Gibbs Phase Rule (Examples)
Summary
TLDRThe video script discusses the Gibbs Phase Rule, which determines the degrees of freedom in a system by subtracting the number of coexisting phases from the number of components and adding two. Examples include single-component systems, multi-component solutions like air and carbonated water, solid solutions like brass, and complex systems with multiple phases and components. The rule is shown to be applicable regardless of system complexity, illustrating how it dictates the number of variables that can be independently controlled.
Takeaways
- đ The Gibbs Phase Rule states that the number of degrees of freedom in a system is equal to the number of components minus the number of coexisting phases plus two.
- đ In a single-component system, the degrees of freedom are calculated as 1 (for the component) + 2 (from the rule), resulting in 3 degrees of freedom.
- đĄïž For a two-component single-phase system, like a gaseous mixture of nitrogen and oxygen, the degrees of freedom are also three, allowing specification of temperature, pressure, and composition.
- đ§ In the case of carbonated water, a two-component system with liquid and gas phases, the degrees of freedom are reduced to two, as the pressure of the vapor phase components is determined by phase equilibrium.
- đ© Brass, a solid mixture of copper and zinc, has three degrees of freedom, allowing for the specification of the mole fraction of copper, temperature, and pressure, with the mole fraction of zinc being determined by the first.
- đŹ A saturated sucrose solution has two degrees of freedom, as the concentration of sugar is fixed at the saturation point, leaving only temperature and pressure as variables.
- đ§Ș For a system with three components in three phases, such as a liquid solution of water and propanol with a dissolved solute like sugar or salt, the degrees of freedom are two, despite the complexity of the system.
- đĄïžđŠ The phase rule applies to both simple and complex systems, indicating that the number of variables that can be independently controlled is limited by the components and phases present.
- đ The rule helps in understanding that once certain variables are set, others will be determined by the equilibrium conditions of the system.
- đ In a saturated solution, increasing the concentration of the solute beyond the saturation point will result in precipitation, and decreasing it will cause dissolution to maintain equilibrium.
- đ€ïž The phase rule is a fundamental principle in thermodynamics that helps predict the behavior of systems at equilibrium, regardless of the number of components or phases involved.
Q & A
What does the Gibbs Phase Rule state?
-The Gibbs Phase Rule states that the number of degrees of freedom in a system is equal to the number of components minus the number of phases coexisting at equilibrium, plus two.
How many degrees of freedom are there in a single-component system according to the Gibbs Phase Rule?
-In a single-component system, there are three degrees of freedom. This is calculated as the number of components (1) minus the number of phases (assumed to be 1), plus two.
What is an example of a two-component single-phase system and its degrees of freedom?
-An example of a two-component single-phase system is a mixture of nitrogen and oxygen, like air. The degrees of freedom for this system is three, calculated as the number of components (2) minus the number of phases (1), plus two.
How does the Gibbs Phase Rule apply to a system with two components in two different phases?
-For a system with two components in two different phases, such as a carbonated water system with liquid water and gaseous CO2, the degrees of freedom is two. This is calculated as the number of components (2) minus the number of phases (2), plus two.
What is an example of a solid phase system with two components and its degrees of freedom?
-An example of a solid phase system with two components is brass, which is a mixture of copper and zinc. The degrees of freedom for this system is three, calculated as the number of components (2) minus the number of phases (1, the solid phase), plus two.
What happens to the degrees of freedom when a solution becomes saturated with a solute?
-When a solution becomes saturated with a solute, the degrees of freedom decrease by one. For a two-component system with two phases coexisting (like a saturated sugar solution), the degrees of freedom are two, as you can specify temperature and pressure but not the concentration of the solute independently.
Why can't you specify more than two degrees of freedom in a saturated solution with two components and two phases?
-In a saturated solution with two components and two phases, you can only specify two degrees of freedom because the concentration of the solute is fixed at the saturation point. Any attempt to change the concentration will result in precipitation or dissolution to maintain equilibrium.
What is the degrees of freedom for a system with three components in three phases?
