applied physical chemistry
TRANSCRIPT
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PHASE DIAGRAMSPHASE DIAGRAMS
Chapter 6Chapter 6
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Phase DiagramsPhase Diagrams
Lets apply our knowledge of theLets apply our knowledge of the
thermodynamics of simple mixtures to discussthermodynamics of simple mixtures to discuss
the physical changes of mixtures when they arethe physical changes of mixtures when they are
heated or cooled and when their compositionsheated or cooled and when their compositions
are changed.are changed.
We will see how phase diagrams can be used toWe will see how phase diagrams can be used to
judge whether two substances are mutuallyjudge whether two substances are mutuallymiscible.miscible.
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Phase DiagramsPhase Diagrams
We will see whether equilibrium can exist over aWe will see whether equilibrium can exist over a
range of conditions or whether a system must berange of conditions or whether a system must be
bought to a definite pressure, temperature andbought to a definite pressure, temperature and
composition before equilibrium is established.composition before equilibrium is established.
Phase diagrams are industrially and commerciallyPhase diagrams are industrially and commercially
important.important.
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Phase DiagramsPhase Diagrams
Semiconductor, ceramics, steel and alloySemiconductor, ceramics, steel and alloy
industries rely heavily on phase diagrams toindustries rely heavily on phase diagrams to
ensure uniformity of a product.ensure uniformity of a product.
Phase diagrams are also the basis for separationPhase diagrams are also the basis for separation
procedures in the petroleum industry and theprocedures in the petroleum industry and the
formulation of foods and cosmetic preparations.formulation of foods and cosmetic preparations.
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DefinitionsDefinitions
A phase is a state of matter that is uniformA phase is a state of matter that is uniform
throughout, not only in composition but also inthroughout, not only in composition but also in
physical state.physical state.
A pure gasA pure gas
A gaseous mixtureA gaseous mixture
Two totally miscible liquidsTwo totally miscible liquids A crystalA crystal
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DefinitionsDefinitions
A solution of sodium chlorideA solution of sodium chloride
IceIce
A slurry of ice and waterA slurry of ice and water
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DefinitionsDefinitions
An alloy of two metals?An alloy of two metals?
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DefinitionsDefinitions
An alloy of two metals is a two phase system ifAn alloy of two metals is a two phase system if
the metals are immiscible, but a single phasethe metals are immiscible, but a single phase
system if they are miscible.system if they are miscible.
Dispersion can be uniform on a macroscopicDispersion can be uniform on a macroscopic
level, but not on a microscopic scale.level, but not on a microscopic scale.
Dispersions are important in many advancedDispersions are important in many advanced
materials.materials.
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DefinitionsDefinitions
Heat treatment cycles are used to achieve theHeat treatment cycles are used to achieve the
precipitation of a fine dispersion of particles ofprecipitation of a fine dispersion of particles of
one phase within a matrix formed by a saturatedone phase within a matrix formed by a saturated
solid solution phase.solid solution phase.
The ability to control this microstructureThe ability to control this microstructure
resulting from phase equilibria makes it possibleresulting from phase equilibria makes it possible
to tailor the mechanical properties of theto tailor the mechanical properties of thematerials.materials.
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DefinitionsDefinitions
A constituent of a system is a chemical speciesA constituent of a system is a chemical species
(an ion or a molecule) that is present.(an ion or a molecule) that is present.
A
mixture of water and ethanol has twoA
mixture of water and ethanol has twoconstituents.constituents.
A solution of sodium chloride has threeA solution of sodium chloride has three
constituents: Naconstituents: Na++, Cl, Cl--, H, H22O.O.
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DefinitionsDefinitions
A component is a chemically independentA component is a chemically independent
constituent of a system.constituent of a system.
The number of components in a system is theThe number of components in a system is theminimum number of independent speciesminimum number of independent species
necessary to define the composition of all thenecessary to define the composition of all the
phases present in the system.phases present in the system.
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DefinitionsDefinitions
When no reaction takes place and there are noWhen no reaction takes place and there are no
other constraints, the number of components isother constraints, the number of components is
the equal to the number of constituents.the equal to the number of constituents.
Pure water is a one component systemPure water is a one component system
A mixture of ethanol and water is twoA mixture of ethanol and water is two
component system.component system.
