EXERCISE 2TERNARY SYSTEMS

Andrew Nico S. Lozano

CHEM 112.1 2L

2nd Semester A.Y. 2009-2010

GIBBS PHASE RULE

Gibbs Phase Rule

formulated by J. Willard Gibbs of Yale University

A general expression for the number of intensive variables that have to be specified for a multiphase system at equilibrium

A rule for discussing phase diagrams; applicable for all phase diagrams

Gibbs Phase Rule

Basic formula:

2F C P Where:

F = degrees of freedom = number of variables that can be varied

C = Number of components in a system P = Number of phases 2 = means that temperature and pressure

are varied

Gibbs Phase Rule

If either temperature or pressure is held constant:

If both temperature and pressure are held constant:

1F C P

F C P

TERNARY SYSTEM

Ternary System

A system having three (3) components C = 3 Gibbs Phase Rule:

2

5

F C P

F P

Ternary System

Problem:Cannot be illustrated graphically, since there

are four (4) or more parameters that can be varied

Solution for this case:Keep the temperature and pressure

constant

Ternary System

By keeping temperature and pressure constant:

In any number of phases, one can already illustrate the system using what was called a Gibbs-Roozeboom Diagram

3

F C P

F P

GIBBS-ROOZEBOOM DIAGRAM

Gibbs-Roozeboom Diagram

An equilateral triangle representing a ternary system at constant temperature and pressure

Gibbs-Roozeboom Diagram

The components are in pure state at the apices:

Apex A:Component A is pure

Apex B:Component B is pure

Apex C:Component C is pure

Gibbs-Roozeboom Diagram

The Binary systems (only 2 components as the third component is absent) are illustrated at the edges of the triangle.

i.e.

Edge A-B - mixture consists only of components A and B - %C=0, meaning C is absent

Edge A-B

Gibbs-Roozeboom Diagram

Any point inside the triangle would mean a ternary system of composition XA, XB and XC

XA + XB + XC = 1

XA = %A/100

XB = %B/100

XC = %C/100

Other important parts of the diagram

Binodal CurveThe area below such curve represents a

region of immiscibility ○ Region where which a system will not exist as

a homogeneous mixture.

Tie LineA line with which its endpoints determine the

composition of the two phasesdetermined experimentally and drawn within

the binodal curve

Other important parts of the diagram

Delta pointServes as a guide for finding the plait point

Plait PointIn this point, the two phases will have

identical compositionsUsually not located on the maximum of the

binodal curve○ The tie lines are not horizontal

A sample Gibbs-Roozeboom diagram

Plait Point

Binodal Curve

Tie lines

Delta point

MATERIALS

Apparatus

Separatory funnels Erlenmeyer Flasks Burets and Buret holders Beakers

Reagents

H2O

CHCl3 CH3COOH NaOH KHP phenolphthalein

PROCEDURE

Construction of the binodal curve for the H2O-CHCl3-CH3COOH System

Method used: Turbidimetric methodSample is titrated until the first sign of

turbidity or cloudiness is observed○ Scattering of light by the very small droplets of

a second phase that forms upon titration of sufficient amounts and shaking results to the cloudiness of the mixture

Construction of the binodal curve for the H2O-CHCl3-CH3COOH System

Solutions of CH3COOH and H2O at different concentrations of 15, 30, 45, 60 and 70 %

(v/v) were subjected to turbidimetric analysis using CHCl3 as titrant

The % composition by weight was

determined for each mixture after turbidimetry

Points were plotted on

the diagram

Construction of the binodal curve for the H2O-CHCl3-CH3COOH System

Solutions of CH3COOH and CHCl3 at different

concentrations of 15, 30, 45, 60 and 70 % (v/v) with

respect to CH3COOH were subjected to

turbidimetric analysis,this time using H2O as titrant.

The % composition by

weight was determined for each mixture

after turbidimetry

Points were plotted on the

diagram as well.

