the Raoult’s law graph that there is a positive deviation of the experimental plot from the Raoult’s law plot. The positive deviation as mentioned is result from the solutions having vapour pressure higher than predicted that is caused by the intermolecular interaction of acetone-toluene to be weaker than the acetone-acetone and toluene-toluene interaction. This result is logical as the difference in polarity between the components of these solutions can be easily determined where the acetone is polar and the toluene is non-polar which is known and can be predicted that the result will form positive deviation.

It can also be observed that each component obeys Raoult’s law in the limit as its mole fraction goes to one. This as the experimental partial pressure forms a polynomial curve of order two and approaches the Raoult’s law standard liner plot as mole fraction goes to one..

Deviation from Raoult’s law

As mentioned, there is positive deviation from Raoult’s law. This shows that the molecules of the acetone-toluene mixture prefer to be in the vapour phase than the liquid phase. There is higher partial pressure recorded than predicted by Raoult’s law which implies that there is more vapour phase molecules than expected. This shows that the vapour phase is more favoured and hence the acetone-acetone and toluene-toluene interactions are preferred over acetone-toluene interaction in the liquid phase. These acetone-acetone and toluene-toluene interactions are affected by the intermolecular forces which is going to be discussed in the following paragraph. It can also be explained that acetone cannot form hydrogen bonds with toluene as both molecules wants to escape into the vapour phase and thus the vapour pressure is higher than that predicted from Raoult’s law.

Intermolecular forces

Intermolecular forces are defined as the attractive or repulsive forces between molecular entities excluding those due to bond formation, electrostatic interaction between ions or ionic groups and neutral molecules. In this experiment, acetone is polar while toluene is non-polar. This will result in dipole-dipole induced forces that are formed between polar and non-polar component. Acetone-acetone interaction will be the dipole-dipole interaction while the interaction between toluene-toluene will be London forces. From the result of the Raoult’s law plot, the positive deviation suggests that the acetone-toluene interaction is weaker than the acetone-acetone and toluene-toluene interaction. Hence, interpretation of the results shows that the induced dipole interaction is weaker than dipole-dipole and London force present in the mixture of the solutions.

Also, the boiling point of acetone (56.05oC) [1] is lower than the boiling point of toluene (110.63oC)[1]. It is predicted for acetone to have a lower boiling point due to its high vapour pressure which leads to high volatility. This coincides with the experimental data collected where the partial pressure of acetone is higher than the partial pressure of toluene. Therefore, acetone will evaporate at a faster rate after interaction with toluene as the interaction is not preferred, thus forcing more acetone molecules into the vapour phase. Acetone prefers to be in the vapour phase as it is further apart from the toluene molecules and hence less interaction with the toluene molecules.

Phase Diagram

The liquid-vapour phase diagram shows clearly the part the location of liquid, liquid-vapour and vapour phase.

The bubble point line that is constructed by plotting the total partial pressure of both acetone and toluene versus the liquid-phase mole fraction of toluene indicates that the partial pressure at certain mole fraction of the toluene will cause the toluene to boil and changes from liquid to vapour phase once passed the bubble point line.

The dew point line is that is constructed by plotting the total partial pressure of both acetone and toluene versus the vapour-phase mole fraction of toluene, y toluene, indicate that the partial pressure at certain mole fraction of toluene will cause the toluene vapour to condense and change back to water phase.

The phase diagram can be also be used to find out the vapour-phase mole fraction or the liquid-phase mole fraction of the mixture at a given total pressure of both compounds. Thus, it gives the composition of the mixture at a given pressure. From the phase diagram, it can also be used to calculate back to find the absorbance value of unknown solution mixture of acetone and toluene through finding the liquid-phase or vapour-phase mole fraction of acetone and toluene with a known pressure. The phase diagram also show that by varying the total pressure of the mixture can give rise to different composition of acetone and toluene. This diagram matches the theory where at higher pressure, there will be higher composition of toluene at liquid-phase than vapour-phase as at higher pressure, lower vapour pressure will be obtained and more liquid will be formed when the vapour molecule are forced back to liquid phase. On the other hand, at low pressure, the phase diagram gives a higher mole fraction at the vapour phase for toluene as compare to the mole fraction in the liquid-phase which matches the theory of hiving lower pressure that allow more molecules to go into vapour phase which result in higher vapour pressure.