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DefinitionsDefinitions
An aqueous solution of sodium chloride is a twoAn aqueous solution of sodium chloride is a two
component system, because by charge balance,component system, because by charge balance,
the number of Nathe number of Na++ ions must be the same as theions must be the same as the
number of Clnumber of Cl-- ions.ions.
A system that consists of hydrogen, oxygen andA system that consists of hydrogen, oxygen and
water at room temperature has threewater at room temperature has three
components.components.
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DefinitionsDefinitions
When a reaction can occur under the conditionsWhen a reaction can occur under the conditions
prevailing in the system, we need to decide theprevailing in the system, we need to decide the
minimum number of species that, after allowingminimum number of species that, after allowing
for reactions in which one species is synthesizedfor reactions in which one species is synthesized
from others, can be used to specify thefrom others, can be used to specify the
composition of all the phases.composition of all the phases.
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DefinitionsDefinitions
CaCOCaCO3(s)3(s) CaOCaO(s)(s) + CO+ CO2(g)2(g)
3 phases3 phases
3 constituents3 constituentsTo specify the composition of the gas phase, weTo specify the composition of the gas phase, we
need the species COneed the species CO22, and to specify the, and to specify the
composition of the solid phase on the right, wecomposition of the solid phase on the right, we
need the species CaO.need the species CaO.
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DefinitionsDefinitions
CaCOCaCO3(s)3(s) CaOCaO(s)(s) + CO+ CO2(g)2(g)
We do not need an additional species to specifyWe do not need an additional species to specify
the composition of the phase on the right,the composition of the phase on the right,because its identity (CaCObecause its identity (CaCO33) can be expressed in) can be expressed in
terms of the other two constituents by makingterms of the other two constituents by making
use of the stoichiometry of the reaction.use of the stoichiometry of the reaction.
2 component system.2 component system.
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DefinitionsDefinitions
NHNH44ClCl(s)(s) NHNH3(g)3(g) + HCl+ HCl(g)(g)
2 phases2 phases
3constituents
3constituents
1 component1 component
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DefinitionsDefinitions
The number of phases, P.The number of phases, P.
The number of components, C.The number of components, C.
The variance of the system, F is the number ofThe variance of the system, F is the number ofintensive variables (e.g. p and T) that can beintensive variables (e.g. p and T) that can be
changed independently without disturbing thechanged independently without disturbing the
number of phases in equilibrium.number of phases in equilibrium.
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Phase RulePhase Rule
F = CF = C P + 2P + 2
This is not an empirical rule based uponThis is not an empirical rule based upon
observations, it can be derived from chemicalobservations, it can be derived from chemical
thermodynamics (Justification 6.1).thermodynamics (Justification 6.1).
For a one component system F = 3For a one component system F = 3 PP
When only one phase is present, F = 2 and bothWhen only one phase is present, F = 2 and both
p and T can be varied without changing thep and T can be varied without changing the
number of phases.number of phases.
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Phase RulePhase Rule
When two phases are present, F = 1 whichWhen two phases are present, F = 1 which
implies that pressure is not freely variable if theimplies that pressure is not freely variable if the
pressure is set. This is why at a givenpressure is set. This is why at a given
temperature a liquid has a characteristic vaportemperature a liquid has a characteristic vapor
pressure.pressure.
When three phases are present, F = 0. ThisWhen three phases are present, F = 0. This
special case occurs only at a definite temperaturespecial case occurs only at a definite temperatureand pressure that is characteristic of theand pressure that is characteristic of the
substance.substance.
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Experimental ProceduresExperimental Procedures
Thermal analysisThermal analysis a sample is allowed to coola sample is allowed to cool
and it temperature is monitored. When a phaseand it temperature is monitored. When a phase
transition occurs, cooling may stop until thetransition occurs, cooling may stop until the
phase transition is complete and is easilyphase transition is complete and is easily
observed on a thermogram.observed on a thermogram.
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Experimental ProceduresExperimental Procedures
Modern work on phase transitions often dealModern work on phase transitions often deal
with systems at very high pressures and morewith systems at very high pressures and more
sophisticated detection properties must besophisticated detection properties must be
adopted.adopted.
A diamond anvil cell is capable of producingA diamond anvil cell is capable of producing
extremely high pressures.extremely high pressures.