Construction of Tie Lines

Four 100g g mixtures containing the H2O-CHCl3-CH3COOH were prepared

such that there will be approximately equal volumes

of conjugate phases.

Each was equilibrated in a 250-mL separatory funnel at

25 °C.

The conjugate phases were separated and transferred into 125-mL Erlenmeyer flasks, properly labeled.

The density of each phase was measured using a

pycnometer.

5.0 mL aliquots of each conjugate phase was titrated with 1.0M NaOH, previously standardized with KHP, up to

the phenolphthalein end point.

The values of the %w/w CH3COOH were located on

the binodal curve of the diagram for each conjugate

phase.

Drawing a straight line along the two points corresponding

to each prepared sample gave the tie lines

Determination of delta and plait points

Each tie line was extended until

the tie lines intercept at a certain point

The point of intersection

gave the delta point

A tangential line was drawn along the binodal curve, starting from the

delta point

The point where the binodal curve

and the tangential line meet gives the

plait point

RESULTS AND DISCUSSION

Titration of A-B with C

Solution number

%A(v/v)

vol A, ml

mass A, g

vol B, ml

mass B, g

vol C, ml

mass C, g

total mass, g

%(w/w)A %(w/w)B %(w/w)C

total %(w/w)

1 15 3.75 3.94 0.2 0.20 21.25 31.32 35.46 11.10 0.56 88.33 100.00

2 30 7.50 7.88 0.4 0.40 17.50 25.80 34.07 23.11 1.17 75.71 100.00

3 45 11.25 11.81 2.2 2.19 13.75 20.27 34.27 34.47 6.40 59.13 100.00

4 60 15.00 15.75 5.4 5.38 10.00 14.74 35.87 43.90 15.01 41.09 100.00

5 75 17.50 18.38 8.4 8.38 7.50 11.06 37.81 48.60 22.15 29.24 100.00

where: A=CH3COOH, B=H2O, C=CHCL3

Titration of A-C with B

Solutionnumber

%A(v/v)vol A,

mlmass A,

gvol B,

mlmass B,

gvol C,

mlmass C,

gtotal

mass, g%(w/w)

A%(w/w)

B%(w/w)