In the centre region of the phase diagram consist of a two phase region of liquid and vapour phase. A point in this region will not be corresponding to the state of the system as the region consists of vapour phase and liquid phase. Therefore, a “tie-line” needs to draw in the region to intersect the bubble point line and the dew point line boundary. The intersection of the tie line with the bubble point line on the liquid-phase of the region tells the composition of the liquid phase and the intersection of the tie line with the dew point line on the vapour side tells the composition of the vapour-phase.

Possible limitation or possible source of error

Firstly, a source of error will be the using of pipetting for acetone where acetone are highly volatile and will evaporate at fast speed which will cause pipetting error. It can be observed during the experiment that there are already bubbles forming when pipetting the acetone which shows that small amount of acetone pipette out have already been evaporated. Hence, to counter to this problem, it will be optimal to carry out the pipetting at a faster speed and to have consistency in the pipetting for all the solution.

Also, it is important to cover the cap of the volumetric flask and the cuvette once solutions have been added into the volumetric flask or the cotton in the cuvette as quickly as possible. This is important as acetone is highly volatile and will be easily evaporate into the environment which will cause lesser concentration of acetone in the cuvette and result in lesser acetone absorbance and affect the accuracy of result. Hence, it can be suggest a cuvette with a stopper top should be used instead of an open top cuvette to prevent the vapour from escaping.

It is also observed that during the experiment when too much pressure is applied to the cap of the cuvette, condensation will occur. This is because the high external pressure will reduce the vapour pressure in the cuvette and force the vapour phase of the mixture of solution back into liquid phase which condense and from water droplet in the cuvette. It is also similar when the cotton was too wet with solution and solution drip into the cuvette. The spectrum desired is that of the vapour pressure and not that of the liquid phase, so it is important that the windows of the cuvette remain dry. Although cotton, being hydrophilic, could supress the vapour pressure of the more polar liquid component, this effect is believed to be small when the cotton is thoroughly saturated with liquid. When these phenomenon happen, the droplet have to be flush dry with air and new cotton will have to re-insert back into cuvette for adding of the solution. This is because the solution droplet will hinder the ultraviolet-visible light from passing through the cuvette and will absorb more light than the vapour phase which will show inaccurate result of the spectra.

For this experiment, quartz cuvettes are used as the quartz cuvette will not absorb Ultraviolet light and will not interfere with the absorbance of acetone or toluene. It will be transparent to the UV -VIS light and thus, the absorbance of acetone and toluene is not inclusive of the absorbance of the cuvette and hence, the result gotten will be accurate.

The baseline is important for this experiment as it will determine the absorbance of the vapour and minute changes of baseline will lead to great margin of error despite using lambda max as absorbance of the acetone and toluene. It is important to put two cuvettes with the transparent side facing the beam and do as little disturbance to the surface of the cuvette as possible to retain consistence baseline. It is suggested to wipe the transparent side every time to ensure best transparency of the quartz cuvette.

Lastly, it is important to note that more data points will be needed for ensuring accuracy and precision of the result as volatility of acetone is high and it is of high probability of error in evaporating the acetone and result in lower partial pressure of acetone than expected. Repeating the experiment several times can also help to reduce such error and improve consistency.

Conclusion

In conclusion, this experiment have studied the effect of Raoult’s law and the binary liquid-vapour phase diagram of acetone and toluene which shows positive deviation from Raoult’s law which further enhanced the fact of only ideal solution obey Raoult’s law.