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Experimental ProceduresExperimental Procedures
A sample is placed in a cavity between to gemA sample is placed in a cavity between to gem--
quality diamonds and then pressure is exerted byquality diamonds and then pressure is exerted by
turning a screw. Pressures up to ~2Mbar can beturning a screw. Pressures up to ~2Mbar can be
achieved.achieved.
One application is the study the transition ofOne application is the study the transition of
covalent solids to metallic solids.covalent solids to metallic solids.
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Experimental ProceduresExperimental Procedures
Iodine, IIodine, I22, becomes metallic at ~ 200 kbar and, becomes metallic at ~ 200 kbar and
makes a transition to a monatomic metallic solidmakes a transition to a monatomic metallic solid
at around 210 kbar.at around 210 kbar.
Relevant to the structure of material deep insideRelevant to the structure of material deep inside
the Earth and in the interiors of giant planets,the Earth and in the interiors of giant planets,
where even hydrogen may be metallic.where even hydrogen may be metallic.
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Two Component SystemsTwo Component Systems
When two components are present in a system,When two components are present in a system,
C = 2, so F = 4C = 2, so F = 4 P.P.
If the temperature is constant, the remainingIf the temperature is constant, the remaining
variance is F = 3variance is F = 3 P.P.
F indicates that one of the degrees of freedom hasF indicates that one of the degrees of freedom has
been discardedbeen discarded in this case the temperature.in this case the temperature.
The two remaining degrees of freedom are theThe two remaining degrees of freedom are thepressure and the compositionpressure and the composition
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Two Component SystemsTwo Component Systems
The partial vapor pressure of the components of anThe partial vapor pressure of the components of an
ideal solution of two volatile liquids are related toideal solution of two volatile liquids are related to
the composition of the liquid mixture by Raoultsthe composition of the liquid mixture by Raoults
Law:Law:pA ! xApA
*pB ! xBpB
*
p ! pA p
B! x
Ap
A
* x
Bp
B
*! x
Ap
A
* (1 x
A)p
B
*
p ! xApA* pB
* xApB
*
p ! pB* (pA
* pB
* )xA
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Two Component SystemsTwo Component Systems
This expression shows that the total vapor pressureThis expression shows that the total vapor pressure
(at a fixed temperature) changes linearly with the(at a fixed temperature) changes linearly with thecomposition from pcomposition from pBB
** to pto pAA
** as xas xAA
changes from 0changes from 0
to 1.to 1.
p ! pB* (pA
* pB
* )xA
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p ! pB* (pA
* pB
*)xA
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Two Component SystemsTwo Component Systems
The compositions of the liquid vapor that are inThe compositions of the liquid vapor that are in
mutual equilibrium are not necessarily the same.mutual equilibrium are not necessarily the same.
The more volatile the component, the higherThe more volatile the component, the higher
amount of that substance should be in the vapor.amount of that substance should be in the vapor. yy
AAand yand yBB are the mole fractions ofA and B in theare the mole fractions ofA and B in the
gas.gas.
yA ! pAp
yB ! pBp
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yA!p
A
p!
xAp
A
*
pB (pA* pB
*
)xA
yB!1 y
A
pA
*
pB
*
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p !pA
* pB*
pA* (pB
* pA
*)yA
pA*
pB*
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p !pA
* pB*
pA* (pB
* pA
*)yA
ppA
*! pB
*
pA*
when yA is zero
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Two Component SystemsTwo Component Systems
If we are interested in distillation, both vaporIf we are interested in distillation, both vapor
and liquid compositions are of equal interest.and liquid compositions are of equal interest.
So it makes sense to present data showing bothSo it makes sense to present data showing both
the dependence of vapor and liquid compositionthe dependence of vapor and liquid composition
upon mole fraction.upon mole fraction.
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The lever ruleThe lever rule
A point in the twoA point in the two--phase of a phase diagramphase of a phase diagram
indicates not only qualitatively that both liquidindicates not only qualitatively that both liquid
and vapor present, but represents quantitativelyand vapor present, but represents quantitatively
the relative amounts of each.the relative amounts of each.