-For a system with three components in three phases, the degrees of freedom is two. This is calculated as the number of components (3) minus the number of phases (3), plus two.
How does the presence of a non-volatile solute in a two-component two-phase system affect the degrees of freedom?
-The presence of a non-volatile solute in a two-component two-phase system does not change the degrees of freedom. The system still has two degrees of freedom, as the non-volatile solute will precipitate into a solid phase and does not affect the vapor pressure equilibrium of the volatile components.
Can the Gibbs Phase Rule be applied to complex systems with multiple components and phases?
-Yes, the Gibbs Phase Rule can be applied to any system, no matter how complex, with multiple components and phases. It will accurately determine the number of independent variables that can be controlled in the system.
What is the significance of the Gibbs Phase Rule in understanding phase equilibrium?
-The Gibbs Phase Rule is significant in understanding phase equilibrium as it provides a quantitative relationship between the number of components, phases, and degrees of freedom in a system. It helps predict the behavior of a system when variables such as temperature, pressure, and composition are altered.
Outlines
đ Introduction to Gibbs Phase Rule
The first paragraph introduces the Gibbs Phase Rule, which is a fundamental concept in thermodynamics. It explains that the number of degrees of freedom in a system is determined by the formula: the number of components minus the number of coexisting phases plus two. The paragraph provides examples to illustrate this rule, including single-component systems and multi-component single-phase systems like air. It also discusses the case of carbonated water, a two-component two-phase system, and how the degrees of freedom are limited once the system reaches a certain state of equilibrium.
đ Applying the Gibbs Phase Rule to Various Systems
This paragraph delves deeper into applying the Gibbs Phase Rule to different types of systems, starting with a solid phase example using brass, a mixture of copper and zinc. It then moves on to a single-phase solution of sucrose in water, explaining how the degrees of freedom change when the solution becomes saturated and precipitates the solute. The discussion includes the loss of a degree of freedom when the system reaches saturation, and the inability to independently control all variables in such a state.
đ Complex Systems and the Gibbs Phase Rule
The final paragraph explores the application of the Gibbs Phase Rule to more complex systems, including a three-component three-phase system with a liquid, vapor, and solid phase. It uses the example of a solution of water and propanol with a dissolved solute like sugar or salt, which can precipitate in the solid phase. The paragraph emphasizes that despite the complexity of the system, the Gibbs Phase Rule accurately predicts the number of degrees of freedom, illustrating that the rule is universally applicable regardless of the system's composition or phase distribution.
Mindmap
Keywords
đĄGibbs Phase Rule
đĄDegrees of Freedom
đĄComponents
đĄPhases
đĄEquilibrium
đĄMole Fraction
đĄVapor Pressure
đĄSaturation
đĄNon-Volatile Solute
đĄThermodynamic Variables
Highlights
Introduction to the Gibbs Phase Rule and its significance in determining the degrees of freedom in a system.
Explanation of the formula for the Gibbs Phase Rule: F = C - P + 2, where F is degrees of freedom, C is components, and P is phases.
Application of the Gibbs Phase Rule to a single component system, resulting in three degrees of freedom.
Example of a two-component single phase system, such as air, with three degrees of freedom.
Discussion on the degrees of freedom in a carbonated water system, illustrating the rule's application to two-phase systems.
Exploring degrees of freedom in a solid phase system, like brass, which has three degrees of freedom.
Analysis of a single-phase solution, such as sugar water, and its three degrees of freedom.
Transition from a single-phase to a two-phase system with a saturated sucrose solution and the resulting loss of a degree of freedom.
Clarification on why the concentration of sugar in a saturated solution cannot be independently specified.
Complex example involving a three-component system with three phases, demonstrating the rule's versatility.
Explanation of the limited degrees of freedom in a three-component, three-phase system, despite its complexity.
Illustration of how the Gibbs Phase Rule applies to systems with varying components and phases, emphasizing its universality.
Final summary emphasizing that the Gibbs Phase Rule dictates the number of variables that can be controlled in any system.
