Binary Solid—Liquid DiagramMaricris Monica N. CabrerosChem 112.1 – 1L

•There are three common phases of matter: solid, liquid and gas. A substance can exist in a particular phase or phases under a given set of conditions like temperature, pressure and composition.

Gibbs Phase Rule

•F = C – P + 2

•F is the variance or number of degrees of freedom which can be varied without affecting the number of phases

• C as the number of components present • P for the number of phases present

•In this exercise, the pressure was held constant and the system was considered to be condensed. Thus reducing the equation to:

•F= C – P + 1

Binary solid-liquid system

•the two components are miscible with each other at liquid phase but are insoluble in one another as solids.

•also considered as pure solids and two component liquid system

Thermal analysis

•technique used to construct phase diagrams by relating it to the substances’ cooling curves

•From this system, a eutectic temperature (TE) can be found at which the phases can co-exist in equilibrium at fixed pressure

Binary Phase Diagram

•A binary phase diagram is a temperature - composition map which indicates the equilibrium phases present at a given temperature and composition.

•The eutectic composition (XE) and eutectic temperature (TE) are given by the intersection of the two liquid curves.

•The curves in graph (b) are plots of temperature against time obtained when liquid solutions of various compositions are allowed to cool.

•When the composition of the system reached the eutectic composition, component B begins to form together with A where the two continue to solidify at the eutectic temperature until no liquid remains, thus arrest occurs.

Arrest Temperature

Objectives

•Construct cooling curves of naphthalene-diphenylamine system

•Construct Binary solid-liquid phase diagram for the naphthalene-diphenylamine system from cooling curves

Objectives

•Determine Breaks and arrest temperature from the phase diagram

•Determine eutectic temperature and eutectic composition

MethodologyA amount of diphenylamine and B amount of naphthalene

Place into a test-tubePlace in a hot-bath to aid dissolution

Run No. mass of A mass of B1 0 5.072 1 5.073 1.5 5.074 2.5 5.07

5 5 5.07

6 5.03 0

7 5.03 1.01

8 5.03 0.675

Maintain temperature for specific run *

Place test-tube with thermometer into the set-up, fill with ice

Read temperature every 10 seconds until 20o C or arrest curve is obtained

* 90 C for runs 1-5, 62 C for runs 6-8a

Repeat for two trials except for runs 4 and 5

For the next run, use previous set-up and just add the necessary amounts A and BRecord dataDispose set-up by reheating, until melted then dispose at appropriate waste bin

Experimental Set - up

Results and DiscussionRun No.

XbBreak T, C Arrest T, C

I IIavera

geI II average

1 1 - - - 79 76 77.5

20.87003

277.5

77.5 77.5 27 27 27

30.81694

472 72.5 72.25 29 27 28

4 0.72809 70 70 70 30.5 30.5 30.5

50.57243

868 68 68 36 36 36

6 0 - - - 53 53.5 53.25

70.20956

253 53 53 35.5 35 35.25

80.15051

646 55 50.5 34 36 35

•Pure substance will have no breaks since it is only characteristic to mixtures so the cooling curves of naphthalene (run 1) and diphenylamine (run 6) consist of a single halt at the temperature corresponding to their melting point

Observation

•As the liquid solution cools at fast pace until solid appear.

• At this time, the rate of cooling is observed as slightly decreasing while the solids begin to fully form.

• At this point, the mixture approaches the eutectic composition.

Observation

•When this point was reached, the rest of the solution solidifies which gives a constant temperature.

•The solid begins to cool leading to another increase in rate of cooling until the mixture has completely solidified and a second rate of cooling occurred.

•From the various set of cooling curves, a liquidus portion of a phase diagram was obtained by plotting the break temperature as a function of composition.

• The halt from the curve then defines the eutectic temperature.

• Then from a fit of the two liquidus curves and a fit of the eutectic temperature, the euctectic composition was defined from the mutual intersection of the lines

Determination of the eutectic temperature and composition

combinations of naphthalene (A) and diphenylamine (B) at temperatures just above their melting points.

•Liquid A mixed homogeneously with liquid b

•Solid B in heterogeneous equilibrium with solution

•Solid A in heterogeneous equilibrium with solution

•Solid A mixed with solid B.

•occur at lower temperature than it will begin to occur in pure diphenylamine due to F.P. lowering

•represents the maximum solubility of

diphenylamine in naphthalene at given temperature

Appearance of diphenylamine

Determination of the eutectic temperature and composition

• the system does not form solid solution, that the components exist in their own separate pure phase in solid state.

•the system is sufficiently diluted so it behaves ideally

Assumptions

•the following equation can be used to relate the temperature, mole fraction of substance, and even the enthalpy of fusion.

Clausius-Clapeyron equation.

•1) vapor behaves as an ideal gas;• 2) volume of the condensed phase is

negligible in contrast to the volume of the vapor; and

•3) the enthalphy change accompanying the vaporization is independent of temperature applies

Theoretical Eutectic Temperature and Compositionfor A = diphenylamine

for B = naphthalene

•Since both equations are equal to 1/𝑇𝑒,

−4.306549229×10−4ln𝑋𝐵+2.830055186×10−3 = −4.654084107×10−4ln(1−𝑋𝐵)+3.06626192×10−3

•f(x) = −4.306549229×10−4lnXB + 2.830055186×10−3 + 4.654084107×10−4ln(1−XB) − 3.06626192×10−3

•f′(x) = 0 =( −4.306549229×10−4 / 𝑋𝐵) +( 4.654084107×10−4)/ 1−𝑋𝐵

•Using Newton Raphson MethodAnd assuming, XB = 0.5

•Xn+1=x−(f(x) / f′(x))

• XB=0.357957449

•XA=1−0.3580 or XA=0.642042551

•Te=305.5782036 K

Parameter Eutectic Temperature,

C

Euctectic compositionMole

fraction of naphthalene

Mole fraction of

diphenylamine

Theoretical value

32 0.357957449

0.642042551

Experimental value

32. 95 0.36 0.64

Percent error, %

2.96875 0.570613 -0.31813

at the eutectic point

•solid naphthalene, •solid diphenylamine, and •the liquid mixture.

Gibbs Phase Rule•the degrees of freedom, F, is equal to

zero, 0, so the eutectic point is therefore invariant at a fixed pressure.

•F= C – P + 1•F=2-3+1

•F=0

Importance of Phase Diagram•preparation of countless commercial

chemical products in which great effort is taken to ensure that the final product is attractive practically and physically.

Conclusion•The phase diagram of naphthalene and

diphenylamine, a mixture of miscible liquids but completely immiscible solids illustrates the equilibrium relationship between phases of the mixture.

•The eutectic point is the lowest melting point of the mixture in which three phases can be seen, the solid naphthalene, solid diphenylamine and the liquid mixture. From this, F=0, or there is invariance at the eutectic point.

There are four possible combinations of the mixture, or regions in the diagram.

•The first consist of both liquid A and B.• Next is composed of solid A and liquid

mixture, while the third id made of solid B and also liquid mixture.

• The last region which is below the E.P consist of solid A and B

References

• Atkins, P.W. 2006. Physical Chemistry. 8th ed. New York: Oxford University Press. pp. 176,189- 193.

• D. P. Shoemaker, C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 5thEdition, McGraw-Hill, New York, 1994, pp. 195-197, 238-246. (6th edition, pp 179-182, 215-

• 222.)• G. P. Matthews, Experimental Physical Chemistry,

Clarendon Press, Oxford, 1985, pp. 46-48, 52-53.