To find the relative amounts of two phasesTo find the relative amounts of two phases EE
andand FF that are in equilibrium, we measure thethat are in equilibrium, we measure the
distances ldistances lEE and land lFF along the horizontal tie line,along the horizontal tie line,and then use the lever rule.and then use the lever rule.
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The lever ruleThe lever rule
Where nWhere nEE is the amount of phaseis the amount of phase EE and nand nFF is theis the
amount of phaseamount of phase FF..
nE lE ! nF lF
nE
nF!
lF
lE
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TemperatureTemperature--compositioncomposition
diagramsdiagramsTo discuss distillation we need a temperatureTo discuss distillation we need a temperature--
composition diagram instead of a pressurecomposition diagram instead of a pressure--
composition diagram.composition diagram. Such a diagram shows composition at differentSuch a diagram shows composition at different
temperatures at a constant pressure (typically 1temperatures at a constant pressure (typically 1
atm).atm).
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TemperatureTemperature--compositioncomposition
diagramsdiagrams In a simple distillation the vapor is withdrawnIn a simple distillation the vapor is withdrawn
and condensed. This technique is used toand condensed. This technique is used to
separate a volatile liquid from a nonseparate a volatile liquid from a non--volatilevolatile
solute or solid.solute or solid.
In a fractional distillation, the boiling andIn a fractional distillation, the boiling and
condensation cycle is repeated successively. Thiscondensation cycle is repeated successively. This
technique is used to separate volatile liquids.technique is used to separate volatile liquids.
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TemperatureTemperature--compositioncomposition
diagramsdiagramsThe efficiency of a fractionating column isThe efficiency of a fractionating column is
expressed in terms of the number of theoreticalexpressed in terms of the number of theoretical
plates, the number of effective vaporization andplates, the number of effective vaporization and
condensation steps that are required to achieve acondensation steps that are required to achieve a
condensate of given composition from a givencondensate of given composition from a given
distillate.distillate.
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AzeotropesAzeotropes
Although many liquids have temperatureAlthough many liquids have temperature--
composition phase diagrams resembling the idealcomposition phase diagrams resembling the ideal
version, a number of important liquids deviate fromversion, a number of important liquids deviate from
ideality.ideality. If a maximum occurs in the phase diagram,If a maximum occurs in the phase diagram,
favorable interactions between A and B moleculesfavorable interactions between A and B molecules
stabilize the liquid.stabilize the liquid.
If a maximum occurs in the phase diagram,If a maximum occurs in the phase diagram,
unfavorable interactions between A and Bunfavorable interactions between A and B
molecules demolecules de--stabilize the liquid.stabilize the liquid.
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AzeotropesAzeotropes
An azeotrope is a mixture of two (or more) miscibleAn azeotrope is a mixture of two (or more) miscible
liquids that when boiled produce the sameliquids that when boiled produce the same
composition in the vapor phase as that is present incomposition in the vapor phase as that is present in
the original mixture.the original mixture.
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Immiscible liquidsImmiscible liquids
Lets consider the distillation of two immiscibleLets consider the distillation of two immiscible
liquids, such as octane and water.liquids, such as octane and water.
The system can be considered as the jointThe system can be considered as the joint
distillation of the separated components.distillation of the separated components.
Total vapor pressure p = pTotal vapor pressure p = pAA
** + p+ pBB**
Mixture boils when p = 1 atm, and so the mixtureMixture boils when p = 1 atm, and so the mixture
boils at a lower temperature than either componentboils at a lower temperature than either componentwould alone.would alone.
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LiquidLiquid--liquid phaseliquid phase
diagramsdiagrams Lets consider temperatureLets consider temperature--composition diagramscomposition diagramsfor systems that consist of pairs of partially misciblefor systems that consist of pairs of partially miscible
liquids.liquids.
Partially miscible liquids are liquids that do not mixPartially miscible liquids are liquids that do not mix
at all proportions at all temperatures.at all proportions at all temperatures.
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Phase separationPhase separation
Suppose a small amount of liquids B is added toSuppose a small amount of liquids B is added to
another liquid A at a temperature T.another liquid A at a temperature T.
If it dissolves completely the binary mixture is aIf it dissolves completely the binary mixture is a
single phase.single phase.
As more B is added, A becomes saturated in B andAs more B is added, A becomes saturated in B and
no more B dissolvesno more B dissolves 2 phases.2 phases.