Transcripts
all right so the gibbs phase rule
tells us that the number of degrees of
freedom we have the flexibility to
choose is equal to the number of
components of a solution
of a system minus the number of phases
coexisting at equilibrium in that system
plus two so let's work a few examples
and make sure
that makes sense to us we can first do a
couple of examples where we already know
the answer
the
case of a single component system we
just have one component
so c equals 1 then if i just plug x
equals 1 into this equation
1 plus 2 is equal to 3 minus 5
and that's the same result we've gotten
previously for the number of degrees of
freedom
accessible to us in a single component
system
so the gibbs phase rule is a more
generalized version
of the rule we've used previously for
single phases
if we want to talk about multiple
component solutions or systems
the two examples we considered by hand
in the previous lecture
the first of those was a gaseous system
with a composition
something like air a mixture of nitrogen
and oxygen so that was a
two component single phase system
the number of degrees of freedom is two
components
minus one phase plus two
so two minus one plus two that equals
three and that's
the result we convinced ourselves uh
was reasonable for that system for
example
we could specify the temperature and the
pressure and the composition
of that mixture but once we've specified
three variables i can't also specify the
mole fraction of oxygen
per the other example we thought about
in the previous lecture was carbonated
water
a mixture of co2 and h2o
in the liquid and gas phases
coexisting so the picture we drew in
that case was
liquid water dissolved co2
water and co2 both in the gas phase
that's again a two component system co2
and h2o
two phases coexisting with each other
so the number of degrees of freedom
components
minus phases plus 2
that gives me 2. so we have only two
variables we can specify
again that matches what we convinced
ourselves was the case
in that example i can dissolve a certain
concentration
of co2 i can set the temperature to
whatever i want but then the pressures
of the vapor phase components will be
determined
by the phase equilibrium so for example
i could set
temperature and concentration of co2
i could set i could put the
system under whatever pressure i want i
can choose the temperature i can choose
the pressure but once i've determined
the pressure
if the pressure in the vapor phase is
higher
than the vapor pressure of co2 it will
dissolve into the liquid if the pressure
is higher than the vapor pressure
of h2o it will dissolve it will condense
down into the liquid phase
so i can choose
two variables but once i've chosen those
two the other ones will be
determined for me to work a few examples
we haven't considered yet
let's do one in the solid phase
let's take a mixture of two compounds in
the solid phase so for example
brass is a mixture of copper and zinc
how many degrees of freedom i'm am i
allowed to specify
for a chunk of brass so that's
two components copper and zinc
one phase i'm just talking about the
solid so there's only a single phase
so components minus
phases plus two two minus 1 plus 2 is
again equal to 3 that's the same math as
in
this situation so is that reasonable can
i think of three different variables
that i could specify
for a sample of solid brass
i can i can specify
the mole fraction of copper
in that sample and then i can take that
sample and i can
heat it to whatever temperature i want i
can set the i can put it under some
amount of pressure
there's no contradiction between doing
all those three things at the same time
but again i couldn't also independently
set the mole fraction of the other
component once i choose
the mole fraction of copper mole
fraction of zinc is determined for me
let's take uh
as a multi-phase system instead of solid
instead of liquid and vapor phase let's
do one
actually first let's do
a solution with only a single phase so
let's
say
pure liquid so there's no vapor in this
case
just a container canning liquid and
let's do
i want to eventually consider a solution
that we could
over saturate so let's take a solute
like sugar
sucrose i'll dissolve some sugar in
water to make a sugar water solution
so that's two components
single phase again like every time we've
considered two components single phase
two minus one plus two
is going to work out to three different
variables that we could independently
specify
and again that makes sense in this case
i can choose a composition variable i
can choose
the concentration of sucrose i can make
a one molar
solution of sucrose i can make a half
molar solution of sucrose
i can place that sample at any
temperature i want
and any pressure i want within a certain
range of
possible values so that's very much like
the single phase systems we've
considered in the gas phase or the
the solid phase but now
let's take that the concentration of
that sucrose solution to a point where
it's saturated
i'll keep dissolving
sucrose in my water until it's so