Ctotal %

1 15 3.75 3.94 21.25 21.19 0.8 1.18 26.30 14.97 80.55 4.48 100.00

2 30 7.50 7.88 17.50 17.45 1.0 1.47 26.80 29.39 65.11 5.50 100.00

3 45 11.25 11.81 13.75 13.71 1.6 2.36 27.88 42.37 49.17 8.46 100.00

4 60 15.00 15.75 10.00 9.97 4.2 6.19 31.91 49.36 31.24 19.40 100.00

5 75 17.50 18.38 7.50 7.48 10.4 15.33 41.18 44.62 18.16 37.22 100.00

where: A=CH3COOH, B=H2O, C=CHCl3

Computed data for the Construction of the Binodal Curve

Sample Layer Volume A, ml vol B, ml vol C, ml

mass pycnome

ter, g

mass pycnometer +soln,

g

mass soln, g

mass pycnometer+wate

r, g

mass water, g

ρwater, g/mol

ρsoln, g/mol

P1upper 9.52 35.15 37.31 16.461 27.046 10.585 26.768 10.307 0.99704 1.023932

lower 9.52 35.15 37.31 16.461 31.425 14.964 26.768 10.307 0.99704 1.447531

P2upper 14.29 30.13 37.31 16.15 26.8 10.65 26.398 10.248 0.99704 1.036151

lower 14.29 30.13 37.31 16.15 30.834 14.684 26.398 10.248 0.99704 1.428624

P3upper 19.05 25.11 37.31 15.788 26.342 10.554 26.338 10.55 0.99704 0.997418

lower 19.05 25.11 37.31 16.616 31.171 14.555 26.906 10.29 0.99704 1.410293

P4upper 23.81 20.09 37.31 16.616 28.44 11.824 26.906 10.29 0.99704 1.145676

lower 23.81 20.09 37.31 15.788 30.39 14.602 26.338 10.55 0.99704 1.379979

Determination of the Delta and Plait points

Sample Layer Volume of aliquot, mL

ρsoln, g/ml mass of aliquot, g

NaOH concentration, mol/L

volume of NaOH

used, ml

MM A, g/mol mass A, g %(w/w)A

P1upper 5 1.023932 5.119661 0.9613 17.9 60.052 1.033331 20.1836

lower 5 1.447531 7.237657 0.9613 4.65 60.052 0.268435 3.7089

P2upper 5 1.036151 5.180755 0.9613 22.3 60.052 1.287334 24.8484

lower 5 1.428624 7.143118 0.9613 7.9 60.052 0.456051 6.3845

P3upper 5 0.997418 4.98709 0.9613 26 60.052 1.500928 30.0963

lower 5 1.410293 7.051466 0.9613 11.4 60.052 0.658099 9.3328

P4upper 5 1.145676 5.728378 0.9613 34.6 60.052 1.997388 34.8683

lower 5 1.379979 6.899895 0.9613 16.6 60.052 0.958285 13.8884

Sample Calculations

Construction of the Binodal Curve

,

(1.05 / )(3.75 ) 3.9375 3.94

A A A used

A

m V

m g mL mL g g

%( / ) 100%

3.94%( / ) 100% 11.10%

3.94 0.20 31.32

AA

A B C

A

mw w

m m m

gw w

g g g

Sample Calculations

Construction of the Tie Lines2 2

2

2

,

, ,

26.768 16.461 10.307

27.046 16.461 10.585

10.5850.99704 /

H O pycnometer H O pycnometer empty

H O

solution lower pycnometer solution pycnometer empty

solutionsolution water

H O

m m m

m g g g

m m m g g g

m gg mL

m

3, ,

1.023932 /10.307

5 1.023932 / 5.119661

117.9 0.9613 60.052 1.033331

1000

1.03%( / ) 100%

aliquot aliquot solution

A NaOH used NaOH M CH COOH

A

AA

aliquot

g mLg

m V mL g mL g

m V C M

mol g Lm mL g

L mol mL

mw w

m

3331

100% 20.1836%5.119661

g

g

Resulting Gibbs-Roozeboom Diagram

where: A=CH3COOHB=H2OC=CHCl3

Resulting Gibbs-Roozeboom Diagram

Delta point

Tie Lines

Plait point (P)Tangential line

Point b1 Point b2

Arc b1-P – CHCl3-rich phase

Arc P-b2 – H2O-rich phase

Overall Inferences

CH3COOH-H2O; CH3COOH-CHCl3Miscible; CH3COOH exhibits hydrogen

bonding with water and London interaction with CHCl3

H2O-CHCl3Only partially miscible; the two compounds

are of opposing polarities, hence the great tendency to form two phases, especially between points b1 and b2.

Applications

Mining, geological, pharmaceutical, metallurgical and agricultural studies and industries

Ex.metallic alloys, such as stainless steel (metallurgy); Shephard’s diagram (agriculture and geology)

Applications

Applications

Notes The last two Gibbs-Roozeboom Diagrams were

pre-made diagrams print-screened from the Ternary diagram plotter of the Chemix School software – Trial version: (URL: http://www.chemix-chemistry-software.com/chemistry-software.html).

The rest of the ternary diagrams were drawn using the Ternary diagram plotter of the Chemix School software and print-screened to prevent the inclusion of the software name in the presentation, a potential eyesore when presented. :P

REFERENCES

Alberty, R.A. and R.J. Silbey. 2001. Physical Chemistry. 3rd ed. MA, USA: John Wiley and Sons, Inc. p. 159.

Tamayo, J.P. 2008. CHEM 112: Physical Chemistry II Lecture Notes. UPLB:Institute of Chemistry. p. 64-66.

END