Most abundant phase is A saturated with B.Most abundant phase is A saturated with B. Minor phase is B saturated with A.Minor phase is B saturated with A.
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Phase separationPhase separation
The relative abundance of each phase is given byThe relative abundance of each phase is given by
the lever rule.the lever rule.
As the amount of B increases the composition ofAs the amount of B increases the composition of
each phase stays the same, but the amount of eacheach phase stays the same, but the amount of each
changes with the lever rule.changes with the lever rule.
Eventually a point is reached when so much B isEventually a point is reached when so much B is
present that it can dissolve all the A, and systempresent that it can dissolve all the A, and systemreverts to a single phase.reverts to a single phase.
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Critical solutionCritical solution
temperaturestemperatures The upper critical solution temperature, TThe upper critical solution temperature, Tucuc is theis thehighest temperature at which phase separationhighest temperature at which phase separation
occurs.occurs.
Above the critical temperature the two componentsAbove the critical temperature the two components
are fully miscible.are fully miscible.
On the molecular level, this can be interpreted asOn the molecular level, this can be interpreted as
the kinetic energy of each molecule over comingthe kinetic energy of each molecule over comingmolecular interactions that want molecules of onemolecular interactions that want molecules of one
type to come close together.type to come close together.
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Critical solutionCritical solution
temperaturestemperatures Some systems show a lower critical solutionSome systems show a lower critical solutiontemperature, Ttemperature, Tlclc..
Below this temperature the two components mix inBelow this temperature the two components mix in
all proportions and above which they form twoall proportions and above which they form two
phases.phases.
An example is water and triethylamine.An example is water and triethylamine.
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Critical solutionCritical solution
temperaturestemperatures The molecular reason for this is that water andThe molecular reason for this is that water andtriethylamine form a weak molecular complex. Attriethylamine form a weak molecular complex. At
higher temperatures the complexes break up andhigher temperatures the complexes break up and
the two components are less miscible.the two components are less miscible.
Some systems have upper and lower criticalSome systems have upper and lower critical
solution temperatures.solution temperatures.
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Distillation of partiallyDistillation of partially
miscible liquidsmiscible liquids What happens when you distill partially miscibleWhat happens when you distill partially miscibleliquids?liquids?
A pair of liquids that are partially miscible oftenA pair of liquids that are partially miscible often
form a lowform a low--boiling azeotrope.boiling azeotrope.
Two possibilities can exist: one in which the liquidTwo possibilities can exist: one in which the liquid
become fully miscible before they boil; the other inbecome fully miscible before they boil; the other in
which boiling occurs before mixing is complete.which boiling occurs before mixing is complete.
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LiquidLiquid--solid phase diagramssolid phase diagrams
The knowledge of temperatureThe knowledge of temperature--compositioncomposition
diagrams for solid mixtures guides the design ofdiagrams for solid mixtures guides the design of
important industrial processes, such as theimportant industrial processes, such as the
manufacture of liquid crystal displays andmanufacture of liquid crystal displays andsemiconductors.semiconductors.
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EutecticsEutectics
The isopleth at e corresponds to the eutecticThe isopleth at e corresponds to the eutectic
composition, the mixture with the lowest meltingcomposition, the mixture with the lowest melting
point.point.
A liquid with a eutectic composition freezes at aA liquid with a eutectic composition freezes at asingle temperature without depositing solid A or B.single temperature without depositing solid A or B.
A solid with the eutectic composition melts withoutA solid with the eutectic composition melts without
any change of composition at the lowestany change of composition at the lowesttemperature of any mixture.temperature of any mixture.
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EutecticsEutectics
SolderSolder 67% tin and 33% lead by mass melts at67% tin and 33% lead by mass melts at
183183rrC.C.
23% NaCl and 77% H23% NaCl and 77% H22O by mass forms a eutecticO by mass forms a eutectic
mixture which melts atmixture which melts at --21.121.1 rrC. Above thisC. Above thistemperature the mixture melts.temperature the mixture melts.
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Reacting SystemsReacting Systems
Many binary mixtures react produce compounds.Many binary mixtures react produce compounds.
Gallium arsenide is a technologically importantGallium arsenide is a technologically important
exampleexample semiconductor.semiconductor.
Ga + AsGa + As GaAsGaAs
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