Analysis of the Deviations from Ideality of a Methanol-Water

System through Functions of Mixing

Sarah Rudy Mark SleeperDavid Watts Tyler Garrett

Executive Summary• Main objective included observing deviations from ideality of a

methanol-water solution through heat of mixing, volume of mixing, and analyses of partial pressures of mixing.

• Accomplished by varying molar fractions of methanol and water.• Used a calorimeter to observe heat outputs for exothermic

reaction.• Used pycnometers to measure mass of liquid and calculate

density changes of solutions.• Provided partial pressures of methanol and water at different

mole fractions.

Introduction• What is an ideal solution?

– Interactions between solute and solvent molecules are the same as those between two identical molecules

• How does this translate to the experiment?– Does not absorb or produce heat– Exhibits volume equal to the sum of the volume of its

separate parts– Displays vapor pressure as a linear function of molar

composition• Extensive properties of a solution are directly proportional to

the size of the system.– X = n1 * X1 + n2 * X2

Heat of Mixing

Experimental• Mixing of methanol and water in order to

observe deviations from ideality.

Water and Methanol

Water and WaterMethanol and Methanol

Experimental (cont’d)• Heat of Mixing

– CSC 2-Drop Calorimeter

Data and Results

Data Acquired

Literature Data: Comparison of Experimental Excess Molar Enthalpies To Simulation Data

Vlcek, L.; Nezbeda, I. Excess Properties Of Aqueous Mixtures Of Methanol:  Simple Models Versus Experiment. Journal of Molecular Liquids 2007; pp 161.

Data and Results (cont’d)

• Mixing water and methanol is exothermic.• Deviation from ideality increased as the

solution approached 1:1 ratio of methanol and water.

Modification 1• Objective

– How does varying the starting solution’s temperature affect the heat of mixing?

Modification 1 (cont’d)Heat of Mixing in Methanol and Water Mixtures at Varied Temperature

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mole Fraction of Water

Heat

of

Mix

ing

[J/m

ol]

25 degrees C

35 degrees C

Ideal

Modification 1(cont’d)• Results

– At the higher temperature, the heat of mixing was closer to the ideal value.

• Explanation– At an elevated temperature, the mixture acts more ideally.

The molecules move faster and therefore have higher energy.

– This also means that more space between the molecules is available. The solution mixes faster and easier than at lower temperatures

Modification 2• Objective

– To show how intermolecular forces affect the ideality of the volume of mixing and heat of mixing.

– To show this, isopropanol was substituted for methanol in the mixture with H2O

Methanol Isopropanol

Modification 2(cont’d)

Water and Isopropanol Mixture Water and Methanol Mixture

Modification 2(cont’d)Affect of Intermolecular forces on Heat of Mixing

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

100

200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mole fraction of Water

Heat

of

Mix

ing

[J/m

ol]

Methanol and Water

Isopropanol and Water

Ideal

Modification 2(cont’d)• Results

– The Isopropanol and water mixture proved to be closer to ideal than the mixture of methanol and water.

– Isopropanol and water contain stronger molecular forces than do methanol and water. Isopropanol and water more readily mix making it the more ideal solution

– Isopropanol is more polar

Volume of Mixing

Experimental

• Seven solutions were prepared– Covers a range of mole

ratios

Mole Ratio Methanol

Mole Ratio Water

1 0

.8 .2

.6 .4

.4 .6

.2 .8

Experimental

• Volume of mixing is dependant upon density– Ideal Volume of Mixing:

– Real Volume of Mixing:

d

MXMXV 2211

2

22

1

11

d

MX

d

MXVideal

Experimental

• Pycnometers were used– Allow bubbles to escape– Accurate density measurement

Experimental

• Constant temperature is needed.– Water bath at 25°C was used

• The mass of each solution could then be calculated .

pycnometeremptypycnometerfullsolution MMM

Experimental

• Density of mixture could then be calculated:

Mole Fraction of Water

Density of Solution (g/mL)

  0 0.790

 0.2  0.846

 0.4 0.868

  0.6  0.905

 0.8  0.942

solution

solutionsolution V

Md

Literature Data: Comparison of Experimental Volume of Mixings to Simulation Data

Partial Pressure of Mixing

Partial Pressure of Mixing

Partial Pressure of Mixing (Cont.)

• Due to the exothermic nature of the mixing, the partial pressure of mixing deviated from ideality.– Because of an increased temperature of the

system, components vaporized to a larger extent than if the solution were ideal.

Conclusion

• The mixing of methanol and water is non-ideal– Heat is evolved upon mixing– Volume upon mixing does not equal the sum of the

volumes of the components– A non-linear relationship was observed between the

partial pressure of methanol and its mole fraction.

• Modifications:– An increase in temperature causes the mixture to behave

more ideally with regards to heat of mixing.– The size of the alcohol effects the ideality of the mixture.

References• 1. McQuarrie, D.A.; Simon, J.D. Physical Chemistry: a Molecular Approach. University

Science Books: Sausalito, CA, 1997; p 638.• 2. Block Diagram Of the CSC Model 4400 Isothermal Microcalorimeter; May 1998; 24

Sept. 2008 <http://www.devicelink.com/mpb/archive/98/05/9805b50a.gif>.• 3. Material Safety Data Sheet; 14 March 2001; Iowa State University; 17 Sept. 2008 <

http://avogadro.chem.iastate.edu/MSDS/Methanol.htm>.• 4. Perrot, Pierre. A to Z of Thermodynamics. Oxford University Press: Oxford, 1998.• 5. Liquid (State of Matter): Endothermic and Exothermic Solutions; Britannica Online

Encyclopedia Website; 1 Oct. 2008 <http://www.britannica.com/EBchecked/topic/343026/liquid>

• 6. Vlcek, L.; Nezbeda, I. Excess Properties Of Aqueous Mixtures Of Methanol: Simple Models Versus Experiment. Journal of Molecular Liquids 2007; pp 131-132, 158-162.

• 7. Harris, Daniel C. Quantitative Chemical Analysis, 7th ed.; W.H. Freeman and Company: New York, 2007; p 65.

• 8. Ideal Solution; Britannica Online Encyclopedia Website; 1 Oct. 2008 <http://www.britannica.com/EBchecked/topic/281790/ideal-solution>.