concentrated that the sucrose begins to
precipitate
so i'm recording this in south carolina
where we like our sweet tea so
the way to make sweet tea is there's all
so much water
that it precipitates and sits on the
bottom of the solution so that saturated
solution now i've got
two components and two different phases
in coexistence
water and sucrose are the two components
the two phases are the liquid phase and
the solid phase
so now the number of degrees of freedom
two minus two plus two
that works out to two degrees of freedom
that's a different answer than i had for
this saturated solution this solution
below the saturation concentration so
which
variable have i lost why does it make
sense that i can no longer specify all
three of these
concentrate these thermodynamic
variables at the same time
i could specify
the temperature and the pressure i can
certainly take my sugar water solution
and heat it up or cool it down make it
any range of temperatures
i can put it under some pressure there's
nothing to stop me from doing that
but what i can't specify any longer is
the concentration of sugar
so i can only specify temperature and
pressure if i try to
increase the concentration of sugar to
even more concentrated concentrations if
i add more sugar
sugar into this solution then what's
going to happen is it won't stay in
solution
it will just precipitate out the keeping
the concentration of the solution at the
saturation concentration
likewise if i try to reduce the
concentration
up here in the liquid phase by removing
some sucrose molecules from the liquid
phase
because of the equilibrium between these
two phases some solid molecules will
just dissolve
and replace the moltens i've taken out
of the liquid solution so
the the sucrose concentration is fixed
at the
saturation concentration at this
particular temperature and pressure
so the gibbs phase rule is correctly
telling us that we've lost a degree of
freedom
in this case and as one final example
just to take something even more
complicated to show you that
you don't need just simple two-phase
cases you don't need two component
solutions let's
make an example
that's even more complicated let's say
we have a
liquid in equilibrium with vapor let's
make it a two component solution
so i've got who knows water and
propanol in this liquid solution
both of those are volatile solvents and
they'll have vapor
up in the gas phase but now into this
two component two phase solution let's
also dissolve a solute so let's dissolve
a third component maybe sugar or salt or
something else
that's in the liquid phase if it's salt
it's a non-volatile solute so there
won't be any up in the vapor phase
but it will if i'm at saturation
conditions precipitate down into the
solid phase
so now i've got three components
propanol and salt or or three different
components
in three different phases vapor phase
liquid phase solid phase
so that tells me the number of degrees
of freedom in this case is three
components
minus three phases plus two i still
only despite the complicated uh setup of
the system i've only got
two degrees of freedom that i'm allowed
to specify according to
the gibbs phase rule so does that make
sense
why can't i specify more than just two
degrees of freedom
as an example i can
dissolve i can certainly set the mole
fraction of compound on a
in the liquid phase so i can make a 50
50
mixture of the two solvents if i want to
i can heat or cool that system down to
whatever temperature i'm interested in
but i can't choose the mole fraction of
c
since i'm at saturation then this is
going to be the saturation concentration
i can't choose the amount of a in the
vapor phase at this particular
temperature the vapor pressure of a is
some number
at this particular temperature the vapor
pressure of b is some number so those
two pressures are going to add to some
total pressure
in the gas phase so i can't choose the
pressure
to apply on the gas phase if i try to
make it some different value
then either more molecules of a or b
will evaporate to replace
the to raise the pressure or
a and b will condense to lower the
pressure so once i've chosen those two
degrees of freedom or any two degrees of
freedom that i try to choose
independently all the other ones will be
determined so it doesn't matter how
complicated the system is doesn't matter
how many components how many phases
doesn't matter if some components
contain all the phases
some contain only one phase some contain
only
some contain only some one of the
components some phases may contain a
subset of the components
as complicated as a system as you can
construct the gibbs phase will tell you
how many different variables you can try
to control at the same time
Voir Plus de Vidéos Connexes
Gibbs Phase Rule
Phases present in the system
Large Tailwind Components â What to do About All Those Classes
Prop Drilling | Lecture 107 | React.JS đ„
Belajar Membuat ERD (Entity Relationship Diagram) | Belajar UML & Perancangan Sistem
NĂMERO ELEVADO A EXPONENTE CERO DA UNO - Super facil - Para principiantes
5.0 / 5 (0 votes)